COMPARISON OF CYCLIC AND BURST TEST RESULT WITH FE SIMULATION OF A LOCALLY THINNED PIPE BEND

全文分为作者个人简介和正文两个部分：作者个人简介：Hello everyone, I am an author dedicated to creating and sharing high-quality document templates. In this era of information overload, accurate and efficient communication has become especially important. I firmly believe that good communication can build bridges between people, playing an indispensable role in academia, career, and daily life. Therefore, I decided to invest my knowledge and skills into creating valuable documents to help people find inspiration and direction when needed.正文：浮来山千年银杏树的四季变化英语作文全文共3篇示例，供读者参考篇1The Ancient Ginkgo Trees of Mount Fulai: A Yearly Journey Through the SeasonsAs a student who has grown up in the shadow of the majestic Mount Fulai, I have had the privilege of witnessingfirsthand the remarkable transformation of the ancient ginkgo trees that adorn its slopes. These living relics, standing tall and proud, have weathered the test of time, their resilience a testament to the enduring beauty of nature.Spring's AwakeningAs the winter chill begins to dissipate, the ginkgo trees on Mount Fulai awaken from their slumber, ready to embrace the warmth of the new season. The bare branches, which have been stripped of their foliage during the colder months, slowly come to life, adorned with delicate green buds that unfurl like tiny flags heralding the arrival of spring.It is during this time that the mountain takes on a vibrant, emerald hue, as the ginkgo trees join the chorus of rebirth that echoes through the landscape. The air is filled with the sweet fragrance of blossoming flowers, mingling with the earthy scent of the forest floor, creating a symphony of aromas that delights the senses.Summer's Lush EmbraceAs the days grow longer and the sun's rays become more intense, the ginkgo trees of Mount Fulai bask in the glory of summer. Their fan-shaped leaves, a rich shade of green, spreadout in a magnificent canopy, providing cool respite from the heat for hikers and nature enthusiasts alike.It is during this season that the trees truly come into their own, standing tall and proud, their branches swaying gently in the warm breeze. The paths that wind through the mountain are lined with these living giants, creating a verdant tunnel that transports visitors to a realm of tranquility and serenity.Autumn's Golden SplendorAs the summer heat gives way to the crisp coolness of autumn, the ginkgo trees of Mount Fulai undergo a breathtaking transformation. Their leaves, once a vibrant green, slowly begin to turn a brilliant golden hue, painting the mountainside in a tapestry of warm, autumnal tones.It is during this time that the ancient ginkgo trees truly shine, their golden crowns standing in stark contrast against the deep blues and grays of the autumn sky. The air is filled with the gentle rustling of falling leaves, creating a natural orchestra that accompanies the crunch of footsteps on the leaf-strewn paths.Winter's Quiet ReposeAs the last leaves flutter to the ground, the ginkgo trees of Mount Fulai prepare for the long winter ahead. Their barebranches, stripped of their golden finery, stand as silent sentinels against the backdrop of snow-capped peaks and frosted landscapes.It is during this season that the mountain takes on a hushed, almost reverent air, with the ancient ginkgo trees standing as reminders of the cyclical nature of life. Their stark silhouettes against the winter sky are a sight to behold, a testament to their resilience and endurance in the face of nature's harshest conditions.A Living LegacyAs I reflect on the changing seasons and the ancient ginkgo trees that have graced Mount Fulai for centuries, I am struck by the profound connection between these living relics and the history of our region. These trees have witnessed the ebb and flow of civilizations, standing as silent witnesses to the passage of time and the ever-changing landscape.They remind us of the importance of preserving our natural heritage, for they are not mere plants, but living links to our past, present, and future. Each season brings with it a new chapter in the story of these ancient ginkgo trees, a tale woven into the very fabric of Mount Fulai, and one that will continue to be told for generations to come.As I gaze upon these majestic trees, I am filled with a sense of wonder and gratitude, for they have taught me the true meaning of resilience, beauty, and the enduring power of nature. The ancient ginkgo trees of Mount Fulai are more than just trees; they are living embodiments of the cycles of life, reminding us that even in the face of adversity, beauty and renewal are always possible.篇2The Ancient Ginkgo of Fuliaoyama: A Journey Through the SeasonsHigh atop the mist-shrouded peak of Fuliaoyama in western Tokyo stands a living relic of the ancient world. The famed ginkgo tree, estimated to be over a millennium old, stands as a solitary monument to the enduring majesty of nature. Through the turning of the seasons, this towering botanical survivor bears witness to the eternal cycle of life, death, and rebirth that defines our planet. Let me take you on a journey through the year in the life of this arboreal wonder.SpringAs the cold grip of winter reluctantly loosens its hold, the first tender buds appear on the ginkgo's gnarled branches likeemerald pearls awaiting their unveiling. The newly formed leaves, soft as a baby's skin, unfurl in the gentle spring breezes, slowly at first, then in a torrent of vivid green renewal. The tree seems to shrug off the weight of its years as its canopy thickens, basking in the return of the warm sun's nourishing rays.It is a time of reawakening in nature, when colors and fragrances long subdued burst forth in a symphonic celebration of life's perpetual recommencement. I enjoy wandering the ancient forest paths at this time of year, inhaling the rich, loamy scents and listening to the raucous chatter of birds building their seasonal homes. The natural world appears renewed, energized, the circle once more unbroken.SummerThe days grow long and sultry as summer casts its blazing spell over the mountain. Yet the colossal ginkgo stands unperturbed, its dense fan-shaped leaves offering welcome poolsof shade to weary hikers traversing the trails. I've spent many a hot afternoon reclining against the tree's furrowed trunk, feeling the reassuring solidity of a life force persevering through untold eons of time.When the summer rains come, the deep green of the ginkgo's foliage takes on an almost iridescent glow in theshimmering droplets. A crisp, clean scent pervades the air as the storm passes, a primal ozonic incense offered up to the heavens. Through drought, deluge, or searing heat, the ancient tree remains steadfast, a verdant bulwark against the unrelenting onslaught of the seasons.AutumnBut it is in autumn when the ginkgo truly transforms into nature's grandest spectacle. As the temperatures begin their descent, the deep green mantle of summer gives way to a polychrome kaleidoscope of unrestrained brilliance. Golden yellow fans, deeper burnt oranges, and streaks of blazing crimson spill forth first at the highest branches before cascading down in a torrent of incandescent color.The scarlet-tinged ginkgo leaves, unlike the mulched brown offerings from other trees, remain defiantly vibrantly for weeks. They cloak the mountainside in a shimmering amber tapestry before fluttering earthward in gentle zephyrs, creating a dense carpet to insulate and nourish the ancient tree's roots over the harsh winter to come. I savor these autumnal days most, wandering beneath the fiery canopy, my senses heightened by nature's grand farewell.WinterAt last, even the ginkgo's tenacious foliage submits to the inevitable, and the tree stands in monumental silhouette once more against the steel gray skies of winter. Snow frosts the intricate latticework of branches with ethereal white lace. I've huddled beneath the frozen sentrylike boughs on many a blustery evening as dusk envelops the mountain, finding an austere beauty in the ginkgo's stripped splendor.Yet the tree's core remains vibrant and resilient even in this most desolate season. Its thick, corded roots reach deep into the bones of the mountain itself, undaunted by the harshest frosts. Within its dense inner sanctum, the miraculous blueprint for resurrection is carefully conserved, awaiting its cyclical reawakening with the return of spring's verdant summons.So grows the eternal continuum, the seamless transitions from birth, to death, to birth anew. The ancient ginkgo bears perpetual witness, its cyclic renaissance a soothing balm for the transitory concerns that distract us in our daily lives. This living monument of immutable time is both my teacher and my muse, reminding me that for those who embrace the natural rhythms, each season's passing is a mere transition, never an ending. With patience and rugged perseverance, yet another renaissanceawaits just over the horizon. Like a true friend, the ancient ginkgo will be there to greet me again with open arms.篇3The Ancient Ginkgo of Furaisani: A Year in the LifeAs I gaze out over the serene grounds of Chion-in Temple in Kyoto, my eyes are inevitably drawn to the towering ginkgo tree that dominates the landscape. This remarkable living fossil, estimated to be over a thousand years old, stands as a testament to the enduring beauty and resilience of nature. Throughout the changing seasons, the ancient ginkgo of Furaisani undergoes a mesmerizing transformation, reminding us of the cyclical rhythm of life itself.Spring's AwakeningAfter the long, frigid embrace of winter, the first whispers of spring herald the ginkgo's reawakening. As the warm sunrays caress the earth, tiny emerald buds begin to emerge from the seemingly lifeless branches. It is a sight of profound hope, as if the tree itself is exhaling a sigh of relief, ready to embrace the vibrant hues of the new season.With each passing day, the tender leaves unfurl, their delicate fans unfurling to greet the world. The ginkgo's foliagetakes on a brilliant shade of green, so vivid and radiant that it seems to glow from within. This verdant canopy casts a dappled pattern of light and shadow on the ancient temple grounds, creating a serene and inviting atmosphere for visitors and worshippers alike.As spring reaches its peak, the ginkgo tree becomes a verdant oasis amidst the bustling city of Kyoto. Its branches sway gently in the cool breeze, as if performing a graceful dance to welcome the new season. The air is filled with the sweet, earthy scent of freshly unfurled leaves, a fragrance that evokes memories of childhood adventures in the great outdoors.Summer's Lush EmbraceAs the days grow longer and warmer, the ginkgo tree settles into the lush embrace of summer. Its leaves, now fully matured, take on a deeper, richer hue of emerald, casting a cool shade over the temple grounds. Visitors and locals alike seek refuge beneath its sprawling canopy, finding solace from the sweltering heat and respite from the hustle and bustle of city life.During this season, the ginkgo tree stands as a majestic guardian, its branches reaching skyward as if in silent prayer. The gentle rustling of its leaves creates a soothing melody, an accompaniment to the tranquil ambiance of Chion-in Temple.Beneath its boughs, one can almost feel the passage of time slowing down, inviting contemplation and introspection.As summer reaches its zenith, the ginkgo tree becomes a living embodiment of nature's abundance. Its leaves, thick and lush, provide a nurturing canopy for the myriad creatures that call this ancient sanctuary home. Birds flit among the branches, weaving intricate melodies, while squirrels scamper playfully along the gnarled trunk, adding to the symphony of life that surrounds this remarkable tree.Autumn's Golden SplendorAs the days grow shorter and the air takes on a crisp, autumnal chill, the ginkgo tree begins its most spectacular transformation. Its lush green foliage gradually gives way to a breathtaking display of golden hues, as if the tree itself is setting ablaze with the fiery colors of autumn.The leaves, once a verdant emerald, take on a rich, burnished tone, their fans turning a stunning array of yellows, oranges, and reds. This vibrant tapestry is a true spectacle, drawing visitors from near and far to witness the ginkgo's annual show of brilliance.As the weeks pass, the golden leaves begin to flutter gracefully to the ground, carpeting the temple grounds in a shimmering blanket of warmth. Each step through this autumnal wonderland is accompanied by a gentle crunch, a symphony of nature's own making. The air is filled with the earthy scent of fallen leaves, a fragrance that evokes memories of cozy evenings spent by the fireplace.Despite the beauty of this seasonal transformation, there is a bittersweet undertone to autumn's arrival. For as the ginkgo tree sheds its radiant foliage, it reminds us of the impermanence of all things, and the inevitability of change.Winter's Quiet ResilienceAs the chill of winter descends upon Kyoto, the ginkgo tree stands bare, its branches stripped of their colorful adornments. Yet, even in this stark, seemingly lifeless state, the ancient ginkgo exudes a quiet resilience and a profound sense of endurance.Its twisted and gnarled trunk, a testament to the countless seasons it has weathered, takes on a haunting beauty in the winter light. The intricate patterns of its bark, formed over centuries of growth, become more pronounced, inviting one to trace the tree's history with their fingertips.Despite the icy winds and occasional snowfall, the ginkgo tree remains steadfast, its roots firmly anchored in the earth. It is a reminder of the enduring strength of nature, and the capacity of life to persist even in the harshest of conditions.As the winter solstice approaches, the ginkgo tree takes on a solemn, almost reverent atmosphere. Its bare branches stretch skyward, their silhouettes etched against the pale winter sky. In this tranquil state, the tree invites quiet contemplation, a moment to reflect on the cycles of life and the resilience of the natural world.Throughout the ebb and flow of the seasons, the ancient ginkgo of Furaisani stands as a living embodiment of nature's enduring beauty and resilience. Its annual transformation is a testament to the cyclical rhythm of life itself, reminding us of the importance of embracing change and finding wonder in the most humble of moments.As I sit beneath its boughs, watching the ever-shifting tapestry of colors and textures, I am filled with a profound sense of gratitude for this remarkable living fossil. For in its enduring presence, the ginkgo tree teaches us invaluable lessons about perseverance, adaptation, and the interconnectedness of all life. It is a living reminder that even in the face of adversity, beautyand resilience can flourish, inspiring us to embrace theever-changing tapestry of the natural world with wonder and reverence.。

