Strength,Modulus of Elasticity,and Brittleness Index of
Rubberized Concrete
L.Zheng 1;X.Sharon Huo 2;and Y .Yuan 3
Abstract:This paper presents a study of rubberized concretes designed by replacing coarse aggregate in normal concrete with ground and crushed scrap tire rubber in various volume ratios.The objective of the study was to investigate the effect of rubber types and rubber content on strength and deformation properties.The compressive strength,static,and dynamic modulus of elasticity of rubberized concrete were tested and studied.The stress-strain hysteresis loops were obtained by loading,unloading,and reloading on specimens.Brittleness index values were calculated based on the hysteretic loops.The experiments revealed that strength and modulus elasticity of rubberized concrete decreased with the increasing amount of rubber https://www.doczj.com/doc/906583573.html,pressive strength and modulus of elasticity of crushed rubberized concrete were lower than that of ground rubberized concrete.An American Concrete Institute equation could reasonably predict modulus of elasticity of rubberized concrete.Brittleness index values of rubberized concrete were lower than that of normal concrete,which means that rubberized concrete had higher ductility performance than that of normal concrete.DOI:10.1061/?ASCE ?0899-1561?2008?20:11?692?
CE Database subject headings:Concrete;Recycling;Aggregates;Toughness;Brittleness;Waste management;Elasticity;Ultrasonic methods .
Introduction
Solid waste disposal is a major environmental issue for cities around the world.American motorists discard approximately 290million tires each year,which is approximately one tire for every person in the United States.Around 16million of these tires are retreated or reused,leaving roughly 274million scrap tires to be managed annually.In 2003,the total numbers of scrap tires going to market was about 233million.About 40million scrap tires are estimated to be disposed of in land?lls.In addition,275million tires that have accumulated over the years are currently stockpiled throughout the United States ?Rubber Manufacturers Association 2004?.These stockpiles are dangerous not only due to potential environmental threat but also from ?re hazards and they provide breeding grounds for rats,mice,and mosquitoes.Because of rapid depletion of available sites for waste disposal,disposing of waste tires in land?lls is becoming unacceptable.Over the years,dis-posal of waste tires has become one of the serious problems for the environment.Innovative solutions to solve the tire disposal problem have long been in development.
Cement-based concrete is a brittle material in general and is of
high rigidity.In some applications such as foundation pads and traf?c barriers,it is desirable for concrete to have high toughness and good impact resistance.Although concrete is the most com-monly used construction material,it does not always ful?ll these requirements.It has been observed from previous research that the properties of concrete would change when used automobile-tire chips are added into concrete.Top?u ?1995?,Toutanji ?1996?,Eldin and Senouci ?1993?,and Top?u and Avcular ?1997?reported that adding rubber to traditional concrete could increase the de-formability or ductility of rubberized concrete members.Fattuhi and Clark ?1996?suggested various interesting applications where rubberized concrete could possibly be used.These include the following areas:?1?where vibration damping is required,such as in foundation pads for machinery and in railway stations;?2?where resistance to impact or explosion is required,such as in road traf?c barriers and railway buffers;and ?3?where high-strength requirement is not crucial,such as trench ?lling,pipe bedding,arti?cial reef construction,pile heads,and paving slabs.Making use of used tire chips as an addition to the concrete ma-trix may be an economical and ecological solution.
Nehdi and Khan ?2001?and Siddique and Naik ?2004?pre-sented comprehensive reviews on this topic.They mentioned that maximum size and grading of rubber granules used by researchers varied considerably.Khatib and Bayomy ?1999?developed a characteristic function to qualify the reduction in strength due to the addition of rubber.To improve the strength of rubberized concrete,Li et al.?2004?applied a pretreatment to rubber chips before mixing them into https://www.doczj.com/doc/906583573.html,ing the ?nite-element analy-sis method,Huang et al.?2004?did an evaluation on the effect of various design parameters such as maximum rubber chip size and stiffness of the coarse aggregate on the composite strength of rubberized concrete.Hernández-Olivares et al.?2002?investi-gated the dynamic characteristics of rubberized concrete material.Because of the unique elasticity properties of rubber material,the rubberized concrete showed potential advantages in reducing or
1Ph.D.Student,Dept.of Civil and Environmental Engineering,Tennessee Technological Univ.,1020Stadium Dr.,Prescott Hall 314,Cookeville,TN 38505.E-mail:lzheng21@https://www.doczj.com/doc/906583573.html, 2
Professor,Dept.of Civil and Environmental Engineering,Tennessee Technological Univ.,1020Stadium Dr.,Prescott Hall 216,Cookeville,TN 38505?corresponding author ?.E-mail:xhuo@https://www.doczj.com/doc/906583573.html, 3
Professor,School of Civil Engineering,Tongji Univ.,Shanghai 200092,China.E-mail:yuany@https://www.doczj.com/doc/906583573.html,
Note.Associate Editor:Byung Hwan Oh.Discussion open until April 1,2009.Separate discussions must be submitted for individual papers.The manuscript for this paper was submitted for review and possible publication on August 21,2006;approved on March 7,2008.This paper is part of the Journal of Materials in Civil Engineering ,V ol.20,No.11,November 1,2008.?ASCE,ISSN 0899-1561/2008/11-692–699/$25.00.