Variable amplitude fatigue of bonded aluminum jointsA.E.Nolting *,P.R.Underhill,D.L.DuQuesnayDepartment of Mechanical Engineering,Royal Military College of Canada,P.O.Box 17000Station Forces,Kingston,Ont.,Canada K7K 7B4Received 1June 2006;received in revised form 16January 2007;accepted 21January 2007Available online 2April 2007AbstractThe effect of variable amplitude loading on the fatigue life and failure mode of adhesively bonded double strap (DS)joints made from clad and bare 2024-T3aluminum was investigated.Under constant amplitude loading,the clad specimens failed through the adhesive or the substrate at high and low stress levels,respectively.The presence of overload cycles shifted the failure mode towards adhesive failure.The specimens made from bare aluminum failed only in the adhesive.Effective stress range vs.failure life curves developed for the bare and clad specimens were used in conjunction with a linear damage summation to predict the failure lives of double strap specimens sub-jected to two variable amplitude aircraft load spectra with reasonable accuracy.Ó2007Elsevier Ltd.All rights reserved.Keywords:Aluminum;Bonding;Adhesive;Cladding;Variable amplitude;Fatigue;Aircraft1.IntroductionThe use of adhesive bonding as a joining method and for patch repairs is increasing in many industries,includ-ing automotive and aerospace.Bonded patch repairs are often performed in the aerospace industry to restore stiff-ness to under-designed areas or locations that have been damaged by corrosion and/or fatigue cracks [1].Bonded doublers are advantageous compared to mechanically fas-tened doublers because their application method does not require the creation of new rivet or bolt holes which could be detrimental to the structure [1].Other advantages include a reduction in fretting between the doubler and the substrate [2]and protection against crevice corrosion [1,3].However,there is a perceived unreliability associated with adhesive bonding that limits its use in industry.When subjected to cyclic loading,fatigue cracks can initiate in the adhesive or at the adhesive/adherend interface.These cracks can propagate and eventually cause failure of the bond.Debonding typically initiates at the edge of thepatches where the stress concentration and peel stresses are highest [4–6]and proceeds towards the center of the patch.Exposure to water,extreme temperature changes or chemicals can accelerate the debonding process by weakening the adhesive and/or the bond interface [7–9].The bond strength is also quite sensitive to surface prepa-ration [3,10]and it can be difficult to achieve ideal bond-ing conditions in the field.Recent research has also indicated that patching over clad material can result in substrate failures at the edges of bonded patches [11,12].However,the Royal Australian Air Force reports that many of their patch repairs have been in service for longer than 20years without durability issues arising from envi-ronmental or fatigue damage [1].To increase confidence in the reliability of bonded joints in fatigue sensitive areas,it is important to develop reliable methods for predicting fatigue lives.These calculations are complicated by a number of factors that are inherent to bonded joints.For example,there are multiple failure modes for a bonded joint,including cohesive or interface failure through the adhesive and failure of the adherends.The transfer of force through the adhesive often results in mixed mode loading,especially in non-symmetric joints.0142-1123/$-see front matter Ó2007Elsevier Ltd.All rights reserved.doi:10.1016/j.ijfatigue.2007.01.027*Corresponding author.Tel.:+19024273434;fax:+19024273435.E-mail address:anolting@ (A.E.Nolting)./locate/ijfatigueAvailable online at International Journal of Fatigue 30(2008)178–187International Journalof FatigueA comprehensive list of the issues plaguing fatigue analysis of bonded joints is given by de Goeij et al.[13].Most of the research into the fatigue behaviour of adhe-sive bonds concentrates on constant amplitude loading. Jethwa and Kinloch[14]conducted fatigue tests on adhe-sively bonded double cantilever beam specimens to pro-duce maximum Mode I strain energy vs.crack growth rate(G Imax vs.d a/d N)curves for different environmental conditions.As an extension of this work,Curley et al.[15]usedfinite element analysis and analytical solutions to determine the total strain energy(G TOTAL=G I+G II) in cracked single lap shear joints.They used the G TOTAL analysis and the G I max vs.d a/d N curves to predict the fati-gue lives of the single lap shear specimens.The fatigue life predictions based on both thefinite element analysis and the analytical solutions of G TOTAL were in good agreement with test results.Dessureault and Spelt[16]examined the correlation between the threshold strain energy release rate in fatigue(G th)and the quasi-static critical energy release rate(G c)for specimens with different loading modes(Mode I,II and mixed Mode I–II).They found that in terms of %G c,mixed mode loading was more damaging than single mode loading.They also found that crack propagation rates were very sensitive to strain energy release and con-cluded that damage tolerance design methods were not appropriate for adhesive bonds.Johnson and Mall[17]cal-culated the total strain energy release rate in the adhesive layer of bonded joints usingfinite element methods.They found that the threshold strain energy release rate,G th, was similar for joints with varying geometries.They also concluded that bonded joints should be designed below the fatigue growth threshold because small changes in the applied stresses resulted in large changes in crack growth, which made the analysis very sensitive to slight errors in the applied loads.Many of the structures that utilize adhesive bonding are subjected to variable amplitude loading.It has been well documented that fatigue damage in metal is dependent on load history.Tensile overload cycles of near yield mag-nitude and compressive overloads have been shown to accelerate crack growth[18,19]while crack growth retarda-tion has been observed on long cracks following tensile overloads that were well below the yield strength of the material[20–22].Fatigue life predictions need to take into account the effect of variable amplitude loading in order to obtain accurate results.There are some phenomenological fatigue models that account for accelerated fatigue damage by introducing a‘cycle mix’term into the cumulative dam-age summation[23,24].The cycle mix term adds to the damage summation when a large change in the mean stress occurs.The terms are usually calibrated to a specific load-ing spectrum using empirically determined constants. DuQuesnay et al.[25,26]used crack closure and an effective stress range damage parameter to explain the effect of var-iable amplitude loading on fatigue damage.They assumed that a crack only causes damage when it is open at the tip. Consequently,if a crack is fully open over the entire load-ing cycle,it will cause the most damage that a cycle of that stress range can possibly cause.Since the crack opening stress is affected by the load history,the stress range over which a crack is open and the damage that the cycle causes are also affected by the load history.DuQuesnay et al. developed effective stress range vs.failure life(D S effvs. N f)curves for fully open loading cycles[26]which represent the maximum amount of damage that could be caused at a given stress range.A linear cumulative damage summation conducted using the D S effvs.N f curves therefore represents the maximum amount of damage that the variable ampli-tude loading spectrum can cause.This approach has been shown to produce an accurate or at least conservative esti-mation of fatigue life[27].In Mode II shear loading,crack closure is caused by the interference of asperities on the crack faces as they slide over one another.Topper et al.[28]found that applying a mean stress normal to the crack interfaces would decrease the interference of the interfaces and increase the damage caused by a given shear stress range.They found that nor-mal stresses applied constantly or as periodic overloads had the same effect of increasing the effective stress range of the cycles.Variable amplitude loading is such an important issue in fatigue life prediction of metal structures that it is reason-able to assume that variable amplitude loading will also affect crack growth in bonded structures.However,the research on variable amplitude loading of adhesively bonded joints is quite limited when compared to the research on constant amplitude loading.Erpolat et al.[23]used the Palgrem–Miner theory(P–M)and an extended P–M theory to predict the service life of various variable amplitude loading spectra.Both the P–M rule and the extended P–M rule consistently produced uncon-servative fatigue life predictions.Incorporating a‘cycle mix factor’into the damage summation produced life esti-mates that were in much better agreement with test results. Yang and Du[29]used a statistical model and constant amplitude data to determine the life of variable amplitude loading spectra.Afitting parameter was used to calibrate the model and Yang and Du state that this parameter might have to be adjusted for each different spectrum. Using a fracture mechanics approach,Ashcroft[30]and Erpolat et al.[31]studied the effect of periodic overload spectra on crack growth in epoxy/carbonfibre reinforced polymer strap lap and double cantilever beam joints, respectively.In both studies,the authors produced strain energy release rate vs.crack growth rate curves(D G vs.d a/d N)using constant amplitude loading.These curves were then used to predict the crack growth of specimens subjected to periodic overload spectra.The predictions underestimated the crack growth,and both studies con-cluded that the overload cycles accelerated the damage caused by the smaller cycles.Ashcroft[30]introduced a parameter w to shift the crack growth curve to the left.This increased the damage predicted by the D G vs.d a/d N curve and consolidated the predicted and observed crack growthA.E.Nolting et al./International Journal of Fatigue30(2008)178–187179rates.The parameter w is dependent on the relative number and magnitude of the overloads,and therefore must be determined for every spectrum.The majority of work on the fatigue behaviour of bonded joints has not examined the effect of a cladding layer on the failure mode.DuQuesnay et al.[11]tested sin-gle lap shear specimens constructed of both bare and clad 2024-T3aluminum under constant amplitude loading. They found that as the applied stress range decreased, the failure mode of the clad specimens changed from fail-ure of the adhesive to failure of the substrate.The substrate failures initiated in the cladding layer at the edge of the patch and propagated into the substrate.To accurately predict the failure mode of adhesive bonds in service load-ing,the effect of variable amplitude loading on the failure mode must be determined.The purpose of this paper is to examine the effect of overload cycles and variable amplitude loading on the fati-gue behaviour of bare and clad adhesively bonded double strap joints.Four sets of fatigue tests were conducted.Thefirst set was constant amplitude tests that compared the fatigue behaviour of bare and clad joints.The next ser-ies of tests subjected the specimens to periodic overload spectra to determine the effect of overload cycles on fatigue life and failure mode.The third test series was effective stress range vs.fatigue life tests,as described by DuQue-snay et al.[26].These were periodic overload tests that are designed to estimate the upper bound of the damage caused by the small cycles in the loading spectrum.The effective stress range vs.failure life curve was used in con-junction with a linear cumulative damage summation to calculate the fatigue lives of specimens subjected to variable amplitude loading spectra.In the fourth series of tests, specimens were subjected to those variable amplitude load-ing spectra and the test results compared to the calculated fatigue lives.2.Test methodologyDouble strap(DS)specimens were constructed from 3.2mm thick2024-T351aluminum alloy sheet in either the bare or clad condition.The aluminum used to make the bare or clad specimens came from the same heat of material.The thickness of the cladding layer was measured using a charge coupled device(CCD)camera that inter-faced with an optical microscope.The thickness of the cladding layer was measured to be0.09mm with a stan-dard deviation of0.005mm.The specimens were made in 150mm wide plates that were cut intofive fatigue speci-mens after the bonding process was completed(Fig.1). The cut sides were milled and lightly sanded in the longitu-dinal direction with400grit sandpaper.Thefinal dimen-sions of the double strap specimens are given in Fig.1. Unclad(bare)aluminum was used for the patches,while either bare or clad aluminum was used for the substrate. The loading direction of the substrate was aligned with the rolling direction of the material.An FM73epoxyfilm adhesive in a knit carrier cloth was used to bond the specimens.The bonding technique,which used a30min warm water soak at50°C and a mercapto-propyltrimethoxysilane surface pretreatment,is described in detail in Underhill et al.[32].The thickness of the adhe-sive was measured using a CCD camera that interfaced with an optical microscope.The thickness of the adhesive was found to be0.13mm with a standard deviation of 0.027mm.The width of the specimens,the substrate thick-ness and the length of the overlap were measured and the applied loads were calculated from the desired stress and the measured specimen dimensions.Reported shear stress values refer to the nominal shear stress in the specimen, as calculated using the area between the patches and the substrate on the side with the shortest overlap(Fig.2). The axial stress values were calculated using the applied load and the area of the substrate material only.The failure mode of each test was reported as a number from0to6,where0represented a fully adhesive failure,6 was a substrate failure and1–5were adhesive failures with varying amounts of damage caused to the cladding layer. Examples of different damage levels are shown in Fig.3. Fig.3a–c show side views of adhesive-failure fracture sur-face,while Fig.3d shows an end view of a substrate-failure fracture surface.Fatigue testing was conducted in load control on servo-hydraulic load frames with closed loop control systems. The test frequency was chosen to minimize the duration of the tests and to keep the errors below1%of the overload cycles.This resulted in test frequencies that variedbetween Fig.1.Double strap specimens,all dimensions inmm.Fig.2.Area used to calculate the nominal shear stress.180 A.E.Nolting et al./International Journal of Fatigue30(2008)178–1875and 15Hz.A number of test series were conducted and are described in the following sections.2.1.Constant amplitude testsConstant amplitude fatigue tests (Fig.4a)were con-ducted at R =0for both the bare and clad alloys.The max-imum stress of the test varied from 22MPa nominal shear stress to the runout stress,with a runout defined as 5·106cycles without failure.The axial stress in the sub-strate at 22MPa nominal shear corresponds to approxi-mately 255MPa of axial stress in the substrate,which is below the yield stress (360MPa)of bare 2024-T3alumi-num [26].2.2.Periodic overload testsA series of tests were conducted to investigate the effect of periodic overloads on the fatigue life and failure mode ofthe double strap specimens.The test spectra consisted of a repeated block of cycles containing an overload cycle fol-lowed by a fixed number of small cycles,as shown in Fig.4b.The magnitudes of the overload and small cycles were held constant at 22and 14MPa nominal shear,respectively,and the minimum stress of all the cycles was 0MPa.These stress levels were chosen because during R =0constant amplitude testing,the clad specimens failed exclusively by adhesive failure at 22MPa and by substrate failure at 14MPa.The number of small cycles following the overload varied between tests and was either 40,80,400or 2000cycles.2.3.Effective stress vs.fatigue life testingThe third series of tests were conducted to produce an ‘effective stress vs.failure life’curve for the double strap specimens (Fig.4c).An effective stress vs.failure life curve represents the damage caused by fully open (i.e.,fullydam-Fig.3.Examples of specimen failure types:(a)Rank 0(fully adhesive failure),constant amplitude loading 0–22MPa shear,N f =1.0·104cycles;(b)Rank 2,constant amplitude loading 0–20MPa shear,N f =3.0·104cycles;(c)Rank 5,variable amplitude loading,1cycle 0–22MPa shear followed by 2000cycles 0–14MPa shear,N f =7.1·105cycles and (d)Rank 6(substrate failure),constant amplitude loading 0–16MPa,N f =1.4·105cycles.A.E.Nolting et al./International Journal of Fatigue 30(2008)178–187181aging)loading cycles and can be used to obtain accurate,or at least conservative,fatigue life predictions using linear cumulative damages summations [26].The opening stress of the crack is depressed by introducing overload cycles.This allows the small cycles following the overload to be fully damaging.The equivalent failure life of the small cycles (N eq )is calculated for each test by forcing the Pal-grem–Miner equation to equal one,subtracting the damage caused by the overload cycles and solving for the failure life of the small cycles,(N fsc )Damage summation ¼1¼N sc N fsc þN olN fol ð1Þsuch that N eq ¼N fsc¼N sc1ÀN olfolwhere N sc and N ol are the number of small cycles and over-load cycles applied to the test specimen,respectively,and N fol is the failure life of the overload cycle,calculated as the average of at least three constant amplitude tests.The maximum stress of all the cycles in these periodic overload tests was kept constant at 22MPa nominal shear and the number of small cycles between overloads was kept constant at 80cycles (Fig.4).The shear stress range of thesmall cycles (i.e.,the minimum stress of the small cycles)varied between tests.2.4.Variable amplitude testingIn the last series of tests,the specimens were subjected to one of two variable amplitude aircraft loading spectra.The first spectrum was taken from the CF 18Hornet fighter and had 2498cycles representing 28.9flight hours.The normal-ized spectrum had a maximum tensile stress of 1.000and a minimum stress of À0.115.The spectrum was scaled to make the maximum and minimum stresses in the spectrum 22MPa and À2.5MPa,respectively.The second spectrum was taken from the CC 130Hercules transport aircraft.It represents moderate aircraft usage,contains 38,253cycles and corresponds to 126flight hours.The normalized spec-trum,which had a maximum tensile stress of 1.000and minimum stress of À0.704,was scaled to make the maxi-mum and minimum stress in the spectrum 22and À15.5MPa nominal shear,respectively.3.Results3.1.Constant amplitude testingThe results of the constant amplitude testing for the bare and clad 2024-T3double strap specimens are presented in Fig.5,with the failure mode indicated by the shape of the symbols.Each data point represents one fatigue test.All of the bare specimens,and the clad specimens subjected to high stress levels,failed by adhesive failure.As the cyclic stress applied to the clad specimens decreased,the failure mode remained essentially adhesive,but increasing amounts of damage to the cladding layer was observed on the bonded surfaces.At the lowest stresses,the clad specimens failed by substrate failure.The fatigue lives of the bare and clad specimens were similar at higher stress levels.At lower stress levels,the clad specimens had shorter fatigue lives than the corresponding bare specimens.This is clearly illustrated in therunoutFig.4.Loading spectra:(a)constant amplitude;(b)periodic overload;and (c)effective stress –failure lifetesting.Fig.5.Constant amplitude shear stress vs.failure life.182 A.E.Nolting et al./International Journal of Fatigue 30(2008)178–187stresses for the bare and clad specimens,which were11and 8MPa shear,respectively.The axial stress in the clad spec-imens at runout was90MPa,which is below the reported fatigue limit of160MPa for smooth,bare2024-T351spec-imens at R=0[26].The fracture surfaces were examined with a light micro-scope at40·magnification.The bare specimen surfaces revealed cohesive failures which initiated at the edge of the patch close to the substrate/adhesive interface.The knit carrier cloth weakened the adhesive and caused the crack path to deviate through the knit carrier clothfibres (Fig.6a and b).As the crack propagated,it moved from the substrate/adhesive interface to the patch/adhesive interface.The clad specimens that experienced adhesive or transi-tional failures had apparent adhesive failures initiating at the substrate/adhesive interface at the edge of the patch. Cohesive failure occurred through thefibres of the knit car-rier cloth(Fig.6b).As with the bare specimens,the loca-tion of debonding switched from the substrate/adhesive interface to the patch/adhesive interface.Damage in the form of cladding pull-out occurred on the cladding layer at low applied stresses(Fig.3a and b).Thefirst occurrences of pull-out appeared near the edge of the patch.As the cyc-lic loads applied to the specimens decreased,the size,num-ber and distance from the patch edge of the cladding pull-out increased.The most severe damage was still observed at the edge of the patch,and the severity(size and number) of the pull-out decreased further away from the patch edge. The pulled-out material was attached to the adhesive on the mating failure surface.On the specimens that failed by substrate failure,fatigue cracks were observed to have initiated in the cladding layer at the edge of the patch.The substrate failures at the high-est stress level showed multiple initiation sites(Fig.7a).As the stress level dropped,the number of initiation sites decreased(Fig.7b).3.2.Periodic overload spectraPeriodic overload tests were conducted to determine if the presence of overload cycles affected the damage caused by the smaller cycles and the failure mode of the specimens. The former was examined by conducting a linear cumula-tive damage summation for each of the tests in this series. The linear damage summation assumes that damage caused by any individual cycle is not affected by the load history of the specimen.If this is true,then the damage summationP nfof any individual test should tend to 1,where n is the number of each unique cycle appliedto Fig.6.Typical adhesive failure surfaces:(a)bare specimens and(b)cladspecimens.Fig.7.Crack initiation in the clad layer:(a)constant amplitude,12–0MPa,N f=4.7·105cycles and(b)constant amplitude,10–0MPa, N f=8.0·105cycles.A.E.Nolting et al./International Journal of Fatigue30(2008)178–187183the specimen and N f is the number of those cycles that will cause failure in constant amplitude loading.A damage summation of less than1indicates that the presence of overloads increases the damage caused by the small cycles, whereas a damage summation greater than1indicates that the presence of overload cycles decreases the damage caused by the small cycles.The linear damage summation was calculated for each test using the following equationDamage sum¼N fn scscN fscþ1scN fol!ð2ÞThe fatigue lives of the constant amplitude overload cycles and the small cycles,N fol and N fsc,respectively,were each taken as the average of at least three constant amplitude tests.N f is the number of cycles to failure for each individ-ual test,while n sc is the number of small cycles applied be-tween overload cycles.The results of the PM damage summation are presented in Fig.8.Each data point in Fig.8represents one fatigue test.The damage summations for both the bare and clad specimens were generally below1,indicating that the pres-ence of overload cycles increases the damage caused by the small cycles.The damage summation increased as the num-ber of small cycles between overloads increased,until it reached approximately1at2000small cycles between over-loads.This suggests that the small cycles directly following the overload cycle are the most damaging and that the effect of the overload cycle becomes negligible if the occur-rence of the overload cycles is sufficiently low.This is con-sistent with observations of metals cycled under periodic overload spectra[18,21].The failure mode of the clad specimens was also affected by the presence of periodic overload cycles.Constant amplitude(CA)testing at22and14MPa resulted in fully adhesive and substrate failures,respectively.However, the periodic overload tests produced only transitional fail-ures.The amount of cladding damage observed on the frac-ture surfaces increased as the number of small cycles between overloads increased.No substrate failures were observed for the specimens tested with periodic overload spectra,even when the effect of the overloads on the dam-age summation was negligible.This indicates that the pres-ence of any overloads will change the failure mode from substrate to transitional,and the more frequently the over-loads occur,the less cladding damage will be present on the bonding surfaces.This series of test was also used to determine the number of small cycles that should be applied following the over-load cycle in the effective stress range vs.failure life testing spectra.The damage caused by the small cycles at40and 80cycles following the overload was approximately con-stant(Fig.8).During effective stress range vs.failure life testing,it is necessary that all of the small cycles in the loading spectrum be fully open and therefore fully effective. The damage summation in Fig.8did not change between 40and80small cycles,which implies that all of the small cycles in those spectra were fully open.Eighty small cycles between overloads was chosen for the effective stress range vs.failure life tests to ensure that all of the small cycles were fully open and to maximize the damage caused by the small cycles in that loadingspectrum.Fig.8.Palgrem–Miner damage summation of periodic overloadtests.Fig.9.Constant amplitude and effective life data for bare2024-T3aluminum.Fig.10.Constant amplitude and effective life data for clad2024-T3aluminum.184 A.E.Nolting et al./International Journal of Fatigue30(2008)178–1873.3.Effective stress vs.fatigue life curve testingThe equivalent fatigue lives of the small cycles calculated from this series of tests using Eq.(1)are plotted with the constant amplitude data in Figs.9and 10for the bare and clad aluminum,respectively.Each data point in these graphs represents one fatigue test.As expected,the equiv-alent fatigue lives of the small cycles in the periodic over-load tests were more damaging and therefore had shorter fatigue lives than constant amplitude tests with the same applied stress range.A curve fit which includes the effective stress range vs.failure life data and the constant amplitude data at 22MPa was used to calculate the fatigues lives of the specimens in variable amplitude loading in Section 3.4.When these curve fits for the bare and clad specimens are plotted on the same axis,it becomes evident that despite the different failure modes,the fatigue lives of the bare and clad specimens are essentially the same (Fig.11).All of the bare specimens failed by adhesive failure.As with the constant amplitude data,the failure mode of the clad specimens evolved from fully adhesive to transitional to substrate failures as the applied stress decreased.How-ever,these transitions occurred at lower stress levels during the effective stress life testing.This was caused by the pres-ence of the overload cycles,which,as shown in the periodic overload data,caused the failure mode to shift towards the ‘adhesive failure’end of the failure mode spectrum.3.4.Variable amplitude testingThe fatigue lives and failure modes of the variable amplitude testing are presented in Table 1.All of the bare specimens and the clad specimens subjected to the CC-130loading spectrum failed by fully adhesive failure.The clad specimens subjected to the CF-18spectrum failed mostly by adhesive failure,with a minor amount of damage to the cladding layer on the failure surface.The difference in the failure mode of the clad specimens between the two loading spectra is attributed to the magnitude of the largest cycle in the spectrum,which was considerably larger for the CC-130loading spectrum.The expected fatigue lives of the specimens were calcu-lated using a cumulative damage summation and the effec-tive stress range vs.fatigue life curves of the clad and bare materials as shown in Fig.11.Variable amplitude fatigue life predictions based on constant amplitude fatigue life data have been reported to give unconservative fatigue life predictions [23,33].However,when effective stress range vs.failure life data (which represents the most damage that can occur at a give stress range)is used,fatigue life predictions based on linear damage summations should produce accu-rate or conservative fatigue life predictions [27].The spec-tra were rainflow-counted and all cycles with a stress range smaller than 4MPa were assumed to cause no dam-age and were not included in the damage summations.The largest cycle in the CC-130spectrum ranged from 22to 15.5MPa nominal shear.The fatigue lives of cycles with stress ranges beyond 22MPa nominal shear were extrapo-lated from the effective stress range vs.fatigue life data.Since the bare and clad specimens had similar fatigue lives under adhesive failure,the bare specimen data were used in the clad specimen calculation for all cycles with a stress range greater than 22MPa nominal shear.Constant ampli-tude tests with maximum and minimum loads of 22and –15.5MPa,respectively were conducted on the bare and clad specimens to confirm that the extrapolated fatigue life values were reasonably accurate.The constant amplitude tests yielded fatigue lives of 933and 1287cycles for the bare specimens and 1593and 581cycles for the clad spec-imens.The fatigue life of this cycle as extrapolated from the bare effective stress range vs.life curve was 771cycles.The extrapolated value is within a factor of two of the test results,indicating that it is reasonable to use the extrapo-lated values.The results of the fatigue life calculations are also presented in Table 1.The effective stress range vs.fatigue life curves for the bare and clad materials were similar,despite the difference in failure mode at lower stress levels and thus the calculated fatigue lives for the bare and clad materials were alsoTable 1Variable amplitude test results Substrate conditionFatigue life N fCalculated fatigue life N fcalcFailure modeCF-F18Spectrum Mostly adhesive Clad7.8·10512.0·105Rank 16.0·105Rank 27.2·105Rank 1Bare5.7·1058.1·105Fully adhesive5.8·1055.1·105CC-130Spectrum Clad 1.0·1061.6·106Fully adhesive 0.84·106Bare1.1·106 1.5·106Fully adhesive1.4·106Fig.11.Effective stress vs.fatigue life curves for clad and bare 2024-T3aluminum.A.E.Nolting et al./International Journal of Fatigue 30(2008)178–187185。

Chaboche Nonlinear Kinematic Hardening ModelSheldon ImaokaMemo Number:STI0805AANSYS Release:12.0.1May4,20081IntroductionThe Chaboche nonlinear kinematic hardening model was added in ANSYS 5.6to complement the existing isotropic and kinematic hardening rules that users relied on.Despite its availability for nearly ten years as of the time of this writing,the Chaboche model has enjoyed limited popularity,in part because of the perceived complexity of calibrating the material parameters. This memo hopes to introduce the basics related to the Chaboche nonlinear kinematic model.Please note that many material parameters for the examples shown in this memo were taken from Reference[5].The author highly recommends obtaining a copy of this book,as it is a useful reference not only for the non-linear kinematic hardening model but also for plasticity and viscoplasticity in general.2Background on Material Behavior2.1Linear vs.Nonlinear Kinematic HardeningThe yield function for the nonlinear kinematic hardening model TB,CHABOCHE is shown below:F= 32({s}−{α})T[M]({s}−{α})−R=0(1) In the above equation,which can be found in Section4of Reference[2],{s} is the deviatoric stress,{α}refers to the back stress,and R represents the yield stress.The back stress is related to the translation of the yield surface, and there is little in Equation(1)that distinguishes it from other kinematic hardening models at this point.1Sheldon’s Tips Chaboche Nonlinear Kinematic Hardening The back stress{α}for the Chaboche model is calculated as follows:{α}=ni=1{αi}(2a){∆α}i=23C i{∆ǫpl}−γi{αi}∆ˆǫpl+1C idC idθ∆θ{α}(2b)whereˆǫpl is the accumulated plastic strain,θis temperature,and C i andγi are the Chaboche material parameters for n number of pairs.In Equation (2b),one may note that thefirst term is the hardening modulus.On the other hand,the second term of the evolution of the back stress is a“recall term”that produces a nonlinear effect.The input consists of defining the elastic properties(e.g.,elastic modulus, Poisson’s ratio)via MP,EX and MP,NUXY,then issuing TB,CHABOCHE,,ntemp,n, where ntemp is the number of temperature sets and n is the number of kine-matic models.Any temperature-dependent group of constants are preceded with the TBTEMP command defining the temperature,while the material pa-rameters for that temperature are entered via the TBDATA command.The first constant is R,or the yield stress of the material—this value may be overridden if an isotropic hardening model is added,as covered in Subsec-tion2.5.The second and third material constants are C1andγ1—these may be followed by additional pairs of C i andγi,depending on the number n of kinematic models requested.2Sheldon’s Tips Chaboche Nonlinear Kinematic Hardening2.2Initial Hardening Modulus3Figure 1:Linear Kinematic Hardening The material parameter C i is the initial hardening modulus .For a single kinematic hardening model (n =1),if γ1is set to zero,the pa-rameter C 1will describe the slope of stress versus equivalent plastic strain.This would represent a linear kinematic hardening model .1One can also reproduce the same behavior with the bilinear kine-matic hardening model (TB,BKIN ),as shown in Figure 1—plots of alinear kinematic hardening model with TB,CHABOCHE as well as TB,BKIN are superimposed,showing identical results.However,one should note that the tangent modulus E tan specified in TB,BKIN is based on total strain,whereas C i in TB,CHABOCHE is based on equivalent plastic ing a stress value σ′>R ,the relationship between C i and E tan is expressed in Equation (3):E tan =σ′−R σ′−R C 1+σ′E elastic −RE elastic(3)It is worth pointing out that there are various plasticity models in ANSYS,where some,such as TB,BKIN ,use equivalent total strain,and others,such as TB,PLASTIC ,use equivalent plastic strain.The Chaboche model in ANSYS uses equivalent plastic strain,and the author prefers this approach,as the elastic modulus and Poisson’s ratio completely describe the elastic behavior,while the nonlinear constitutive model fully defines the plastic behavior.1The term “linear”refers to the relationship of stress and equivalent plastic strain.For ANSYS plasticity models such as “bilinear”or “multilinear”kinematic hardening,these terms describe the relationship between stress and equivalent total strain.3Sheldon’s Tips Chaboche Nonlinear Kinematic Hardening2.3Nonlinear Recall ParameterThe second material parameter,γi,controls the rate at which the hardening modulus decreases with increasing plastic strain.By examining Equation (2b),one can see that the back stress increment{˙α}becomes lower as plastic strain increases.Specifically,a limiting value of C i/γi exists,indicating that the yield surface cannot translate anymore,which manifests itself as a hardening modulus of zero at large plastic strains.A comparison of TB,BKIN with the Chaboche model,including a non-zeroγ1parameter,is shown in Figure2(a).Despite the Chaboche hardening modulus initially being the same as the linear kinematic model,the hard-ening modulus decreases,the rate of which is defined byγi.Figure2(b)is the same plot but at larger strains.One can see the hardening modulus for the Chaboche model decreasing to zero.For this case,the yield stress was assumed to be520MPa.For the Chaboche model, C1=140,600whileγ1=380.Since the limiting value of the back stress{α}is C1γ1=370,one would expect that the asymptotic value would beR+α=890MPa,which matches with the results shown in Figure2(b)..5(a)Small Strain1(b)Larger StrainFigure2:Comparison of Linear and Nonlinear Kinematic Hardening4Sheldon’s Tips Chaboche Nonlinear Kinematic Hardening 2.4Multiple Kinematic Hardening Models1Figure3:Two Kinematic Models A single nonlinear kinematic hard-ening model is described by the two material parameters,C1and γ1,discussed in Subsections2.2and 2.3,respectively.However,a single kinematic