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minimizing vibration and impact effect.Although more and more reports gave evidence of the use of tire rubber in the past decade ?1990s ?,the study on rubberized concrete is still incomplete.Fur-ther research is still needed to optimize the percentage of rubber and particle-size distribution to achieve the desired properties of rubberized concrete.
For a material of high toughness,most of the total energy generated upon fracture is plastic,while for a brittle material,most of the total energy generated upon fracture is elastic.The energy that material absorbs until it is broken is plastic energy.It is desirable for concrete to have more ductility.This study was undertaken to examine how replacing part of the aggregate vol-ume with rubber would improve the ductile property of concrete.In this study,rubberized concrete was proportioned by replac-ing coarse aggregate in normal concrete with scrap tire rubber in various volume ratios and by using two typical sizes of rubber particles.Both cylinder compressive strength and cube compres-sive strength were tested.The relationship between the two strengths was studied.Cylinder specimens were used to get the static modulus of elasticity and the relationships between the static modulus of elasticity and compressive strength were inves-tigated.Cube specimens were used in this research to calculate the dynamic modulus of elasticity of rubberized concrete with the pulse velocity tests.Upon loading,unloading,and reloading on prepared cylinder specimens,the ???hysteresis loops were drawn and brittleness index values were calculated based on a typical hysteresis loop.The variation of brittleness index values was evaluated for different types of rubber particles and compres-sive strength.
The objectives of the research were to investigate:?1?the ef-fect of rubber types and rubber content on cylinder compressive strength,cube compressive strength,static modulus of elasticity,and dynamic modulus of elasticity;?2?the relationship between modulus of elasticity and compressive strength of rubberized con-crete;and ?3?the effect of rubber types and rubber content on the brittleness index of rubberized concretes and the relationship be-tween the brittleness index and compressive strength.
Principles of Analysis
Static Modulus of Elasticity and Dynamic Modulus of Elasticity
The modulus of elasticity is one of the most important elastic properties of concrete since it impacts the serviceability and per-formance of concrete structures.The elastic modulus of concrete is closely related to the property of the cement paste,the stiffness of the selected aggregates,and also the method of determining the modulus.
The static modulus of elasticity was tested and calculated by a method similar to that in ASTM C469?ASTM 2002b ?.The modulus was determined based on the slope between the two linear points on a stress-strain plot.The ?rst point is when longi-tudinal strain is 50millionths and the second point is that the applied load is equal to 40%of the ultimate load.
To determine the dynamic modulus of elasticity,velocities ?V p and V s ?of two kinds of ultrasonic wave,the longitudinal stress wave ?P wave ?and the transverse wave ?S wave ?,in rubberized concrete specimens were measured in this study.The P wave ?primary wave ?is a wave in which particles vibrate parallel to the direction of wave travel,while the S wave ?secondary wave ?is a wave in which particles vibrate perpendicular to the direction of
wave travel.The P wave travels with a higher velocity while the S wave travels somewhat more slowly.With measured V p and V s ,the dynamic modulus of elasticity E d can be calculated by Eq.?1?
E d =
?V s
2?3V p 2?4V s 2
??V p
2?V s 2?
?1?
where V p =elastic wave velocity of the P wave;V s =elastic wave
velocity of the S wave;and ?=density of material.Brittleness Index of Concrete
Top?u ?1997?used the stress-strain ?????hysteresis loops and the corresponding envelope line to evaluate the toughness of rub-berized concrete.???curves were established for repeated load-ing which was applied by loading,unloading,and reloading phases.When the load reached approximately 85%of the maxi-mum concrete carrying capacity,the loading was stopped.Brittle-ness index ?BI ?can be calculated according to energy measured from the areas under the ???curves.As seen in Fig.1,the A1area shows the irreversible plastic energy consumed during the failure and never recovered again ?plastic energy capacity ?;and the A2area shows the recovered deformation energy to be ob-tained just before fracture ?elastic energy capacity ?.BI of concrete specimens in compression is de?ned as the ratio of the elastic deformation energy to irreversible deformation energy,shown as A2/A1.When the ratio A2/A1approaches zero,all energies be-come irreversible,while when the ratio A2/A1goes to in?nity all energies become reversible.For brittle materials such as concrete,which has a larger elastic energy capacity than the plastic energy capacity,the BI value,in general,is higher compared to other ductile materials.The smaller the brittleness index value,the more ductile deformation the material has.Addition of rubber in concrete can reduce the brittleness index values and improve duc-tility of concrete,changing the concrete from brittle material to considerably ductile material.