model may not be suf-ficient to describe the complex re-sponse of a given material,so with TB,CHABOCHE,up to n=5kine-matic models may be superimposed. This superposition of simple mod-els is another salient feature of theChaboche model,and this idea will be expanded upon in the next subsection.Figure3shows a comparison of three results of stress versus plastic strain —single kinematic models“CHAB and“CHAB1B”are plotted with a two-model version“CHAB The“CHAB model contains the same material parameters as“CHAB and“CHAB1B,”and one may be able to visualize how these two kinematic models are superimposed(assuming constant yield stress R)to create the more complex stress-strain response of“CHAB2.”2.5Combined HardeningThe main usage of the Chaboche model is for cyclic loading applications,as will be discussed shortly.Similar to other kinematic hardening models in ANSYS,the yield surface translates in principal stress space,and the elastic domain remains unchanged.For example,when the loading is reversed for a simple tensile specimen,yielding is assumed to occur atσmax−2R,where σmax is the maximum stress prior to unloading—this is the well-known Bauschinger effect.The Chaboche kinematic hardening model,however,can be used in con-junction with an isotropic hardening model.The isotropic hardening model describes the change in the elastic domain for the material,and the user can select from one of the following:•TB,BISO:Bilinear isotropic hardening,where the user specifies the yield stress and tangent modulus(with respect to total strain)•TB,MISO:Multilinear isotropic hardening,where the user specifies up5Sheldon’s Tips Chaboche Nonlinear Kinematic Hardeningto100stress vs.total strain data points•TB,PLASTIC,,,,MISO:Nonlinear plasticity,where the user specifies up to100stress vs.plastic strain data points•TB,NLISO,,,,VOCE:Voce hardening law,where R=k+R oˆǫpl+ R∞ 1−e−bˆǫpl .Material parameters k,R o,R∞,and b are supplied by the user.1.52.5(a)Voce Hardening.5(b)Voce and ChabocheFigure4:Combined HardeningThe Voce hardening law can be thought of as containing two terms—a linear term R oˆǫpl and an asymptotic term R∞ 1−e−bˆǫpl .A sample model is shown in Figure4(a),where“VOCE1A”is the linear term,“VOCE1B”is the asymptotic term,and“VOCE2”is the complete pare Figure4(a)with Figure3,and note the similarities for the case of monotonic, proportional loading.It may be useful to compare the Voce and two-term nonlinear kinematic hardening models further for monotonic loading situations,in order to better understand the material parameters.The initial yield stress k should bedefined the same for both.R∞=C1γ1describes the limiting,asymptoticvalue that is added to the initial yield stress k.The rate at which this decays is defined by b=γ1.The hardening modulus at very large strains is defined by R o=C2,and for the Chaboche model,γ2=0.Two“equivalent,”sample models are compared in Figure4(b),and one can see that the stress-strain response is the same.Of course,the present discussion comparing the two constitutive models is meant to aid the reader in obtaining a better6Sheldon’s Tips Chaboche Nonlinear Kinematic Hardeningunderstanding of the material parameters rather than to incorrectly imply that the two models are interchangeable for cyclic loading applications.The combination of kinematic and isotropic hardening in the Chaboche references 2typically use a form similar to the Voce hardening law but with-out the constant hardening modulus term:R =k +Q 1−e −b ˆǫpl(4)20Figure 5:Cyclic Hardening To understand how this isotropichardening term is used,consider the case of a strain-controlled load-ing of a test specimen.For cyclic hardening,with ±ǫmax loading,the stress response of a sample model is shown in Figure 5.Note that with progressive number of cycles,the elastic domain expands —this difference in the change in the yield stress is described by the addition of the isotropic hardening term.Also,note that with more cycles,the change in the elastic domain stabilizes.This is why the R o term is neglected for many situations,as the elastic domain does not keep increasing indefinitely.To use calibrated material constants,simply specify k ,R ∞=Q ,and b .The user is not limited to using the Voce hardening law (TB,NLISO,,,,VOCE )with the Chaboche nonlinear kinematic hardening model —use of other isotropic hardening models is permitted.Also,please keep in mind that the value of R ∞=Q is typically a function of the strain range,so the material parameters should be reflective of the expected operational strain ranges.2.6Anisotropic Yield FunctionIt is worth pointing out that the Chaboche model in ANSYS (TB,CHABOCHE )assumes a von Mises yield surface by default.The Hill anisotropic yield function (TB,HILL )may be used in conjunction with TB,CHABOCHE ,although details of this will not be covered in the present memo.2See Refs.[3],[4],and [5]7Sheldon’s Tips Chaboche Nonlinear Kinematic Hardening3Calibration of Single ModelPer page 226of Reference [5],tension-compression tests of symmetric,strain-controlled tests can be used to obtain the material parameters k ,C 1,and γ1.The stabilized hysteresis loops corresponding to different strain amplitudes should be used.The following steps (taken from the above reference)can be used to determine the material parameters:1.Determine the yield stress k from the elastic domain (k is usually half the elastic domain size).2.For a given test,determine the plastic strain range ∆ǫpl .3.For a given test,determine the stress range ∆σ.4.Plotting ∆σ2−k against ∆ǫpl2for the multiple tests,estimate the asymp-totic value corresponding to C 1γing the expression ∆σ2−k =C 1γ1tanh(γ1∆ǫpl2),fit the results to solve for C 1and γ1.This can be done,for example,in Microsoft Excel us-ing the Solver Add-In.Note that curve-fitting procedures often benefit from reasonable initial values.Since C 1is the initial hardening modu-lus,the slope after the yield stress can be taken as an estimate of C 1,and through the relation of C 1γ1determined in Step 4,an initial value of γ1can be obtained.3.1Example Using Several StabilizedCyclesCyclic TestS t r e s sFigure 6:Strain-Controlled TestAn example of stress versus plastic strain is shown in Figure 6,where the test specimen is loaded ±ǫa .Looking at the stabilized hysteresis loop,one can see that the elastic do-main is roughly (300+760)=1,060MPa,so the yield stress k can be estimated as 530MPa.The stress range ∆σis around 2×760=1,520MPa.The plastic strain range ∆ǫpl is estimated to be 2×.21%=0.42%.When two additional strain-controlled,cyclic tests are performed,thefollowing sets of data were obtained:(a)k 2=500,∆σ22=840,∆ǫpl 22=0.37%8Sheldon’s Tips Chaboche Nonlinear KinematicHardeningCurve-Fit Data0.0010.0020.0030.0040.0050.0060.0070.0080.0090.01∆εpl/2∆σ/2- kFigure 7:Curve-Fit Dataand (b)k 3=540,∆σ32=900,∆ǫpl32=0.5625%.All three data points areplotted as red dots in Figure 7,with the abscissa being ∆ǫpl2and the ordinatebeing ∆σ2−k .Using Step 4in Section 3,the asymptotic value was estimated to be ≤400MPa.The yield stress k was estimated to be 530MPa based on k 1,k 2,and k 3values.From Figure 6,the initial hardening modulus C 1was estimated as 164,000MPa,so γ1=410—these were used as starting values.The constants C 1=122,000MPa and γ1=314were then obtained —the curve-fit data matches reasonably well with the presented data,and the parameters could be refined further,if needed.3.2Example Using Single Stabilized CycleIf only data from a single strain-controlled test is available,material inden-tification can still be performed,although the derived parameters are best suited for that particular strain range.9Sheldon’s Tips Chaboche Nonlinear Kinematic HardeningUsing the example shown in Figure 6,assume that stress and plastic strain points for the stabilized loop are tabulated as follows:ǫpl i σi (MPa)-0.0021300-0.0014800.05900.0016800.0021760Table 1:Sample Plastic Strain vs.Stress PointsThere are two items that need adjustment:the plastic strain values ǫpl should start from zero,and the stress needs to be converted to the back stress {α}.Shift the plastic strain values such that the first point starts from zero.For the back stress,determine the elastic range (recall from Subsection 3.1that this was determined to be 1060MPa),then subtract the stress by the yield stress,or half the value of the elastic domain.The resulting values are shown below:ǫpl i αi (MPa)0.0-2300.0011-500.0021600.00311500.0042230Table 2:Corrected Plastic Strain vs.Back StressTo determine the C 1and γ1constants,one may consider using the back stress relation αi =C 1γ1 1−e−γ1ǫpli ,although this expression assumes zero initial back stress.Since the model contains non-zero back stress,the first data point is used in the following equation to solve for the other pairs:αi =C 1γ11−e −γ1ǫpl i +α1e −γ1ǫpl i for i >1(5)One can use Microsoft Excel’s Solver Add-In or any other means to perform a fit to determine C 1and γ1.The considerations noted earlier about using the slope after yielding as the initial value of C 1,along with estimating an initial value of γ1from the asymptotic value,still apply,as these will aid any curve-fitting procedure.10Sheldon’s Tips Chaboche Nonlinear Kinematic Hardening For this example,the author obtained values of C1=120,500MPa and γ1=280.While these values differ slightly from C1=122,000MPa and γ1=314obtained in Subsection3.1,please note that(a)the author did not use a digitizer to determine the data points but used rough,visual estimates, and(b)the curve-fit data obtained from several stabilized cycles should be more representative of behavior over a wider strain range.As an alternative or supplement to the option presented in Subsection 3.1,the user may also use the approach outlined in this subsection to man-ually obtain C1andγ1coefficients for various strain ranges to better under-stand the variation of the material parameters that may be present.3.3Example Using Single Tension CurveA user may only have data from a single tension test but may wish to use the nonlinear kinematic hardening model.While this is not recommended since there is no cyclic test data with which to correlate the material parameters, such an approach may be suitable for situations dealing with a few cycles.Plastic strain and stress data will be estimated from thefirst curve of Figure6,which would represent a single tensile loading case:ǫpl iσi(MPa)0.05200.00055800.0016300.00156800.0022720Table3:Plastic Strain vs.Stress for First CurveAs with the situation presented in Subsection3.2,the stress needs to be converted to the back stress.The yield surface should be determined(for example,by using0.2%offset),and this scalar value should be subtracted from the stress values in Table3.Then,{αi}values for each data point can be matched against the following equation:αi=C1γ1 1−e−γ1ǫpl i(6)The user can solve for values of C i andγi—the same procedure to obtain initial values and to perform the curve-fit as explained above still apply for the uniaxial tension case.For this particular set of data that11Sheldon’s Tips Chaboche Nonlinear Kinematic Hardening was approximated from the first curve of Figure 6,the author obtained C 1=135,300MPa and γ1=380.The use of the single uniaxial test data for this specific example resulted in higher estimates of C 1and γ1compared with those obtained in Subsections 3.1and 3.2,although the asymptoticvalue C 1γ1=356MPa is actually the smallest of the three.As noted above,the lack of cyclic test data prevents validation of the derived material parameters for general cyclic applications.Consequently,the author strongly recommends creating a simple one-element model to simulate the cyclic behavior of the calculated material paramters —in this way,the user can see what the numerical cyclic behavior will be for the set of material parameters.With a simple model,the user may also vary the loading for larger strain ranges in order to understand the response in strain ranges for which no test data is present.3.4Comparison ofResultsCyclic TestS t r e s s Figure 8:Comparison of DataFigure 8shows the original data compared with the three sets of cal-culated material parameters.As one can see,the results for this strain range match reasonably well for all three cases,despite some vari-ation in the C 1and γ1values.How-ever,the parameters derived frommultiple stabilized cycles would beexpected to give the best correlationfor different strain ranges.4Rate-Dependent VersionIn ANSYS 12.0.1,a rate-dependent form of the Chaboche model was intro-duced.This is accessed via adding TB,RATE,,,,CHABOCHE in conjunction with the regular TB,CHABOCHE definition without isotropic hardening.The rate-dependent additions to the Chaboche model (Equations (1)and (2))are shown below:˙ǫpl = σ−RK 1m (7)R =K 0+R 0ˆǫpl +R ∞ 1−e−b ˆǫpl (8)12Sheldon’s Tips Chaboche Nonlinear Kinematic Hardening where thefirst4constants for TB,RATE,,,,CHABOCHE are K0,R0,R∞,and b(isotropic hardening Equation(8))while the last2constants are m and K(rate-dependent Equation(7)).These6material constants are input via the TBDATA command.From looking at the above equations,one can see that the rate-dependent Chaboche model incorporates a strain-rate dependent term(similar to Peirce or Perzyna options)with Voce hardening.5ConclusionBackground information on the Chaboche material model was presented in this memo,along with a basic discussion of the calibration of the material constants for a single nonlinear kinematic hardening model.While phenomena such as rachetting,shakedown,mean stress relaxation, and cyclic softening were not introduced,the information in this memo may serve as a starting point for users wishing to combine multiple nonlinear kinematic hardening models or to define combined(isotropic and kinematic) hardening laws.The reader is encouraged to review the cited references, including[1],for additional details on cyclic plasticity and its definition and usage in ANSYS.Revisions to this Document•STI0805A(November14,2009):Updated for12.0.1.Updated Equa-tion(2),added Section4.Added additional information concerning input in Section1.References[1]ANSYS,Inc.Advanced Structural Nonlinearities,First edition,2005.Inventory Number:002205,ANSYS9.0.[2]ANSYS,Inc.Theory Reference for ANSYS and ANSYS Workbench11.0,2007.[3]Jean-Louis Chaboche.Constitutive Equations for Cyclic Plasticity andCyclic Viscoplasticity.International Journal of Plasticity,5:247–302, 1989.13Sheldon’s Tips Chaboche Nonlinear Kinematic Hardening [4]Jean-Louis Chaboche.On Some Modifications of Kinematic Hardeningto Improve the Description of Ratchetting Effects.International Journal of Plasticity,7:661–678,1991.[5]Jean Lemaitre and Jean-Louis Chaboche.Mechanics of Solid Materials.Cambridge University Press,English edition,1990.14Sheldon’s Tips General InformationSheldon’s Tips and TricksSheldon’s Tips and Tricks are available at the following URL:/sheldon tips/Please remember that,with each release of ANSYS,new features and tech-niques may be introduced,so please refer to the ANSYS documentation as well as your local ANSYS support office to verify that these tips are the most up-to-date method of performing tasks.Disclaimer:the author has made attempts to ensure that the informa-tion contained in this memo is accurate.However,the author assumes no liability for any use(or misuse)of the information presented in this docu-ment or accompanyingfiles.Please refer to for the latest version of this document.Also,this memo and any accompanying inputfiles are not official ANSYS,Inc.documentation.ANSYS TrainingANSYS,Inc.as well as ANSYS Channel Partners provide training classes for ANSYS,Workbench,CFX,FLUENT,ANSYS LS-DYNA,AUTODYN, ASAS,AQWA,TAS,and ICEM CFD rmation on training classes and schedules can be found on the following page:/services/ts-courses.aspANSYS Customer PortalCustomers on active maintenance(TECS)can register for a user account and access the ANSYS Customer Portal.Here,browsing documentation, downloading software(including service packs),and submitting technical support incidents are possible:/customer/XANSYS Mailing ListThe XANSYS mailing list is a forum for exchanging ideas,providing and receiving assistance from other users,and general discussions related to ANSYS and Workbench.(Note that it is recommended to contact your local ANSYS support office for technical support.)You can obtain more information by visiting the following URL:/15。

Examination of the K s Overburden Correction Factoron Liquefaction ResistanceJack Montgomery,A.M.ASCE 1;Ross W.Boulanger,F.ASCE 2;and Leslie F.Harder Jr.,M.ASCE 3Abstract:The overburden correction factor (K s )is used to account for the curvature of the cyclic strength envelope with increasing consolidation stress,and it provides part of the basis for extrapolation of liquefaction-triggering correlations based on standard penetration test (SPT)and cone penetration test (CPT)to larger depths than covered by current databases of liquefaction case histories.This paper presents an updated database of laboratory test results de fining K s boratory test results included in previous databases are reexamined in light of current understanding of factors that can affect laboratory measurements of cyclic strengths,including the effects of increasing density with increasing consolidation stress,variable overconsolidation ratios,and other factors.The updated database is used to examine potential biases in the K s relationships used in two SPT-based liquefaction triggering procedures.The first relationship was found to be conservative with respect to the data for clean sands and less conservative for sands with fines contents between 7and 35%.The second relationship was found to provide a reasonably good fit to the data for clean sands and to be slightly unconservative for sands with fines contents between 7and 35%.Implications for practice are discussed.DOI:10.1061/(ASCE)GT.1943-5606.0001172.©2014American Society of Civil Engineers.Author keywords:Liquefaction;Sands;Silty sands;Overburden stress;Laboratory tests.IntroductionThe cyclic strength of sands and other cohesionless soils (e.g.,gravels to nonplastic silts)depends,among other factors,on both the soil density [e.g.,void ratio or relative density (D R )]and the imposed effective stress at consolidation (s c 9),which together determine the state of the soil.Liquefaction-triggering correlations commonly use normalized standard penetration test (SPT)and cone penetration test (CPT)penetration resistances as a proxy for D R and other factors affecting cyclic strength.Seed (1983)introduced the overburden correction factor (K s )to account for the curvature of the cyclic strength envelope with increasing s c 9.This factor was de fined in terms of the soil ’s cyclic resistance ratio (CRR)asK s ¼CRR s 9vc ,a 50CRR s 9vc 51,a 50(1)where CRR s 9v c ,a 50and CRR s 9vc 51,a 505cyclic resistance ratios for vertical effective stress at consolidation (s vc 9)equal to the stress of interest and 101.3kPa (1atm),respectively,and a static shear stress ratio (a 5t s =s vc 9,where t s is the static shear stress)of zero.Both CRR values are assumed to be for a soil that is identical in all respects other than consolidation stress (i.e.,the same D R ,same fabric,same age,same cementation,and same loading history).Studies haveshown that the magnitude of this curvature is dependent on D R and soil type (Vaid and Sivathayalan 1996;Hynes and Olsen 1999).Examples of K s relationships include those from Seed and Harder (1990)and Harder and Boulanger (1997)in Fig.1(a)and those from Youd et al.(2001)and Idriss and Boulanger (2008)in Fig.1(b).The effects of D R and s c 9on the CRR of sands can be expressed through the state parameter (j )(Pillai and Muhunthan 2001;Stamatopoulos 2010)or relative state parameter (j R )(Boulanger 2003;Idriss and Boulanger 2008).Determination of j or j R for in situ soils through laboratory testing is dif ficult owing to issues of disturbance during sampling of cohesionless soils.Boulanger (2003)recommended using an empirical procedure for approxi-mating the critical state line and then referring to the estimated j R as an index.Liquefaction-triggering correlations commonly normalize the SPT or CPT penetration resistances to a reference s vc 9of 101.3kPa (1atm)(assuming the soil ’s D R and all other attributes are un-changed)and correlate this normalized penetration resistance to a normalized CRR for this same reference stress (i.e.,CRR s vc 951).For example,the normalization of SPT blow counts is performed using the overburden correction factor C N as follows:ðN 1Þ60¼C N ðN Þ60(2)where N 605SPT blow count for an energy ratio of 60%;and ðN 1Þ605N 60value for an equivalent s vc 9of 101.3kPa (1atm).Dependence of the liquefaction-triggering correlation on the fines content (FC)is accommodated by adding an increment,D ðN 1Þ60,to the ðN 1Þ60value to obtain an equivalent clean-sand ðN 1Þ60cs to determine the appropriate CRRðN 1Þ60cs ¼ðN 1Þ60þD ðN 1Þ60(3)The relationship for D ðN 1Þ60depends on the liquefaction-triggering correlation.The effect on CRR of variations in s vc 9,t s ,and earthquake magnitude (M )are accounted for by K s ,static shear stress correction (K a ),and magnitude scaling factor (MSF),respectively,as1Ph.D.Candidate,Dept.of Civil and Environmental Engineering,Univ.of California at Davis,Davis,CA 95616(corresponding author).E-mail:jmontgomery@ 2Professor,Dept.of Civil and Environmental Engineering,Univ.of California at Davis,Davis,CA 95616.E-mail:rwboulanger@ 3Senior Water Resources Technical Advisor,HDR Engineering,Inc.,2365Iron Point Rd.,Folsom,CA 95630.E-mail:les.harder@Note.This manuscript was submitted on July 25,2013;approved on July 7,2014;published online on August 7,2014.Discussion period open until January 7,2015;separate discussions must be submitted for in-dividual papers.This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering ,©ASCE,ISSN 1090-0241/04014066(11)/$25.00.D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/22/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .CRR M ,s 9vc ,a ¼CRR M 57:5,s 9vc 51,a 50×MSF ×K s ×K a(4)where CRR M ,s 9v c ,a 5CRR for given values of M ,s vc 9,and a ;and CRR M 57:5,s 9v c 51,a 505value of CRR for M 57:5,s vc 95101:3kPa ð1atm Þ,and a 50,as obtained from case history –based correlations.A second approach to evaluating the CRR of sand is to normalize the SPT or CPT penetration resistances (i.e.,N 60or q c )to a reference s vc 9of 101.3kPa (1atm),but this time assuming the soil remains at the same state (i.e.,same state parameter or relative state parameter)with all other attributes unchanged (e.g.,Boulanger and Idriss 2004).The resulting state-based normalized penetration resistances [i.e.,using a C N j to obtain a ðN 1j Þ60or q c 1j ]can then be correlated more directly to the soil ’s CRR M 57:5,s 9v c 51,a 50without the need for further stress adjustment through K s .A third approach is to correlate the penetration resistance directly to j ,which can then be correlated to the cyclic strength of the soil (e.g.,Jefferies and Been 2006).This paper focuses on the K s factor used within the first of the three approaches described.The K s and C N factors provide the basis for extrapolating the case-history data on liquefaction triggering from depths less than approximately 15m and s vc 9less than ap-proximately 150kPa (Boulanger et al.2012)to much greater depths and stresses,such as those encountered under large embankment dams.The K s factor can be evaluated through laboratory element tests,whereas the C N factor can be evaluated using calibration chamber tests,numerical analyses,and in situ test data.The K s and C N factors are not independent,however,because they are both in fluenced by the same soil properties,often in opposing ways as shown by Boulanger (2003).The interdependency of the K s and C N factors and their algebraic relationship with the alternative state-based overburden normalization factor for penetration resistances (i.e.,C N j )are examined in Boulanger (2003)and Boulanger and Idriss (2004).The purpose of this paper is (1)to document and reexamine the K s database compiled by Harder (1988),as later presented by Seed and Harder (1990),in light of current understanding of factors that can affect laboratory measurements of CRR;(2)to expand the database with additional high-quality data from the literature;(3)to show examples of the important factors that can in fluence the in-terpretation of K s ;and (4)to examine the K s relationships by Youd et al.(2001)and Idriss and Boulanger (2008)using the updated database.Much of the data contained in the Seed and Harder (1990)database came from engineering reports that are not available in thepublished literature.The limitations of that database were not dis-cussed extensively in Youd et al.(2001),which suggests that they were not fully appreciated at that time.It is hoped that this update and reexamination of an in fluential database will contribute to improved understanding and engineering practices for evaluating soil lique-faction during earthquakes.Database on K s RelationshipPrevious investigations of K s have often centered on,or been compared with,a database of cyclic triaxial test results compiled by Harder (1988)and later presented by Seed and Harder (1990),as shown in Fig.1(a).The Seed and Harder (1990)database had 45data points from 18sources and included results for reconstituted soils and undisturbed field samples.There is a signi ficant amount of scatter within these data for a given s c 9,and much of the scatter is likely caused by the variety of soil types,sample preparation methods,and densities represented.The current database for K s ,which is summarized in Montgomery et al.(2012)and Tables S1–S6in the Supplemental Data to this paper,includes a number of additions,deletions,and revisions relative to the database by Seed and Harder (1990).The available data for Upper San Leandro and Lake Arrowhead dams were deleted because they were insuf ficient to reasonably de fine K s .Additional data included laboratory studies on reconstituted sands by Vaid and Thomas (1995),Vaid and Sivathayalan (1996),Koseki et al.(2005),and Manmatharajan and Sivathayalan (2011),and on frozen sand samples by Pillai and Byrne (1994).The failure criterion used to determine CRR values from labo-ratory tests (CRR laboratory )was set at 62:5%single-amplitude (S.A.)axial strain in 15cycles when test details were available.If such details were not available,the failure criterion reported by the original authors was used [e.g.,5%double-amplitude (D.A.)axial strain in 10cycles].The failure criteria for each data set are listed in Tables S1–S6.The effect of selecting different failure criteria on K s is not expected to be large,but the lack of a consistent criterion likely contributes to some of the scatter in the current database.The CRR laboratory values were converted to an equivalent field CRR (CRR M 57:5,s vc 951,a 50)using the methods summarized in Idriss and Boulanger (2008).The speci fic factors used for the conversion are shown in the Supplemental Data.An important step inthisFig.1.The K s relationships:(a)Seed and Harder (1990)and Harder and Boulanger (1997);(b)Youd et al.(2001)and Idriss and Boulanger (2008);1atm 5101:3kPaD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/22/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .conversion is the selection of an appropriate field value of the in situ coef ficient of lateral earth pressure at rest (K o ).In an isotropically consolidated cyclic triaxial test,the laboratory K o is equal to 1.0.However,K o in the field could range from approximately 0.5for a normally consolidated soil to approximately 1.0for moderately overconsolidated soils.The effect of the assumed field K o value on the interpretation of cyclic triaxial or torsional shear test data was evaluated by performing this adjustment with assumed field K o values of 0.5and 1.0.For the simple shear test results,no adjustment for K o was made.The CRR M 57:5,s vc 951,a 50values for isotropically consolidated (laboratory K o 51:0)triaxial tests and anisotropically consolidated (laboratory K o 50:5)torsional shear tests are listed in Tables S1–S6for assumed field K o values of 0.5and 1.0.The results of these conversions were later used for comparing the laboratory results to different K s relationships.The K s results were separated into the four categories plotted separately in Figs.2(a –d):clean sands (sands with 5%fines or less,52points);sands with varying levels of nonplastic or silty fines (14points);clayey sands (two points);and well-compacted speci-mens (12points).Each of the categories is shown with the curve recommended by Seed and Harder (1990)for comparison.The results for the clayey sands (FC of 23to 28%,plasticity indexes of 20to 25),as plotted in Fig.2(c),are considered to be of limited value when examining the liquefaction potential of cohesionless soils.This is because plastic fines have been shown to in fluence the response of a soil to cyclic loading (e.g.,Boulanger and Idriss 2006;Bray and Sancio 2006).The effects of the fines ’plasticity on K s are not clear,but these data were not considered useful for evaluating the behavior of clean sands or sands with primarily nonplastic silty fines,which are traditionally evaluated using liquefaction-triggering curves.For these reasons,the two data points for clayey sands were eliminated from further evaluation.The data from well-compacted soils (FC of 7to 35%,12points),as plotted in Fig.2(d),were also considered to be of limited value.These soils (1)had been compacted to a relative compaction of 95%or larger according to the speci fic compaction standard listed in Table S6;(2)had been compacted to a D R of 100%;or (3)had in situ blow counts of 45.All these soils exhibited high cyclic triaxial strengths (i.e.,CRR laboratory at 15uniform loading cycles greater than 0.6for all specimens and greater than 0.77for half the specimens).In addition,these specimens were likely affected by large variations in overconsolidation ratio (OCR)as discussed in the following section.Because of the high strengths and likely OCR effects,the heavily compacted specimens were not considered to be repre-sentative of traditionally lique fiable soils and were also eliminated.The remaining data for clean sands [Fig.2(a)]and sands with varying levels of silty fines [Fig.2(b)]are considered most appli-cable for developing relationships for lique fiable soils.ThecleanFig.2.The current database is composed of several different soil types:(a)clean sands;(b)sands with varying levels of silt;(c)clayey sands;and (d)well-compacted sands with varying levels of clay and silt;each of the data sets is compared with the curve recommended by Seed and Harder (1990);1atm 5101:3kPaD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/22/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .sand data are all for freshly reconstituted specimens prepared to a range of D R (31–78%)using wet and dry pluviation,moist tamping,and vibratory sample preparation techniques.The data for sands with nonplastic or silty fines are all from field samples that were either reconstituted (four specimens)or undisturbed (10specimens).There is still a large amount of scatter in each of the categories,and the range of densities,failure criteria,and sample preparation methods represented likely contributes to the spread in K s values.Challenges in Interpreting K s from Laboratory Test DataThe interpretation of K s from laboratory data can be inadvertently complicated by changes in the specimen properties that occur as s c 9is increased,such as changes in D R ,OCR,cementation,and fabric.These and other factors cannot be isolated or eliminated from the current K s database.The potential magnitude of such effects is discussed in the following sections.Effect of Relative Density on K sAn example of how D R and s c 9affect CRR and K s values is shown in Fig.3using data from Thermalito Afterbay [California Department of Water Resources (CDWR)1989].Cyclic triaxial tests wereperformed on undisturbed samples of the silty sand foundation obtained using fixed piston samplers.The test results were grouped by average ðN 1Þ60values for the strata from which the samples were obtained.The cyclic strengths of the soils increased with increasing blow count and increasing con finement [Fig.3(a)],as expected.The envelope of cyclic strength versus s c 9is curved,such that the CRR (i.e.,the secant slope of the envelope)decreases as the s c 9is in-creased.The corresponding K s values in Fig.3(b)illustrate how K s curves generally became more strongly dependent on s c 9as the average ðN 1Þ60(and hence D R )of the soil increased and the envelope of cyclic strength versus s c 9became more strongly curved [Fig.3(a)].The dependence of K s on D R can also complicate the inter-pretation of K s from laboratory tests where specimens prepared at the same relative density are consolidated to different stresses,leading to increasing density with increasing s c 9.This effect is il-lustrated by the numerical example in Fig.4.In this example,the specimen is assumed to be clean sand prepared to D R 550%at s c 95100kPa and without any prior stress history.As the specimen is consolidated to the higher s c 95400kPa,the specimen densi fies such that the D R is 54%after consolidation.This is a hypothetical example,and the change in D R during consolidation will vary for different soils.The CRR for each specimen can be estimated using the D R 2ðN 1Þ60correlation,liquefaction-triggering curve,and K s relationship by Idriss and Boulanger (2008),with the results shown as black circles in Fig.4(a).If the change in D R is not accountedfor,Fig.3.