Experiment Study Materials
A target strength of 30MPa was selected for rubberized concrete in the study because the strength value is commonly used in in-frastructural applications.To meet the target compressive strength,a control mixture with a compressive strength of 40MPa was selected.In developing rubberized concrete mix-tures,all mixture proportions were kept constant except for the coarse aggregate constituents,meaning that the ?ne aggregate ?sand ?,cement content,water-cement ratio,and admixture were
ε
Fig.1.De?nition of brittle index
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kept constant.Type I portland cement was used in all mixtures.Sand was river sand,which had 5mm maximum size and 2.5%moisture content.Crushed stone of 31.5mm maximum size was used as coarse aggregate.NF-5was applied as a water reduce admixture.Two groups of rubber were used in the study as shown in Fig.2.One group ?GR-8?is rubber powder of ground tires,as shown in Fig.2?a ?.GR-8represents ground rubber powder of 8-mesh,which means 80%of powder is smaller than the size of 2.6mm.The other group is crushed rubber or used tire chips ?CR-40?,shown in Fig.2?b ?.The surface of each chip is rough and jagged due to the cutting process used.The tire-chip group of rubber has particles that ranges in size from about 15to 4mm,with the steel belt wires included and extended.Rubber replace-ments of 15,30,and 45%by the volume of the coarse aggregate were used and were named Set-15,Set-30,and Set-45,respec-tively.The mixture proportions of concretes and speci?c gravities for each raw material are listed in Table 1.Specimens
Cylinder specimens that were of 150mm in diameter and 300mm in height were used to get the cylinder compressive strength,the static modulus of elasticity,and the hysteresis loops.Cube specimens with dimensions of 150mm were used to ac-
quire the dynamic modulus of elasticity of rubberized concrete with the pulse velocities tested.After that,the cube compressive strength was obtained.For each rubberized concrete set,four specimens were tested for the dynamic modulus of elasticity and compressive strength,and two specimens were tested for the static modulus of elasticity and hysteresis loops.The compressive strengths of specimens were obtained at 28days of concrete age.The average compressive strengths were determined from at least three replicate specimens.Experimental Setup
The U-Sonic ultrasonic detection system was used to measure the two kinds of wave velocities ?V p and V s ?in rubberized concrete specimens.The test setup of the longitudinal wave ?P wave ?and the transverse wave ?S wave ?velocities are shown in Figs.3?a and b ?,respectively.Velocity measurements were made by clamp-ing two disk shaped ultrasonic transducers ?one source,one re-ceiver ?onto opposite sides of the specimen.The longitudinal wave ?P wave ?transducer was coupled with Vaseline and the transducers were coupled with tin foil leaf.Each measurement was made three times at different positions on a specimen
to
(a)
GR-8
(b)CR-40
Fig.2.Various tire rubber used in experiments
Table 1.Material Properties of Concrete Mixtures
Materials
Speci?c gravity Normal concrete ?kg /m 3?Rubberized concrete
GR-8sets ?kg /m 3?
Rubberized concrete
CR-40sets ?kg /m 3?
Set-15Set-30Set-45Set-15Set-30Set-45Water 1.0180180180180180180180Cement 3.20401401401401401401401Sand
2.70660660660660660660660Coarse aggregate 2.631,180
1,003
8266491,003
826649Water reducer
1.18 4.01 4.01 4.01 4.01 4.01 4.01 4.01Ground rubber ?GR-8?0.560.0036.773.4110.2———Crushed rubber ?CR-40?
1.15
0.00
—
—
—
75.8
151.5
227.3
(a)Longitude (P)wave
velocity
(b)Transverse (S)wave velocity
Fig.3.Test setup of pulse velocity for dynamic modulus of elasticity
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improve accuracy.A pulse generator and oscilloscope monitor completed the experimental equipment.The test process was based on ASTM E 494?ASTM 2005?.
An INSTRON universal testing machine was used to get the compressive strength,modulus of elasticity,and hysteresis loops of rubberized concrete.The compressive strength and modulus of elasticity were tested according to ASTM C 39/C 39M ?ASTM 2002a ?and ASTM C469?ASTM 2002b ?,respectively.To evalu-ate the modulus of elasticity,both longitudinal and transverse strain gauges were attached to the prepared cylinder specimens.Prior to evaluating the elastic modulus,four specimens of each set were loaded to obtain the average ultimate compressive strength so that 40%ultimate strength could be determined.
When conducting hysteresis loops of rubberized concrete,two longitude strain gauges were attached symmetrically to the speci-mens.Before the hysteresis loop was drawn,minor loads were applied and the specimen was adjusted until the readings of the two strain gauges were very close to avoid the eccentricity of the loading.Upon loading,unloading,and reloading on the prepared specimens,the hysteretic loops were obtained ?Sinha et al.1964?.Generally,the loading was stopped when loading reached ap-proximate 85%of the maximum load carrying capacity.However,some specimens failed before the load reached the target loading and the last loop could not be closed.In that situation,the ?nal loading stress-strain curve had to be eliminated and the hysteresis loops were counted only to the last closed loop.
Test Results and Analysis Changes on Unit Weight
The densities of each set of specimens were measured before testing for mechanical properties.Because of low speci?c gravity of rubber particles,unit weight of rubberized concrete decreased with the increase in the percentage of rubber content.The effect of rubber content on the unit weight of concrete is shown in Fig.4.For GR-8rubberized concrete,the average unit weight de-creased from 2,399kg /m 3of the control set to 2,245,2,130,and 2,006kg /m 3with the rubber powder content of 15,30,and 45%,respectively.For CR-40rubberized concrete,the average unit weight decreased to the lowest value of 2046kg /m 3at 45%rub-ber content.At 15and 30%rubber content,the average unit weight of CR-40rubberized concrete was very close to that of GR-8rubberized concrete.Variation of the rubber type had less Compressive Strength
The values of cylinder compressive strength for rubberized con-crete are given in Fig.5.As shown in the ?gure,the strength values of the rubberized concrete decreased with the increasing amount of rubber.The average cylinder compressive strength of the normal concrete at 28days was determined to be 38.8MPa.The strength of group CR-40at the content of 15,30,and 45%decreased to 30.1,21.0,and 18.1MPa,with the a decrease of 22.3,45.8,and 53.3%.Although there is also a decrease for GR-8rubberized concrete compressive strength,down to 33.5,25.8,and 19.6MPa at the rubber content of 15,30,and 45%,respec-tively,the decrease was not as much as that for CR-40.It can be concluded that crushed rubber affects cylindrical compressive strength more than ground rubber.