(a)Cyclic triaxial strengths and (b)K s values for undisturbed samples of silty sand (SM)foundation materials from Thermalito Afterbay [data from California Department of Water Resources (CDWR)1989];liq.5liquefaction;1atm 5101:3kPaFig.4.Schematic example showing how sample consolidation can affect (a)cyclic strengths and (b)determination of K s values;samples may have increasing density with increasing s c 9;if this effect is not accounted for,it will lead to a K s curve that is too weakly dependent on s c 9compared with results for specimens at the same relative density;liq.5liquefaction;1atm 5101:3kPaD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/22/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .the interpreted K s[Fig.4(b)]will include both the decrease in CRR caused by the increase in s c9and the increase in CRR caused by increasing density with s c9.These two effects offset each other, leading to the interpretation of a K s curve that is more weakly dependent on s c9(higher K s values at stresses greater than101.3kPa) than would have been measured had the specimens been tested at the same D R,as illustrated by the gray circles in Fig.4(b).Pillai and Byrne(1994)performed a similar analysis of the cyclic testing test data for Duncan Dam and showed a similar effect on the interpretation of K s values.Effect of Specimen Overconsolidation on K sThe effects of OCR varying with s c9can be even more important to the interpretation of K s.Experimental results have shown that the CRR of a soil increases with increasing OCR(e.g.,Ishihara et al.1978; Manmatharajan and Sivathayalan2011).Consider the test results by Manmatharajan and Sivathayalan(2011)from cyclic simple shear tests on Fraser Delta sand consolidated to three s c9values(100,200, and400kPa)and OCR levels(1.0,1.5,and2.0).The samples were prepared such that the D R after consolidation for all samples was approximately41%.The results,as plotted in Fig.5(a),show that the CRR of the sand increases significantly as OCR is increased.The K s curves for each OCR are approximately the same,as shown in Fig. 5(b).Now consider the hypothetical example where a set of samples of this sand with a preconsolidation stress(s p9)of200kPa were tested in the laboratory at s c9of100,200,and400kPa(producing OCR values of2,1,and1,respectively).The hypothetical CRR values are shown as circles in Fig.5(a),from which the inferred K s in Fig.5(b)would show an artificially strong dependence on s c9.For this hypothetical example,the potential error in K s interpretations caused by the OCR varying with s c9was greater in magnitude than,but opposite in di-rection from,the error caused by varying D R(Fig.4).It can be difficult to control or evaluate OCR values when testing either undisturbed or laboratory-prepared specimens.Undisturbed specimens of a normally consolidated soil tested in the laboratory at s c9lower than their in situ s vc9will have OCR values that increase with decreasing s c9.Undisturbed specimens of overconsolidated soil tested at different s c9will have OCR values that decrease as s c9 approaches s p9and are equal to1at higher s c9.Consequently,if specimens having the same s p9are tested at different levels of s c9,the results will likely reflect the combined effects of changing both OCR and s c9.This effect has been observed by Bray and Sancio(2006)in test results on undisturbed samples of potentially liquefiable silts.Compaction in either thefield or laboratory can also lead tooverconsolidation.Frost and Park(2003)showed that the moist-tamped specimens prepared to D R greater than60%are likely to beoverconsolidated at s c9,100kPa.The well-compacted specimens [Fig.2(d)]were eliminated from further consideration in part be-cause of this effect;this included three soils prepared in the labo-ratory to relative compactions of95%or greater through moisttamping,one soil having in situ SPT blow counts of45,and onesoil moist-tamped to D R5100%.Other moist-tamped specimens (prepared to D R less than78%or relative compactions less than87%) were not eliminated because the severity of the effect from moist tamping is difficult to evaluate and is expected to be less significant for lower-density specimens than for well-compacted soils.It is noted,however,that the data for moist-tamped specimens also likely exhibit some effects from changing OCR,especially at low stresses.Natural,sandy deposits are likely to have some amount of over-consolidation in situ(e.g.,because offluctuations in the groundwatertable or erosion of overlying sediments),but the nature of conven-tional sampling and specimen preparation may sufficiently disturb ordisrupt the soil fabric such that the effects of prior overconsolidationon CRR are lost.It is not possible to assess the degree to whichoverconsolidation may or may not have affected the interpretation ofK s values from tests on undisturbed samples in the current database. Other Factors That Influence K sThe CRR of undisturbed soil samples may also be affected by factorssuch as cementation,prior strain history,and aging effects,each ofwhich may be destroyed as the s c9increases.Each of these factors would likely result in the CRR decreasing more rapidly with in-creasing s c9than would occur if all test specimens were identical. This could lead to the interpretation of a K s curve that is too strongly dependent on s c9.However,disturbance from conventional sampling and specimen preparation may disrupt such effects and make them difficult to assess.The CRR of soil is also affected by the method of sample prep-aration or deposition(e.g.,Mulilis et al.1975;Tatsuoka et al.1986)and the failure criterion used to define liquefaction(e.g.,Tatsuokaet al.1986).The method of sample preparation or deposition and thefailure criterion will affect CRR across a broad range of s c9,such that the K s values are expected to be less affected than the individual CRR values.The current database contains results from samples with a variety of preparation methods and failure criteria,which undoubtedly contributes to the scatter in K svalues.Fig.5.Results from cyclic simple shear tests performed on Fraser Delta sand tested at D R541%and three levels of overconsolidation showing(a)cyclic strengths and(b)corresponding overburden correction factors;circles illustrate how these types of data could be misinterpreted if K s iscalculated from three samples with the same preconsolidation stress(s p9)tested at three different consolidation stresses;1atm5101:3kPaDownloadedfromascelibrary.orgbyTongjiUniversityon12/22/14.CopyrightASCE.Forpersonaluseonly;allrightsreserved.The K s factor may also be affected by various soil characteristics including the FC (Stamatopoulos 2010)and fines ’plasticity.This effect is not well constrained by available data,but the current database has been separated according to FC in an attempt to isolate some of these effects.Results for each of the categories and the implications of this dependence on FC are discussed more in the next parison of Database and Current Relationships The relationships by Idriss and Boulanger (2008)and Hynes and Olsen (1999),with the parameters recommended in Youd et al.(2001),are compared with the updated database because they both account for dependence on D R .The Hynes and Olsen (1999)K s relationship,with the limit recommended by Youd et al.(2001),isK s ¼s vc9P a2ð12f Þ#1:0(5)Hynes and Olsen (1999)derived their relationship using stress focus theory (Olsen 1994)to select the exponent f .Youd et al.(2001)suggested values for f of 0.8,0.7,and 0.6for D R of 40,60,and 80%,respectively,with f limited to $0:6and #0:8.These values can be approximated by the linear relationshipf ¼12D R2,0:6#f #0:8(6)Boulanger (2003)derived a separate K s relationship using the ksi R ,which was published in Idriss and Boulanger (2008)asK s ¼12C s ln s vc 9P a#1:1(7)where the factor C s is de fined in terms of D R asC s ¼118:9217:3D R#0:3(8)D R can be estimated from the SPT blow count asD R ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðN 1Þ60csC ds (9)where the value of C d was taken as 46by Idriss and Boulanger (2008).No single measure of density [i.e.,D R ,ðN 1Þ60,relative com-paction]is common to all data sets in the database.One approximate measure of density common to all soils is the equivalent field CRR M 57:5,s vc 951,a 50.If the liquefaction-triggering curve is assumed to be unique,the field CRR M 57:5,s vc 951,a 50can be related to an equivalent ðN 1Þ60cs and then to a K s value for a given s c 9.The effect of the assumed field K o value on the calculation of CRR M 57:5,s vc 951,a 50was evaluated by performing this adjustment with assumed field K o values of 0.5and 1.0.This process was previously described,and an example calculation is shown in the Supplemental Data.Results for Clean SandsThe K s data for clean sands tested in triaxial or torsional shear were separated into three bins with CRR M 57:5,s vc 951,a 50values of 0.07–0.11[Fig.6(a)],0.14–0.17[Fig.6(c)],and 0.22–0.25[Fig.6(e)],for an assumed field K o of 0.5.The relationships from Youd et al.(2001)and Idriss and Boulanger (2008)are shown in these figures for D R values that correspond to a CRR M 57:5,s 9v c 51,a 50value at the middle of each bin ’s range (e.g.,CRR M 57:5,s vc 951,a 50values of 0.09,0.155,and 0.235for K o of 0.5;0.135,0.225,and 0.35for K o of 1.0).Trends in the K s data become steeper as CRR M 57:5,s vc 951,a 50increases,as expected.The Idriss and Boulanger (2008)relationship is in rea-sonable agreement with the clean sand data,whereas the Youd et al.(2001)relationship is generally conservative.The test data for clean sands tested in simple shear were separated into bins of approximately equal size and similarly compared with the relationships (Fig.7).The K s values for these data points fall well above the values predicted by the relationships by Youd et al.(2001)and Idriss and Boulanger (2008),although the values are much closer to the latter.These tests were all from water-pluviated specimens of Fraser River sand.Residuals between individual data points and their corre-sponding model predictions for all test types are shown versus CRR M 57:5,s vc 951,a 50in Fig.8(for a field K o 50:5).The K s re-lationship by Youd et al.(2001)was not applicable at s vc 9,101:3kPa ð1atm Þas part of its coupling with the Seed et al.(1985)liquefaction-triggering correlation,and thus the residuals for s vc 9,101:3kPa ð1atm Þusing the Youd et al.(2001)relationship are not signi ficant.The residuals from these clean sand specimens show that the relationship by Idriss and Boulanger (2008)provides a reasonably good fit [Fig.8(a)],whereas the relationship by Youd et al.(2001)generally underpredicts K s [Fig.8(b)].For s vc 9.101:3kPa ð1atm Þ,the relationship by Idriss and Boulanger (2008)has an average residual near 0.0%for a K o of 0.5over the full range of strengths and s vc 9values.The relationship by Youd et al.(2001)predicts lower K s values over the full range of strengths and s vc 9values,with an average residual of 16.3%for a K o of 0.5.For s vc 9,101:3kPa ð1atm Þ,the relationship by Idriss and Boulanger (2008)fits the data similarly well,with an average residual of 0.0%at a K o of 0.5.The degree of fit between the data and models was also examined for a field K o of 1.0(Montgomery et al.2012).This greater K o value increases the CRR M 57:5,s vc 951,a 50by approximately 50%,which pro-duces K s curves with stronger dependence on s vc 9(i.e.,steeper curves).The choice of K o does not,however,affect the measured K s values.For s vc 9.101:3kPa ð1atm Þ,using K o 51:0increased the average residuals from 0.0to 2.4%for the model by Idriss and Boulanger (2008)and from 16.3to 19.9%for the model by Youd et al.(2001).For s vc 9,101:3kPa ð1atm Þ,using K o 51:0reduced the average residuals from 0.0%to 21:0%for the model by Idriss and Boulanger (2008).These results illustrate that using K o of 0.5in the present scheme for evaluating models is slightly conservative for s vc 9.101:3kPa ð1atm Þand that the effect of K o is secondary to the differences between models.Results for Silty SandsThe test data for sands with varying levels of silty fines,all from cyclic triaxial tests,were similarly compared with the two K s rela-tionships as shown in Figs.9(a –e).Much of the data fall in a narrower range of CRR M 57:5,s vc 951,a 50values,with a large number of the specimens having a CRR M 57:5,s vc 951,a 50close to 0.14for a K o of 0.5.A trend of lower K s values with increasing CRR M 57:5,s vc 951,a 50can be seen across the bins.The data for the looser specimens [Figs.9(a and b)]generally fall between the two relationships,whereas the two points in the higher or denser bin [Figs.9(e and f)]agree better with Youd et al.(2001).Residuals for specimens with FC 57e 35%are shown versus CRR M 57:5,s vc 951,a 50in Fig.10(for a field K o 50:5).For s vc 9.101:3kPa ð1atm Þ,the relationship by Idriss and Boulanger (2008)overpredicts K s values,with an average residual of 29:6%D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/22/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .。

春天叶子英语小作文Title: The Arrival of Spring Leaves。

Spring brings with it a vibrant transformation in nature, as trees awaken from their winter slumber and adorn themselves with fresh, green leaves. The emergence of these leaves symbolizes renewal, growth, and the promise of warmer days ahead.Firstly, let's delve into the significance of spring leaves. As winter recedes, trees undergo a remarkable process called bud break, where tiny buds on the branches begin to swell and eventually burst open, revealing delicate, young leaves. This process is not merely a biological phenomenon; it carries profound symbolism. Spring leaves signify the resilience of life, as even in the harshest of winters, nature finds a way to rejuvenate itself. 。

Moreover, spring leaves embody the essence of vitalityand energy. Their vibrant green hues infuse landscapes with a sense of freshness and vigor, breathing new life into the surroundings. As the sun's warmth intensifies and daylight hours lengthen, these leaves undergo photosynthesis, converting sunlight into energy and releasing oxygen into the atmosphere. Thus, they play a crucial role in maintaining ecological balance and sustaining life on our planet.Furthermore, spring leaves hold cultural and emotional significance across various societies. In many cultures, the sight of fresh leaves signifies the onset offestivities and celebrations, marking the end of gloomy winter months. People eagerly anticipate the arrival of spring leaves as a harbinger of joy, hope, and new beginnings. Artists and poets often draw inspiration from the verdant beauty of spring leaves, capturing their ephemeral charm in paintings, poems, and songs.From a scientific perspective, the emergence of spring leaves serves as an indicator of environmental changes. Researchers study the timing of leaf emergence as part ofphenology—the study of cyclic and seasonal natural phenomena. Changes in leaf-out dates can provide valuable insights into climate patterns, helping scientists monitor the effects of climate change on ecosystems.In addition to their aesthetic and ecological significance, spring leaves offer practical benefits. They provide shade from the scorching sun, shelter for wildlife, and contribute to soil moisture retention. Moreover, the rustling sound of leaves in the gentle breeze creates a soothing ambiance, inviting contemplation and relaxation.However, the arrival of spring leaves also poses challenges. For allergy sufferers, the increase in pollen levels can trigger allergic reactions, causing discomfort and respiratory problems. Additionally, the dense foliage can obstruct views and hinder outdoor activities, necessitating regular pruning and maintenance.In conclusion, the emergence of spring leaves heralds a season of renewal, growth, and optimism. Beyond their aesthetic beauty, these leaves embody the resilience andvitality of nature, offering ecological, cultural, and emotional significance. As we revel in the lush greenery of spring, let us pause to appreciate the profound symbolism encapsulated in each delicate leaf.。

比较两个运动的英语范文English Answer:Comparison of Swimming and Cycling.Swimming and cycling are both excellent forms of exercise that can provide a variety of health benefits. Both activities are low-impact, which makes them ideal for people of all fitness levels. They also both require a high degree of coordination and skill, which can help to improve overall fitness and balance.However, there are also some key differences between swimming and cycling. One of the most obvious differencesis the environment in which each activity takes place. Swimming is an aquatic activity, while cycling is a land-based activity. This difference can have a significant impact on the experience of each activity. For example, swimming can be a more refreshing and invigorating way to cool down on a hot day, while cycling can be a more scenicand enjoyable way to explore a new area.Another key difference between swimming and cycling is the amount of equipment required. Swimming requires a swimsuit and goggles, while cycling requires a bicycle, helmet, and appropriate clothing. The cost of the equipment can also vary significantly, with bicycles typically being more expensive than swimsuits and goggles.Finally, swimming and cycling have different impacts on the body. Swimming is a full-body workout that engages allof the major muscle groups. Cycling, on the other hand, isa more focused workout that primarily targets the legs. Asa result, swimming can be a more effective way to improve overall fitness and strength, while cycling can be a more efficient way to burn calories and lose weight.Chinese Answer:游泳和骑自行车比较。

比较两个运动的英语范文Sports are an integral part of human culture and have been a source of entertainment, physical fitness, and competition for centuries. Among the myriad of sports available, two that have captured the attention of millions worldwide are basketball and soccer. These two sports offer distinct experiences, each with its own unique characteristics, and a comparison between them can provide valuable insights.Basketball, a quintessential American sport, has gained global popularity over the years. The game is characterized by its fast-paced action, dynamic ball handling, and the thrilling moments when players soar through the air to dunk the ball through the hoop. The sport requires a combination of agility, coordination, and strategic thinking, as players must navigate the court, make split-second decisions, and effectively work as a team to score points.One of the most captivating aspects of basketball is the level of athleticism displayed by the players. Elite basketball players possess incredible leaping ability, allowing them to perform awe-inspiringdunks that seem to defy gravity. The constant back-and-forth nature of the game, with players alternating between offense and defense, creates a high-intensity atmosphere that keeps spectators on the edge of their seats.Moreover, basketball has a rich cultural heritage, particularly in the United States, where the sport has become deeply ingrained in the fabric of society. From the playgrounds of urban neighborhoods to the prestigious college and professional leagues, basketball has fostered a sense of community and provided opportunities for individuals from diverse backgrounds to showcase their talents and achieve success.In contrast, soccer, also known as football in many parts of the world, is a sport that has captivated global audiences for centuries. The game is characterized by its emphasis on teamwork, precision, and the skill of controlling and maneuvering the ball with the feet. Unlike basketball, where players primarily use their hands, soccer players must develop exceptional ball control, passing, and shooting abilities using only their feet, creating a unique and captivating style of play.One of the most compelling aspects of soccer is the strategic depth of the game. Effective team coordination, tactical awareness, and the ability to read the flow of the game are essential for success. Players must constantly adapt to the changing dynamics of the field, makingsplit-second decisions that can determine the outcome of a match.Furthermore, soccer has a global reach that surpasses that of basketball. The sport is played and followed by millions of people across the world, transcending cultural and geographical boundaries. Major international tournaments, such as the FIFA World Cup, have become events of immense significance, capturing the attention of billions of viewers and fostering a sense of national pride and unity.While both basketball and soccer share the common thread of being team sports that require physical prowess, athleticism, and strategic thinking, the distinct differences between the two offer unique experiences for both players and spectators. Basketball's fast-paced, high-scoring action and the spectacular displays of individual skill captivate audiences, while soccer's emphasis on teamwork, tactical nuance, and its global reach make it a truly universal sport.Ultimately, the choice between these two sports often comes down to personal preference and the individual's appreciation for the specific attributes that each offers. Both basketball and soccer have the power to inspire, entertain, and unite people, showcasing the incredible diversity and richness of the world of sports.。

一．名词解释（每个4分）1 朊粒2 端粒3 钠钾泵4 操纵子5 内稳态6 生态演替7 孤雌生殖8 共质体途径二．填空（每空1分）1 自然界最小的细胞是2 细胞膜的脂类成分包括磷脂糖脂和3 神经元胞体中粗面内质网和游离核糖体组成的结构称为4 细胞呼吸产生的二氧化碳和消耗的氧气的分子比称为5 植物叶中光合作用的产物运输途径是6 植物细胞停止生长后所形成的细胞壁称为7 植物对光照和黑暗时间长短的反应称为8 C3途径中固定二氧化碳的受体是9 骨骼肌纤维两条Z线之间的一段肌原纤维称为10 与调节血钙有关的一对拮抗激素分别是降钙素和11 响尾蛇探测温血动物所处方位的感受器是12 鸟类体温调节中枢位于中枢神经系统的13 胚珠中的大孢子母细胞来自14 哺乳动物相当于囊胚阶段的胚胎称为15 在生物数量性状表达上，每个基因只有较小的一部分表型效应，这类基因称为16 cDNA的中文表述是17 mullis 等科学家发明的PCR其中文表述是18 限制性内切酶不能切开细菌本身DNA，是因为细菌DNA 的腺嘌呤和胞嘧啶19 细菌内形成的孢子称为20 生物种群在群落中的生活方式和在时间与空间上占有的地位称为三问答1 比较真核细胞和原核细胞的区别2 简述两栖动物的循环系统3 植物在登录之前需要具备的条件4 两侧对称以及三胚层的出现在动物进化史上的重要适应意义。

一名词解释1 核小体2 bread E3 havars hsys4 脊索5 世代交替6 假基因7 生态金字塔8 遗传漂变二判断（只判断）1 如果反应为放能反应，则是自发反应2 细菌转导过程导致基因丢失3 酶可用于细胞外4 光合作用前期，NADP＋的电子来自水。

５呼吸的三个过程是肺换气气体运输气体交换6细菌分泌抗体导致宿主产生抗原7ｃａｐｅａｓｅ２，６，９的功能是启动细胞凋亡8四膜虫实验证明ｒRNA的合成不需要酶9水和NADP＋为最初电子供体和电子受体10维生素A B可溶于水11肾单位的结构是肾小球，肾球囊肾小管12光敏色素是激素，可感受光周期变化13生态位越相似，越不易竞争14PCR实验证明合成ｒRNA不需要酶15物种形成中，前合子隔离较后合子隔离有较强的选择优势若干道用遗传学二大定律的计算题，如F1与隐性测交，结果为２：１：１由RNA 转变成DNA符合中心法则与ｈｆｒ有关的判断植物导管负责体内有机物的运输人剧烈运动，血氧曲线向右移动选择（单选）１哪种生物细胞膜不饱和脂肪酸含量最高ａ南极洲鱼ｂ热带仙人掌ｃ人ｄ热带动物２哪种蛋白无信号肽ａ糖酵解酶ｂ剩余选项为分泌或驻留蛋白３MHC是ａｃａｌｌHLAｉｎｈｕｍａｎｂｈｅｌｐｐｒｅｓｅｎｔａｎｔｉｇｅｎｔｏTｃｅｌｌｓｃａｌｌａｂｏｖｅａｒｅｒｉｇｈｔ４甲状腺作用机理ａ入核直接作用ｂ通过细胞表面受体介导的ｃａｍｐ途径５长日植物指选需最小长日照才开花（英文出题）６使小鼠长大选用ａ细胞衰老ｂ细胞凋亡ｃ加生长素７引起下列疾病的生物属于病毒的是ａ痢疾ｂ白喉ｃ破伤风ｄ乙肝８如果群体中基因型ａａ为４/10000，则群体中基因型Aａ为多少９如果25年为一代，群体中基因型ａａ将为原来一半需要多少代10关于操纵子的描述哪个不对11关于密码子的描述哪个不对12考察神经冲动传导方向（英文出题）13珊瑚属于什么动物（选腔肠）14氧气和二氧化碳在血液中运输的问题15植物在哪种条件下可以正常生长ａ高水ｂ高盐ｃ高风（英文出题）四简答１无籽西瓜育成原理２ｓｙｎａｐｓｅｓｔｒｕｃｔｕｒｅ３转导的几种方式比较４把叶绿体和线粒体分别放在培养皿中，其ｐｈ值怎么变化５动植物感受光机制的比较６动植物和单细胞生物细胞怎么进行渗透调节７有关联会的问题８植物在这些条件下，其蒸腾速率各自将怎样变化ａｈｉｇｈｓａｌｔｂｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｃｈｉｇｈｃｏ２ｄｅｎｓｉｔｙｄｓｔｒｏｎｇｗｉｎｄｅｈｉｇｈｗａｔｅｒ五问答１题必答，２．３题选一道１比较ｃ３ｃ４植物在结构环境适应性对ｃｏ２的吸收，生理特点的异同，举出代表植物２比较真体腔假体腔混合体腔的异同３从进化角度比较脊椎动物各门心脏的结构一名词解释（每个３分，10个）抗原决定簇双受精细胞呼吸反射弧脊索建立者效应生态金字塔等二判断（每个１分，１０个）三选择（每个2分，25个）四填空（每空1分，２０分）１栉蚕属于纲海豆牙属于门２动物细胞最主要的三种细胞连接方式３动物激素的三种主要传递方式为４有关基因频率的计算题５胚珠是由（三个空）部分组成的６尼氏体是由（两个空）组成的五论述题（４０分）１肾单位的结构和功能（１５分）２光敏色素和光周期的机制以及对花开的影响（１５分）３分析鸟类的呼吸系统结构特点，说明为什么鸟类的气体交换效率比哺乳的高（１０分）一名词解释管家基因细胞全能性体液肾单位薄壁组织根压微观进化遗传漂变生物进化分子钟生态因子二选择题１向日葵的管状花的雄蕊群属于ａ聚药雄蕊ｂ单体雄蕊ｃ两体雄蕊ｄ多体雄蕊２鸟类的呼吸系统除了肺以外，还具有一种特殊的气囊，下列对这种气囊的描述不正确的是ａ气囊壁上有丰富的血液供应，可以进行气体交换ｂ气囊与支气管和肺相通ｃ气囊能储存新鲜空气ｄ气囊可以深入到体腔各部分３下列哪一种不属于合子前生殖隔离的范畴ａ群体生活在同一地区的不同栖息地，因此彼此不能相通ｂ杂种合子不能发育或不能达到性成熟阶段ｃ花粉在柱头上无生活力ｄ植物的盛花期的时间不同４类固醇类激素ａ通过第二信使发挥作用ｂ可以扩散进入细胞ｃ其特异性。

Evaluation of Cyclic Softening in Silts and ClaysRoss W.Boulanger,M.ASCE 1;and I.M.Idriss,F.ASCE 2Abstract:Procedures are presented for evaluating the potential for cyclic softening ͑i.e.,onset of significant strains or strength loss ͒in saturated silts and clays during earthquakes.The recommended procedures are applicable for fine-grained soils with sufficient plasticity that they would be characterized as behaving more fundamentally like clays in undrained monotonic or cyclic loading.The procedures are presented in a form that is similar to that used in semiempirical liquefaction procedures.Expressions are developed for a static shear stress correction factor and a magnitude scaling factor.Guidelines and empirical relations are presented for determining cyclic resistance ratios based on different approaches to characterizing fine-grained soil deposits.The potential consequences of cyclic softening,and the major variables affecting such consequences,are discussed.Application of these procedures is demonstrated through the analysis of the Carrefour Shopping Center case history from the 1999Kocaeli earthquake.The proposed procedures,in conjunction with associated liquefaction susceptibility criteria,provide an improved means for distinguishing between the conditions that do and those that do not lead to ground deformations in fine-grained soil deposits during earthquakes.DOI:10.1061/͑ASCE ͒1090-0241͑2007͒133:6͑641͒CE Database subject headings:Silts;Clays;Fine-grained soils;Liquefaction;Earthquakes;Cyclic strength;Soil strength .IntroductionThe first step in evaluating the potential for ground failure in silts or clays during strong earthquake shaking is to determine the dominant behavioral characteristics of the soil,and select the en-gineering procedures that are most appropriate for evaluating its behavior during cyclic undrained loading.Boulanger and Idriss ͑2006͒showed that the monotonic and cyclic undrained loading behavior of low-plasticity silts and clays transitions from being more fundamentally like sands to more fundamentally like clays over a relatively narrow range of plasticity indices ͑PI ͒.For fine-grained soils that behave more fundamentally like clays,the cy-clic and monotonic undrained shear strengths are closely related and show relatively unique stress-history-normalized behaviors.Their cyclic strengths can be estimated based on in situ testing,laboratory testing,and empirical correlations that build upon es-tablished procedures for evaluating the monotonic undrained shear strength of such soils.For fine-grained soils that behave more fundamentally like sands,the cyclic strengths may be more appropriately estimated within the framework of existing standard penetration test ͑SPT ͒and cone penetration test ͑CPT ͒based liq-uefaction correlations.Boulanger and Idriss ͑2006͒recommended that,for practical purposes,fine-grained soils can be expected to exhibit claylike behavior if they have PI Ն7.If a soil plots as CL-ML,the PI criterion may be reduced to PI Ն5and still beconsistent with the available data.Fine-grained soils that fail to meet these criteria should be considered as likely exhibiting sand-like behavior ͑i.e.,liquefiable ͒,unless shown otherwise through appropriate in situ and laboratory testing.This paper presents procedures for evaluating the potential for cyclic softening in claylike fine-grained soils during earthquakes.These procedures are developed in a form similar to that used in semiempirical liquefaction procedures,thereby facilitating paral-lel calculations and direct comparisons of results.The paper is organized as follows.Terminology for representing cyclic stresses and strengths is briefly reviewed,followed by the development of relations between cyclic strengths and monotonic undrained shear strengths for claylike fine-grained soils.This latter step includes developing expressions for a magnitude scaling factor ͑MSF ͒and static shear stress correction factor ͑K ␣͒for claylike soils.Proce-dures are then presented for estimating cyclic strengths in the field based on laboratory tests,in situ tests,and empirical corre-lations.Consequences of cyclic softening and the factors affecting their severity are discussed.The application of these procedures and the associated liquefaction susceptibility criteria are demon-strated for the Carrefour Shopping Center case history from the 1999Kocaeli earthquake ͑Martin et al.2004͒.The results show that the recommended liquefaction susceptibility criteria and the cyclic softening analysis procedures provide an improved means for distinguishing between the conditions that do and those that do not lead to ground deformations in these types of soils.Addi-tional findings and implications for engineering practice are also discussed.Cyclic Stress and Cyclic Resistance RatiosCyclic stresses and strengths are normalized by vertical effective consolidation stress ͑␴v c Ј͒in semiempirical liquefaction proce-dures.The peak cyclic stress ratio ͑CSR peak ͒induced by vertical propagation of shear waves in a level site during earthquake shak-ing is computed as1Professor,Dept.of Civil and Environmental Engineering,Univ.of California,Davis,CA 95616.2Professor Emeritus,Dept.of Civil and Environmental Engineering,Univ.of California,Davis,CA 95616.Note.Discussion open until November 1,2007.Separate discussions must be submitted for individual papers.To extend the closing date by one month,a written request must be filed with the ASCE Managing Editor.The manuscript for this paper was submitted for review and pos-sible publication on September 2,2005;approved on November 29,2006.This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering ,V ol.133,No.6,June 1,2007.©ASCE,ISSN 1090-0241/2007/6-641–652/$25.00.JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ©ASCE /JUNE 2007/641D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U n i v e r s i t y o f L i v e r p o o l o n 10/19/15. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .CSR peak =␶peak␴vcЈ͑1͒where ␶peak is the peak horizontal cyclic shear stress.The CSR peakis then scaled by a factor r e to produce a CSR M that is considered representative of the most significant cycles over the full duration of loading for a given magnitude earthquakeCSR M =r e␶peak ␴vcЈ͑2͒where r e =0.65has been widely used for liquefaction analyses.The cyclic resistance ratio ͑CRR ͒is the CSR value required to cause “failure”by some criterion in the appropriate number of equivalent loading cycles.Procedures for describing the earthquake-induced CSR and a soil’s CRR are interrelated through the soil’s cyclic loading behavior,as illustrated in the following sections.Relating Cyclic Strengths to Undrained Shear StrengthThe cyclic strength of claylike fine-grained soils can also be ex-pressed as a ratio of the soil’s undrained shear strength ͑s u ͒,with the results falling in a relatively narrow range for a variety of soils.This is illustrated in Fig.1,showing the ratio of cyclic shear stress to undrained shear strength ͓␶cyc /s u for direct simple shear ͑DSS ͒tests and q cyc /2s u for triaxial ͑TX ͒tests ͔versus the numberof uniform loading cycles ͑N ͒to failure ͑taken as 3%peak shear strain,or a comparable criterion if data is presented in other forms,such as peak–peak strains ͒for six natural soils having overconsolidation ratios ͑OCR ͒ranging from 1to 4and two tail-ing materials that were normally consolidated ͑OCR=1͒.The characteristics of these soils and two compacted soils are summa-rized in Table 1,including representative Atterberg Limits,the type of cyclic tests performed ͑DSS versus TX ͒,the as-tested OCR,the undrained shear strength ratio ͑s u /␴vc Ј͒when normally consolidated ͑OCR=1͒,the cyclic strength ratios ͑␶cyc /s u ͒re-quired to trigger peak shear strains of approximately 3%in 15and 30uniform cycles of undrained loading,and the ␶cyc /␴vc Јratios required to trigger peak shear strains of approximately 3%in 15and 30uniform cycles of undrained loading when normally con-solidated ͑OCR=1͒.The TX test data for the compacted clays by Seed and Chan ͑1966͒and the DSS test data for the thin-walled tube samples of the natural “CWOC”silt by Woodward-Clyde ͑1992͒do not include data for normally consolidated conditions.The ␶cyc /s u ratios have all been adjusted to an equivalent uniform cyclic loading frequency of 1Hz to be more representative of earthquake loading,based on the observation that cyclic strengths increase about 9%per log cycle of loading rate ͑e.g.,Zergoun and Vaid 1994;Lefebvre and Pfendler 1996͒.The influence of loading rate is why the ␶cyc /s u ratios exceed unity for failure in one load-ing cycle,since the reference value of s u is for conventional monotonic loading rates that are much slower.The CRR of claylike fine-grained soil,for a given magnitude earthquake,can be estimated using the expressionCRR M =C 2Dͩ␶cyc s uͪM =7.5s u␴vcЈMSF K ␣͑3͒where C 2D is a correction for two-dimensional versus one-dimensional cyclic loading,͑␶cyc /s u ͒M =7.5is the ratio of cyclicstress to s u for the number of equivalent uniform cycles represen-tative of an M w =7.5earthquake ͑chosen as the reference magni-tude ͒,MSF is the magnitude scaling factor to approximately account for the correlation between earthquake magnitude and number of equivalent uniform loading cycles,and K ␣is the static shear stress ratio correction factor to approximately account for the effect that sloping ground ͑or initial shear stress ͒has on cyclic strength.Development of the MSF and K ␣relations for claylike fine-grained soils is described in the next two sections,after which the approaches for estimating CRR M in the field are presented.Number of Loading Cycles and Magnitude Scaling FactorThe conversion of irregular cyclic stress time series to an equiva-lent uniform cyclic loading was performed using the approach by Seed et al.͑1975͒.The relation between the CRR ͑liquefaction for sandlike soils,cyclic softening for claylike soils ͒and the number of uniform stress cycles ͑N ͒is approximated using the formCRR =aN −b͑4͒where b =0.337for clean sand ͑e.g.,Idriss and Boulanger 2006͒and b =0.135for clay based on the average of the direct simple shear test results summarized in Table 1.The relative number of cycles to cause failure at two different cyclic stress ratios,CSR A and CSR B ,can be obtained using Eq.͑4͒asFig.1.Cyclic strength ratios to cause cyclic failure versus number of uniform loading cycles at a frequency of 1Hz:͑a ͒natural soils;͑b ͒tailings materials642/JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ©ASCE /JUNE 2007D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U n i v e r s i t y o f L i v e r p o o l o n 10/19/15. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .N A N B =ͩCRR B CRR Aͪ1/b͑5͒Eq.͑5͒can be used to convert an individual cycle at some stresslevel to an equivalent number of cycles at a different stress level,by assuming that the “damage”is equal for both cases if the numbers of cycles are an equal fraction of the respective number of cycles to failure.The number of equivalent uniform loading cycles for M w =7.5and its dependence on r e was evaluated using a set of 124horizontal acceleration time series recorded at NEHRP class D soil sites in 13different earthquakes with M w between 7and 8.For r e =0.65,N clay was generally one to three times N sand ,with the ratio N clay /N sand decreasing with increasing N sand ͑Fig.2͒.At N sand =15,which was the value derived by Seed et al.