The values of cube compressive strength for rubberized con-crete are given in Fig.6.As seen in this ?gure,the strength values of the rubberized concrete decreased considerably with the in-creasing amount of rubber.For GR-8rubberized concrete,the control compressive strength of 53.8MPa reduced to 46.4,35.8,and 27.3MPa with the rubber content of 15,30,and 45%,respec-tively.For CR-40rubberized concrete,the control compressive strengths were 48.5,28,and 25.2MPa with the rubber content of 15,30,and 45%,respectively.Again,crushed rubber caused more reduction on cube compressive strength than ground rubber.Possible reasons attributed to the strength reduction might include that:?1?replacing coarse aggregate with softer rubber particles results in an obvious quantity reduction of strong load-carrying material because coarse aggregate is the most important
1000
1300
160019002200
25000
15
30
45
Rubber Content (%)
U n i t W e i g h t (K g /m 3)
Fig.4.Effect of rubber content on unit weight of concrete
10203040500
153045
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C o m p r e s s i v e S t r e n g t h (M P a )
Fig.5.Effect of rubber content on cylinder compressive strength of concrete
01020304050600
15
30
45
Rubber Content (%)
C o m p r e s s i v e S t r e n g t h (M P a )
Fig.6.Effect of rubber content on cube compressive strength of concrete
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concrete component for load-carrying capacity;?2?the bonding between rubber and mortar is not as good as the bonding between the aggregate and mortar;and ?3?stress concentrations in the paste at the boundaries of the rubber aggregate cause the strength reduction.
The ratio of cylinder compressive strength and cube compres-sive strength for normal concrete is 0.72,which is close to the commonly accepted cylinder/cube strength ratio for normal con-crete,0.75?Neville 1993?.For GR-8rubberized concrete at rub-ber content of 15,30,and 45%,the ratio became 0.68,0.71,and 0.75,respectively,while for CR-40,the ratios were 0.64,0.75,and 0.64,respectively.The result indicates that rubberized con-crete has a slightly lower cylinder /cube strength ratio than that of normal concrete.
Static Modulus of Elasticity
The change in the static modulus of elasticity ?E s ?for two types of rubber,GR-8and CR-40,is shown in Fig.7.The static modu-lus of elasticity of rubberized concrete was lower than that of normal concrete.The average value of modulus of elasticity of normal concrete was 31.8GPa,while for rubberized concrete with ground rubber of 15%,the static modulus of elasticity is 27.1GPa,which is 81%of normal concrete.The modulus of elasticity decreased with the increase of rubber content for both ground and crushed rubberized concrete compared to concrete without any rubber.While rubber content varied from 15to 45%,modulus of elasticity for ground rubberized concrete reduced from 14.8to 29.9%,while for crushed rubberized concrete the value reduced from 27.4to 49.4%compared to the control con-crete.As clearly shown in Fig.7,crushed rubber caused more reduction on static modulus of elasticity of rubberized concrete at a higher percentage replacement of aggregates by rubber.
In the ACI 318-2005building code,the relationship between modulus of elasticity and compressive strength of concrete is
E =0.043w c 1.5?f c
??2?
where E =modulus of elasticity;w c =unit weight;and f c
=cylinder compressive strength.
Using the ACI equation,the static modulus of elasticity of normal concrete ?without rubber ?and rubberized concrete were calculated.For normal concrete,the unit weight was 2,399kg /m 3and the compressive strength was 38.8MPa.The calculated ACI value of modulus of elasticity was 31.5GPa,which was very close to the obtained experimental value of 31.8GPa.For rubber-3
and average compressive strength varied from 16.1to 31.4MPa.The calculated modulus of elasticity of rubberized concrete based on the ACI equation is in the range of 15.8–31.5GPa.Then,the calculated results were compared with the actual test results of modulus of elasticity for rubberized concrete.As shown in Fig.8,for both GR-8and CR-40rubberized concrete,similar trends on the modulus of elasticity were observed.Modulus of elasticity increased with the increase in compressive strength.Further study showed that the type of rubber particles in?uenced the change of modulus of elasticity.With the increase of compressive strength,the modulus of elasticity of ground rubber increased slightly slower than that of crushed rubberized concrete.Based on this study,the ACI equation could reasonably predict the relationship between modulus of elasticity and compressive strength for rub-berized concrete;however,it underpredicted the modulus of elas-ticity of rubberized concrete.Dynamic Modulus of Elasticity
The values of dynamic modulus of elasticity ?E d ?for rubberized concrete tested by pulse velocities are shown in Fig.9.As shown in the ?gure,the dynamic modulus of elasticity of rubberized concrete decreased with the increase of rubber content.For ground rubber concrete,the decrease in dynamic modulus was from 5.7to 28.6%as the rubber amount increased from 15to 45%,while for crushed rubberized concrete,the decrease was from 16.5to 25.0%with the same amount of increase in rubber
10
20
30
400
153045
Rubber Content (%)
S t a t i c M o d u l u s o f E l a s t i c i t y (G P a )
Fig.7.Effect of rubber content on static modulus of
elasticity
010
20
30
403.5
4
4.5
5
5.5
6
S t a t i c M o d u l u s o f E l a s t i c i t y (G P a )
(MPa)
'
c
f Fig.8.Effect of compressive strength on static modulus of elasticity
010
20
3040
500
15
30
45
Rubber Content (%)
D y n a m i c m o d u l u s o f
E l a s t i c i t y (G P a )
Fig.9.Relationship between dynamic modulus of elasticity and rubber content
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content.The crushed rubber concrete introduced more reduction on dynamic modulus of elasticity of rubberized concrete than ground rubber concrete.
Brittleness Index of Rubberized Concrete
Fig.10shows seven typical ?gures of hysteresis loops of speci-mens.Among them Fig.10?a ?is hysteresis loop of normal con-crete;Figs.10?b–d ?are the loops of ground rubberized concrete with the rubber content of 15,30,and 45%,respectively;and Figs.10?e,g,and f ?are the loops of crushed rubber with content of 15,30,and 45%.
The brittleness index calculated from hysteresis loops for the normal concrete is and rubberized concrete is shown in Fig.11.Test results of compressive strength and calculated BI of rubber-ized concrete are shown in Table 2.As indicated in the previous section,a lower brittleness index signi?ed higher ductility of a material.It can be observed from the results obtained that the BI values of rubberized concrete were lower than that of normal
(a)NC
481216202428320
200400600800100012001400160018002000
Strain (με)S t r e s s (M P a
)
(b)GR-8-15
48121620240
200
400
600
800
1000
1200
1400
Strain (με)S t r e s s (M P a
)
(c)GR-8-30
048121620240
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)
(d)GR-8-450481216
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600
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1200
Strain (με)S t r e s s (M P a
)
(e)CR-40-15
04812162024280
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1400
1600
Strain (με)S t r e s s (M P a
)
(f)CR-40-30
0481216200
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)
(g)CR-40-45
4812
02004006008001000120014001600
Strain (με)S t r e s s (M P a )
Fig.10.Test results of hysteresis loops
00.30.60.91.21.50
153045
Rubber Content(%)
B r i t t l e n e s s I n d e x
Fig.11.Relationship between brittleness index and rubber content
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as a good energy absorbing material and the rubberized concrete absorbing more energy that lead to plastic deformation at the time of fracture.For rubberized concrete,the highest BI value was 0.93,which happened on CR-40concrete with a rubber content of 15%,compared to the average BI value of 1.27for normal con-crete.The results clearly showed that rubberized concrete had higher ductility performance than that of normal concrete.Brittle-ness index of both CR-40and GR-8rubberized concrete de-creased linearly with varying rubber content.The more rubber particles,the higher ductility rubberized concrete had.It is very obvious that BI values of CR-40crushed rubberized concrete de-creased faster than that of GR-8ground rubberized concrete.When the rubber content changed from 15to 45%for GR-8rub-berized concrete,the brittleness index decreased from 0.70to 0.59,with only a 15.7%reduction,while for CR-40rubberized concrete,with the rubber content varying from 15to 45%,the BI value decreased from 0.93to 0.46,which was a 50.5%reduction.Although,CR-40rubberized concrete with 45%rubber content yielded a lower BI value than GR-8with the same rubber content,brittleness index of GR-8at 15and 30%rubber contents were much lower than that of CR-40at 15and 30%rubber contents.In addition to the BI value,consideration has to be given to the other mechanical properties of rubberized concrete.In general,use of ground rubber with a rubber content of 15%is more ef?cient in getting a lower brittleness index.
Conclusions
Based on this study,the following conclusions can be drawn:1.The compressive strength,the static modulus of elasticity,
and the dynamic modulus of elasticity of the rubberized con-crete decreased considerably with the increasing amount of rubber content.Crushed rubber caused greater reduction on these three material properties than ground rubber.Rubber-ized concrete had a slightly lower cylinder /cube strength ratio compared with normal concrete;
2.For both GR-8and CR-40rubberized concrete,similar trends
were observed on the relationship of modulus of elasticity versus compressive strength.With the increase of compres-sive strength,the modulus of elasticity of ground rubber in-creased slightly slower than that of crushed rubberized concrete.The ACI equation could reasonably predict the modulus of elasticity for rubberized concrete and was the lower bound for the modulus of elasticity of rubberized concrete;
3.BI values of rubberized concrete were lower than that of
normal concrete,which signi?ed that rubberized concrete had a higher ductility performance than normal concrete.Brittleness index of both CR-40and GR-8rubberized con-
crete decreased linearly with the increase of rubber content.BI values of CR-40rubberized concrete decreased faster than that of GR-8rubberized https://www.doczj.com/doc/906583573.html,e of 15%rubber content in GR-8rubberized concrete yielded a desirable brittleness index.For CR-40rubberized concrete,since the results clearly showed that high rubber content would cause a dra-matic reduction in the strength and modulus of elasticity,the optimal content for crushed rubber should be less than 30%for satisfactory strength and deformation properties.In gen-eral,use of ground rubber is more ef?cient in decreasing brittleness index;and
4.
The relationship between BI value and compressive strength revealed that the brittleness index of GR-8increased at a slower rate than that of CR-40with the increase of compres-sive strength.At the same stress level,the brittleness index of GR-8was lower than that of CR-40.
Acknowledgments
The writers would like to acknowledge the ?nancial support pro-vided by the Science and Technology Commission of Shanghai Municipality ?Grant No.03DZ12024?on this research.In particu-lar,the writers would like to thank Liu Xian,Tian Wei,Tao Jin,Zhao Guixiang and Xiong Jie at Tongji University for their assis-tance during the experiments.The writers would also like to ac-knowledge the support of the Center for Energy System Research at Tennessee Technological University.
References
ASTM.?2002a ?.Standard test method for compressive strength of cylin-drical concrete specimens.C 39/C 39M ,West Conshohocken,Pa.ASTM.?2002b ?.Standard test method for static modulus of elasticity and Poisson’s ratio of concrete in compression,C 469,West Consho-hocken,Pa.
ASTM.?2005?.Measuring ultrasonic velocity in materials,E 494,West Conshohocken,Pa.
Eldin,N.N.,and Senouci,A.B.?1993?.“Rubber-tire particles as con-crete aggregate.”J.Mater.Civ.Eng.,5?4?,478–496.
Fattuhi,N.I.,and Clark,L.A.?1996?.“Cement-based materials contain-ing shredded scrap truck tyre rubber.”Constr.Build.Mater.,10?4?,229–236.
Hernández-Olivares,F.,Barluenga,G.,Bollati,M.,and Witoszek,B.?2002?.“Static and dynamic behaviour of recycled tyre rubber-?lled concrete.”Cem.Concr.Res.,32,1587–1596.
Huang,B.,Li,G.,Pang,S.S.,and Eggers,J.?2004?.“Investigation into waste tire rubber-?lled concrete.”J.Mater.Civ.Eng.,16?3?,187–194.Khatib,Z.K.,and Bayomy,F.M.?1999?.“Rubberized Portland cement concrete.”J.Mater.Civ.Eng.,11?3?,206–213.
Table 2.Test Results of Compressive Strength and Brittleness Index of Rubberized Concrete
Item
Normal concrete Rubberized concrete
GR-8
CR-40Set-15Set-30Set-45Set-15Set-30Set-45Average cylinder compressive strength ?MPa ?38.831.425.320.631.121.016.1Strength change ratio ?%?a —?18.9?34.7?46.8?19.8?45.8?58.4BI value
1.270.700.610.590.930.680.46BI value change ratio ?%?a
—
?45.2
?52.22
?54.1
?27.1
?46.5
?63.8
a
Ratio of change=??rubberized concrete ???normal concrete ??/normal concrete *100%.
698/JOURNAL OF MATERIALS IN CIVIL ENGINEERING ?ASCE /NOVEMBER 2008
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 C h i n a U n i v e r s i t y o f P e t r o l e u m o n 10/29/13. C o p y r i g h t A S C
E .
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 .
Li,G.,Stubble?eld,M.A.,Garrick,G.,Eggers,J.,Abadie,C.,and Huang,B.?2004?.“Development of waste tire modi?ed concrete.”Cem.Concr.Res.,34?12?,2293–2289.
Nehdi,M.,and Khan,A.?2001?.“Cementitious composites containing recycled tire rubber:An overviews of engineering properties and po-tential applications.”Cem.,Concr.,Aggregates ,23?1?,3–10.
Neville, A.M.?1993?.Properties of concrete ,4th Ed.,Longman,London.
Rubber Manufacturers Association.?2004?.U.S.scrap tire markets ,2003Ed.,Washington,D.C.
Siddique,R.,and Naik,T.R.?2004?.“Properties of concrete containing scrap-tire rubber—An overview.”Waste Manage.,24,563–569.
Sinha,B.P.,Gerstle,K.H.,and Tulin,L.G.?1964?.“Stress-strain rela-tions for concrete under cyclic loading.”J.Am.Concr.Inst.,61,?2?,195–211.
Top?u,I.B.?1995?.“The properties of rubberized concretes.”Cem.Concr.Res.,25?2?,304–315.
Top?u,I.B.?1997?.“Assessment of the brittleness index of rubberized concretes.”Cem.Concr.Res.,27?2?,177–183.
Top?u,I.B.,and Avcular,N.?1997?.“Collision behaviors of rubberized concrete.”Cem.Concr.Res.,27?12?,1893–1898.
Toutanji,H.A.?1996?.“The use of rubber tire particles in concrete to replace mineral aggregates.”https://www.doczj.com/doc/906583573.html,pos.,18,135–139.
JOURNAL OF MATERIALS IN CIVIL ENGINEERING ?ASCE /NOVEMBER 2008/699
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 C h i n a U n i v e r s i t y o f P e t r o l e u m o n 10/29/13. C o p y r i g h t A S C
E .
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 .
(E, ν) 与(K, G)的转换关系如下： ) 21(3ν-= E K ) 1(2ν+= E G （7.2） 当ν值接近0.5的时候不能盲目的使用公式3.5，因为计算的K 值将会非常的高，偏离实际值很多。最好是确定好K 值(利用压缩试验或者P 波速度试验估计)，然后再用K 和ν来计算G 值。 表7.1和7.2分别给出了岩土体的一些典型弹性特性值。 岩石的弹性（实验室值）（Goodman,1980） 表7.1 土的弹性特性值（实验室值）（Das,1980） 表7.2 各向异性弹性特性——作为各向异性弹性体的特殊情况，横切各向同性弹性模型需要5 中弹性常量：E 1, E 3, ν12,ν13和G 13；正交各向异性弹性模型有9个弹性模量E 1,E 2,E 3, ν12,ν13,ν23,G 12,G 13和G 23。这些常量的定义见理论篇。 均质的节理或是层状的岩石一般表现出横切各向同性弹性特性。一些学者已经给出了用各向同性弹性特性参数、节理刚度和空间参数来表示的弹性常数的公式。表3.7给出了各向异性岩石的一些典型的特性值。 横切各向同性弹性岩石的弹性常数（实验室） 表7.3
流体弹性特性——用于地下水分析的模型涉及到不可压缩的土粒时用到水的体积模量K f ，如果土粒是可压缩的，则要用到比奥模量M 。纯净水在室温情况下的K f 值是2 Gpa 。其取值依赖于分析的目的。分析稳态流动或是求初始孔隙压力的分布状态（见理论篇第三章流体-固体相互作用分析），则尽量要用比较低的K f ，不用折减。这是由于对于大的K f 流动时间步长很小，并且，力学收敛性也较差。在FLAC 3D 中用到的流动时间步长,? tf 与孔隙度n ，渗透系数k 以及K f 有如下关系： ' f f k K n t ∝ ? （7.3） 对于可变形流体（多数课本中都是将流体设定为不可压缩的）我们可以通过获得的固结系数νC 来决定改变K f 的结果。 f 'K n m k C + = νν （7.4） 其中 3 /4G K 1 m += ν f 'k k γ= 其中，' k ——FLAC 3D 使用的渗透系数 k ——渗透系数，单位和速度单位一样（如米/秒） f γ——水的单位重量 考虑到固结时间常量与νC 成比例，我么可以将K f 的值从其实际值（Pa 9 102?）减少，利用上面得表达式看看其产生的误差。 流动体积模量还会影响无流动但是有空隙压力产生的模型的收敛速率（见1.7节流动与力学的相互作用）。如果K f 是一个通过比较机械模型得到的值，则由于机械变形将会产生孔隙压力。如果K f 远比k 大，则压缩过程就慢，但是一般有可能K f 对其影响很小。例如在土体中，孔隙水中还会包含一些尚未溶解的空气，从而明显的使体积模量减小。 在无流动情况下，饱和体积模量为： n K K K f u + = （7.5） 不排水的泊松比为：
各向异性页岩岩石物理建模及储层脆性评价页岩储层是目前非常规地球物理勘探的研究热点之一。而地震岩石物理分析技术是储层物性参数描述的重要手段。 作为地震弹性参数与储层物性参数之间的“桥梁”,地震岩石物理分析大体可分为“正问题”和“反问题”。正问题主要涉及岩石物理模型的构建及地震属性模拟,而反问题主要包括储层参数反演。 本文从正问题出发,构建了适合页岩储层的各向异性模型。并针对反问题引入网格分析法优化了反演算法。 最终利用反演结果讨论了页岩储层的各向异性特征。同时,分析了页岩储层的热点属性:脆性,优选脆性表征公式,结合井震资料,实现对页岩储层的脆性分析。 本文的主要成果可以归纳如下:(1)论文构建针对页岩储层的各向异性岩石物理模型。模型着重模拟了页岩储层由(1)有机质的富集;(2)黏土的定向排列和(3)扁平状的孔隙形态所引起的各向异性。 模型利用SCA+DEM模拟了页岩中的有机质,并引入成层因子(CL)模拟黏土的成层性强弱,最后利用孔隙纵横比控制了页岩的孔隙形态。实现了对页岩不同各向异性成因的精细模拟。 (2)随后,基于构建的页岩模型,在常规二维孔隙纵横比反演模板的基础上,引入矿物含量作为第三维参数,建立了更符合真实情况的三维孔隙纵横比反演模板,对储层的孔隙形态和孔隙类型进行反演,并利用反演得到的孔隙参数,实现对页岩储层的纵横波速度预测。(3)为了获取更多的储层物性信息,本文构建双扫描反演流程,反演得到表征孔隙形态和黏土成层性强弱的模型参数孔隙纵横比(α)
和成层因子(CL)。 实现对储层各向异性参数的预测,并讨论了各向异性参数与储层物性参数的相互关系。(4)针对反问题,本文通过引入网格分析法,对储层参数的反演算法进行改进。 网格分析法通过将实测测井值正态分布展开,将测井的误差考虑进反演算法中,最终得到待反演参数的概率密度分布图。降低了由测量值不准引起的预测误差,提高了预测结果的可信性。 并预测了目的层的孔隙形态及孔隙类型概率密度分布。(5)优选现有脆性公式,发现基于弹性参数构建的脆性指数的预测精度总体高于基于矿物组分的脆性公式。 基于杨氏模量泊松比构建的脆性指数对岩性的变化较敏感,而拉梅系数构建的脆性表征公式对孔隙流体更为敏感。基于模型,构建岩石物理脆性模板,优选脆性敏感参数。 研究发现低泊松比,中高杨氏模量,往往对应高孔脆性页岩,是页岩开采的“甜点”区域。最终,针对西南四川盆地龙马溪组-五峰组的页岩储层进行脆性评价,叠前同时反演结果和测井脆性分析结果较为吻合,验证了脆性分析结果的稳定性和可靠性。
国外页岩脆性指数评价与致密砂岩评价指标适用性？ 脆性系数的明确的定义： 文献出处：岩石脆性及描述岩爆倾向的脆性系数杨氏模量和泊松比并非直接反映岩石脆性的参数，但是目前一来定性的认为杨氏模量越大，泊松比越小，岩石脆性越好。但其实杨氏模量的大小受控于岩石强度和弹性应变量两个方面。而脆性是指岩石在破裂前发生很小的塑变能力，破裂时全部以弹性能的形式释放出来。 ①利用岩石矿物学方法进行计算（Jarvie, D.，2007） brittlenessidex=石英/石英+碳酸盐+粘土 文献出处：A Practical Use of Shale Petrophysics forStimulation Design Optimization 理想的页岩气特征在脆性指标上是这样评价的：相对较高的硅质或者碳酸盐矿物，粘土含量＜30%。针对国内页岩气的岩心做了X衍射以及全岩矿物组成之后对比美国的页岩气岩心粘土含量总结而来的这个数值。并不是说一定要小于30%，但是只能说这可以作为国内页岩气评价的一个考虑标准。粘土矿物和脆性指数的多少只是对我们工程方面有好处，脆性矿物高，容易压裂改造，粘土矿物高，不容易压力改造，填充进去的石英砂或者陶粒没有起到支撑人工裂缝的作用，而镶嵌在了储层中。 ②利用岩石力学方法杨氏模量和泊松比综合计算（rickman R ,2008）, 文献出处：Petrophysical consideration in evaluation shale gasresources 动态法：通过岩石力学实验直接测量得到，难度在于岩石样品的加工钻取，尤其是对于泥页岩。 静态法：通过波速测量，能较好的反应岩石在水力作用下裂缝扩展能力的参数主要是断裂韧性和裂缝扩展速率因子。可以通过双扭法测量。附件提供了barnett 页岩相关岩石力学参数的测试方法供参考。 文献出处：Natural fractures in the barret shale andimportance for hydrofracture 动静态参数间的关系：Larry Britt, Jerry Schoeffler. The Geomechanics OfA Shale Play: What Makes A Shale Prospective. SPE Eastern RegionalMeetingSPE125525-MS 2009 由于泊松比和杨氏模量的单位有很大的不同，为了评价每个参数对岩石脆性的影响，应该将单位进行均一化处理，然后平均产生百分数表示的脆性系数。Rickman 在文章中提出基于北美泥页岩数据统计的基础上，认为泥页岩的杨氏模量分布在1~8GPa，泊松比分布在0.15~0.4分为内。
(E, ν) 与(K, G)的转换关系如下: ) 21(3ν-= E K ) 1(2ν+= E G (7、2) 当ν值接近0、5的时候不能盲目的使用公式3、5,因为计算的K 值将会非常的高,偏离实际值很多。最好就是确定好K 值(利用压缩试验或者P 波速度试验估计),然后再用K 与ν来计算G 值。 表7、1与7、2分别给出了岩土体的一些典型弹性特性值。 岩石的弹性(实验室值)(Goodman,1980) 表7、1 土的弹性特性值(实验室值)(Das,1980) 表7、2 各向异性弹性特性——作为各向异性弹性体的特殊情况,横切各向同性弹性模型需要5中弹性常量:E 1, E 3, ν12,ν13与G 13;正交各向异性弹性模型有9个弹性模量E 1,E 2,E 3, ν12,ν13,ν23,G 12,G 13与G 23。这些常量的定义见理论篇。 均质的节理或就是层状的岩石一般表现出横切各向同性弹性特性。一些学者已经给出了用各向同性弹性特性参数、节理刚度与空间参数来表示的弹性常数的公式。表3、7给出了各向异性岩石的一些典型的特性值。 横切各向同性弹性岩石的弹性常数(实验室) 表7、3
K f ,如果土粒就是可压缩的,则要用到比奥模量M 。纯净水在室温情况下的K f 值就是2 Gpa 。其取值依赖于分析的目的。分析稳态流动或就是求初始孔隙压力的分布状态(见理论篇第三章流体-固体相互作用分析),则尽量要用比较低的K f ,不用折减。这就是由于对于大的K f 流动时间步长很小,并且,力学收敛性也较差。在FLAC 3D 中用到的流动时间步长,? tf 与孔隙度n,渗透系数k 以及K f 有如下关系: ' f f k K n t ∝ ? (7、3) 对于可变形流体(多数课本中都就是将流体设定为不可压缩的)我们可以通过获得的固结系数νC 来决定改变K f 的结果。 f 'K n m k C + = νν (7、4) 其中 3 /4G K 1 m += ν f 'k k γ= 其中,' k ——FLAC 3D 使用的渗透系数 k ——渗透系数,单位与速度单位一样(如米/秒) f γ——水的单位重量 考虑到固结时间常量与νC 