͑1975͒for sand for M w =7.5and r e =0.65,the geometric mean of N clay /N sand was 1.93͑Fig.2͒and the corresponding value of N clay was 29.The geometric means of N sand and N clay for M w =7.5and r e =0.65determined directly from the set of time series used in this study were slightly larger at 17and 32,respectively.The value of N clay for M w =7.5and r e =0.65was subsequently taken as equal to 30.The variation of N with r e for both sandlike and claylike soils at a single earthquake magnitude ͑M w =7.5͒is shown in Fig.3.This figure illustrates that when r e is less than about 0.75,thesmaller b value for clay results in a larger number of equivalent uniform loading cycles than for sand.In contrast,if the reference stress was instead defined by r e values greater than about 0.75,then the number of equivalent uniform loading cycles would be smaller for clay than for sand.In addition,Liu et al.͑2001͒and Green and Terri ͑2005͒have shown that the number of equivalentTable 1.Normalized Cyclic Strength Ratios for Various Claylike SoilsSoil name͑Reference source ͒PI LL USCS aTest type bOCR ͑s u /␴vc Ј͒for OCR=1Parameterb e For 15uniform cycles fFor 30uniform cycles f͑␶cyc /s u ͒N =15͑␶cyc /␴vc Ј͒N =15for OCR=1͑␶cyc /s u ͒N =30͑␶cyc /␴vc Ј͒N =30for OCR=1Drammen clay͑Andersen et al.1988͒2755CHDSS10.2140.1160.940.2010.870.18640.750.69Boston Blue clay ͑Azzouz et al.1989͒2144CL DSS 10.2050.1490.920.1890.830.1701.380.920.8320.920.83Cloverdale clay͑Zergoun and Vaid 1994͒2450CL-CH TX 10.2800.1290.880.2460.800.224St.Alban clay͑Lefebvre and Pfendler 1996͒2041CL DSS 2.20.248c 0.129 1.010.2500.920.228Itsukaichi clay͑Hyodo et al.1994͒73124MH TX 10.3900.0950.920.3590.870.339Copper tailings slime ͑Moriwaki et al.1982͒1335CLTX 10.4040.1370.640.2600.580.234DSS 10.2410.1490.800.1930.720.174Aggregate tailings slime ͑Romero 1995͒101/236.5ML TX10.3400.0730.680.2310.6480.220Compacted silty clay ͑Seed and Chan 1966͒1437CL TX n.a.n.a.n.a.n.a.n.a. pacted sandy clay ͑Seed and Chan 1966͒1635CL TX n.a.n.a.n.a.n.a.n.a. 1.00n.a.CWOC silt ͑Woodward-Clyde 1992͒1042ML DSS Ϸ2n.a.dn.a.0.77n.a.0.71n.a.Note n.a.ϭnot available.aUnified Soil Classification System.bDSS is direct simple shear,TX is triaxial.For TX tests,s u =q peak /2and ␶cyc =q cyc /2.cFor St.Alban clay,the reported s u /␴vp Јratio is used for the value of s u /␴vc Јat OCR=1;␴vp Јϭvertical preconsolidation stress.dFor CWOC silt,samples were reconsolidated to their in situ overburden stresses.eFitting parameters are for ͑␶cyc /s u ͒=aN −b ,with N ϭnumber of loading cycles.fAll cyclic strength data are based on a peak shear strain of approximately 3%and are adjusted to equivalent 1Hzloading.Fig.2.Ratio of N clay to N sand for NEHRP class D soil sites,M w of 7to 8,and r e =0.65JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ©ASCE /JUNE 2007/643D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U n i v e r s i t y o f L i v e r p o o l o n 10/19/15. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .uniform cycles for sand depends on the earthquake magnitude,distance to the earthquake source,and other factors.These addi-tional refinements would,however,be less important for clay than for sand because clay has a smaller b value.The MSF relation for clay was derived using the form and procedure used by Idriss ͑1999͒for sand.The resulting expression for clayMSF =1.12expͩ−M w4ͪ+0.828͑6͒is compared to that for sand in Fig.4.The MSF value for sand is capped at MSF=1.8for M w Յ5.25,due to the fact that even the smallest magnitude earthquakes have at least one peak cycle of stress.Similarly,the MSF value for clay is capped at MSF =1.13for M w Յ5.25.The MSF cap is lower for clay because the CRR-N relation is much flatter for clay than for sand ͑i.e.,a large change in number of loading cycles has a smaller effect on the cyclic strength for clay ͒.Additional details on the MSF derivation and equivalent number of uniform loading cycle calculations are given in Boulanger and Idriss ͑2004͒.Effect of Static Shear Stresses on Cyclic StrengthSeed ͑1983͒introduced the K ␣correction factor to represent the effects of an initial static shear stress ratio ͑␣͒on the liquefaction resistance of sands.K ␣relations have been obtained from labora-tory studies usingK ␣=͑CRR ͒␣͑CRR ͒␣=0͑7͒which is simply the CRR at some value of ␣,divided by the CRR at ␣=0.The term ␣is the initial static shear stress divided by the effective normal consolidation stress on the plane of interest.For application to field conditions,reference is usually made to hori-zontal planes such that␣=␶s ␴vcЈ͑8͒where ␶s is the horizontal static shear stress.A K ␣factor for claylike soils can similarly be developed from laboratory test data,beginning with a plot of K ␣versus ␶s /͑s u ͒␣=0instead of K ␣versus ␣.Results are shown in Fig.5for tests on Drammen clay ͑OCR of 1and 4;Goulois et al.1985;Andersen et al.1988͒and St.Alban clay ͑OCR of 2.2;Lefebvre and Pfendler 1996͒.This figure was generated for 10uniform loading cycles to cause 3%peak shear strain ͑not including strains induced by the static shear stresses ͒,which required interpolation of the pub-lished data in some cases.The number of loading cycles has a relatively small effect on these K ␣versus ␶s /͑s u ͒␣=0relations,whereas a larger shear strain failure criterion will stretch these relations to the right.For example,using 15%shear strain as the failure criterion stretches the curves for Drammen clay to the right by roughly 15to 25%.The K ␣values are also slightly de-pendent on whether or not the clay was allowed to consolidate under the sustained static shear stress.This is illustrated by the results for Drammen clay in Fig.5,where the K ␣values are lower for those tests that did not allow consolidation under the sustained static shear stress compared to those tests that did allow consoli-dation under the static shear stress.This difference in behavior reflects the fact that the undrained shear strength of clay generally increases when it is consolidated under a sustained static shear stress ͑e.g.,Ladd 1991͒.The tests on St.Alban clay ͑at an OCR of 2.2͒did not allow consolidation under the sustained static shear stress,but the resulting K ␣values are slightly higher than those for the Drammen clay with consolidation under the staticshearFig.3.Number of equivalent uniform stress cycles ͑N ͒versus the ratio of uniform stress to peak stress ͑r e ͒for M w =7.5earthquakes for sand andclayFig.4.Magnitude scaling factor for converting a cyclic stress ratio tothe equivalent cyclic stress ratio for an M w =7.5earthquakeFig.5.K ␣versus ␶s /͑s u ͒␣=0for clay644/JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ©ASCE /JUNE 2007D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U n i v e r s i t y o f L i v e r p o o l o n 10/19/15. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .stress.Despite these various influencing factors,the data in Fig.5fall within a relatively narrow band,particularly for ␶s /͑s u ͒␣=0less than about 0.5.The K ␣results for the Drammen clay with consolidation under the initial static shear stress were used to fit a design relation because:͑1͒Most design situations would assume that the clay-like soils had sufficient time to consolidate under the sustained loading of some structure or embankment prior to the occurrence of the seismic design event,and ͑2͒these results are reasonably representative of the overall data set.The following expressionK ␣=1.344−0.344ͩ1−␶s s uͪ0.638͑9͒closely approximates these Drammen clay results.These specific results were for normally consolidated clay,but the data by Andersen et al.͑1988͒for tests without consolidation under the initial static shear stress showed similar relationships for OCR of 1,4,and 40͑for clarity,Fig.5only shows results for OCR of 1and 4͒.Consequently,it is assumed that Eq.͑9͒can reasonably be applied over a range of OCR.The above expression for K ␣can also be recast as a function of the initial static shear stress ratio ͑␣͒as used for sands.This is accomplished by dividing both the numerator and denominator of the ␶s /s u term by ␴vc Ј,and then replacing the resulting s u /␴vc Јterm with an appropriate empirical relation ͑e.g.,Ladd 1991͒as follows:␶s s u =␶s s u 1/␴vcЈ1/␴vc Ј=␣s u /␴vcЈ=␣0.22·OCR 0.8͑10͒which then produces the expressionK ␣=1.344−0.344ͩ1−␣0.22·OCR 0.8ͪ0.638͑11͒Eq.͑11͒may be used where an estimate of ␣can be more readily made and it enables a direct comparison of K ␣relations for clay-like and sandlike soils.The K ␣versus ␣relation for claylike soils,computed using Eq.͑11͒,is plotted in Fig.6for OCR of 1,2,4,and 8.The K ␣values are lowest for normally consolidated soils and increase with increasing OCR at a given value of ␣.These curves show that the cyclic strength of normally consolidated clays may be negligible if they are already sustaining a static shear stress that isclose to their undrained shear strength.Conversely,the cyclic strength of an OCR=8clay is only reduced slightly by an ␣as high as 0.30.Sands show a similar pattern ͑e.g.,Boulanger 2003͒,in that K ␣values are lowest for the most contractive sands ͑e.g.,loose of critical state ͒and increase with increasing relative den-sity ͑which reduces the tendency for contraction in shear,just like increasing OCR reduces the tendency for claylike soils to contract in shear ͒.Thus,the results for both claylike and sandlike soils show that the effect of an initial static shear stress on cyclic strength is most detrimental when a soil is most contractive.Estimating Cyclic Resistance Ratio of Claylike SoilsThe CRR of claylike fine-grained soils in the field can be esti-mated using three different approaches:͑1͒directly measure the CRR by cyclic laboratory testing;͑2͒empirically estimate CRR based on the undrained shear strength profile;and ͑3͒empirically estimate CRR based on the consolidation stress history profile.The direct measurement of CRR in the first approach provides the highest level of insight and confidence,while the second and third approaches use empirical approximations to gain economy.These different options provide the opportunity to evaluate a site with progressively increasing levels of confidence,while consid-ering the potential benefits that additional information may pro-vide given the uncertainties in the current level of analysis.The successful application of all three approaches requires careful at-tention to the various techniques and issues involved in obtaining field samples,performing laboratory tests,performing in situ tests,and interpreting the combined data sets,as described in Ladd ͑1991͒and Ladd and DeGroot ͑2003͒for example.The following two sections focus on the development of the empirical relations required for the second and third approaches.Empirically Estimating Cyclic Resistance Ratio Based on the Undrained Shear Strength ProfileCyclic strength ratios ͑␶cyc /s u ͒for N =30cycles ͑i.e.,M w =7.5͒are plotted against PI in Fig.7͑a ͒for the soils summarized in Table 1.The different types of soils and test conditions are highlighted in this figure,from which the following observations can be made:•The tailing slimes gave the lowest ratios of ␶cyc /s u ,perhaps being about 20%lower than the natural silts and clays.The tailing slimes data cover a lower range of PIs ͑10.5–13͒than the natural silts and clays ͑10–73͒and are much younger ͓hours in the case of the tests by Romero ͑1995͔͒than the natural silts and clays.Consequently,it is not clear how much of this difference in ␶cyc /s u ratios is due to differences in PI or age.•The compacted silty clay and compacted sandy clay by Seed and Chan ͑1966͒gave the highest ratios of ␶cyc /s u .These specimens were partially saturated and tested in unconsolidated–undrained conditions,such that their state of effective stress was not known.•The triaxial and DSS tests gave comparable ␶cyc /s u ratios for the natural silts and clays,while the triaxial tests on tailing slimes appeared to give ␶cyc /s u ratios that were about 15–20%lower than obtained in DSS tests on tailing slimes.The data in Fig.7͑a ͒are insufficient to define the various factors that may affect the ␶cyc /s u ratio,such as age,PI,soil type,OCR,and test type.Despite these limitations,the data for natural soils do tend to fall within relatively narrow ranges.It is suggested that the ͑␶cyc /s u ͒N =30ratio be taken as 0.83for natural claylikesoilsFig.6.K ␣versus ␣for clay at various OCRJOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ©ASCE /JUNE 2007/645D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U n i v e r s i t y o f L i v e r p o o l o n 10/19/15. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .subjected to DSS loading conditions,with due recognition that the continued compilation of laboratory test data can lead to fu-ture refinements in this estimate.The ͑␶cyc /s u ͒N =30ratios in Fig.7͑a ͒are based on s u values determined at standard loading rates for monotonic CU ͑consoli-dated undrained ͒laboratory tests.Conceptually,these ratios may be adjusted whenever the s u value pertains to a significantly dif-ferent loading rate.For example,corrected vane shear strengths correspond to the long-term strain rate in the field ͑through the empirical VST correction factor ͒which is considerably slower than the standard strain rate in CU laboratory tests.Unconsoli-dated undrained ͑UU ͒triaxial tests use a much higher loading rate than is used for CU tests,but any systematic effects of loading rate are obscured by the more significant effects of sampling dis-turbance and the variable extent to which sampling disturbance manifests itself in CU versus UU tests.In most situations,an additional correction for different s u loading rates will be small relative to the uncertainties that arise from the natural soil hetero-geneity,limitations in laboratory and in situ test results,and limi-tations in the various empirical relations that may be used ͑e.g.,the vane shear correction factor,or the ͑␶cyc /s u ͒N =30ratio from Fig.7͑a ͒͒.While future studies may provide improved guidance on this issue,such a refinement does not seem warranted at this time.Experimental data on the effects of two-directional cyclic loading on the CRR of saturated sands was reviewed by Seed ͑1979͒,who recommended that the CRR for two-dimensional shaking could be estimated as 0.9times the CRR for one-dimensional cyclic loading ͓i.e.,C 2D in Eq.͑3͔͒.Similar experi-mental data are not available for clays,but Boulanger and Idriss ͑2004͒estimated C 2D to be about 0.96based on assuming that theeffect of two-dimensional shaking was comparable to having extra loading cycles under one-dimensional shaking.This C 2D estimate is consistent with the expectation that the reduction for two-dimensional shaking will be less significant for clays than for sands,because clays have a flatter CRR versus N relation.The CRR M =7.5for natural deposits of claylike fine-grained soils can then be estimated asCRR M =7.5=0.96·0.83s u␴vcЈK ␣͑12͒CRR M =7.5=0.8s u␴vcЈK ␣͑13͒For tailing slimes,the above estimate of CRR should tentativelybe reduced by about 20%as suggested by the data in Fig.7͑a ͒.In many situations,the uncertainty in the s u profiles will be greater than the uncertainty in the ͑␶cyc /s u ͒N =30ratio.For those cases where the uncertainty in the ͑␶cyc /s u ͒N =30ratio is important,a detailed cyclic laboratory testing program could be beneficial.Empirically Estimating Cyclic Resistance Ratio Based on the Consolidation Stress History ProfileCyclic strengths may be similarly computed from empirical s u relations in conjunction with an established consolidation stress history profile.The undrained shear strength,s u ,can be related to ␴vc Јand OCR as ͑Ladd and Foott 1974͒s u␴vcЈ=S ·OCR m ͑14͒The CRR M =7.5can then be estimated by combining Eqs.͑13͒and ͑14͒to arrive atCRR M =7.5=0.8·S ·OCR m ·K ␣͑15͒An accurate assessment of the stress history ͑i.e.,OCR ͒is gener-ally the most important step in estimating s u by Eq.͑14͒.For this reason,the parameters m and S are sometimes estimated empiri-cally while engineering efforts focus on the stress history of a site.For homogenous,low-and high-plasticity,sedimentary clays ͑CL and CH ͒,the simplest representation may be the use of S =0.22and m =0.8͑Ladd 1991͒,which are the values that were used to develop Eq.͑11͒.Thus,the CRR may be estimated asCRR M =7.5=0.18·OCR 0.8·K ␣͑16͒This empirical expression emphasizes the importance of stress history and initial static shear stress in determining the cyclic behavior of clay.Values of ͑␶cyc /␴vc Ј͒N =30for the normally consolidated soils in Table 1are plotted versus PI in Fig.7͑b ͒and compared to the value adopted in Eq.͑16͒.The following observations can be made from this figure:•The tailing slimes had similar ͑␶cyc /␴vc Ј͒N =30values to those for the natural clays,despite their differences in PI and age.•The cyclic DSS tests appear to give ͑␶cyc /␴vc Ј͒N =30values that are about 20%smaller than those obtained in cyclic TX tests.As noted in Table 1,the cyclic shear stresses for TX tests were computed based on maximum shear stresses;i.e.,␶cyc =q cyc /2.If the cyclic shear stresses were instead computed for the eventual failure plane as ␶cyc =͑q cyc /2͒cos ͑␾Ј͒,then the ͑␶cyc /␴vc Ј͒N =30values for TX tests would have been about 15%smaller ͑assuming ␾ЈϷ32°͒and the difference between the DSS and TX test results in Fig.7͑b ͒would have beenveryFig.7.Cyclic strengths versus plasticity index for claylikefine-grained soils and proposed relations for design:͑a ͒͑␶cyc /s u ͒N =30;͑b ͒͑␶cyc /␴vc Ј͒N =30for normally consolidated soils646/JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ©ASCE /JUNE 2007D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U n i v e r s i t y o f L i v e r p o o l o n 10/19/15. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .。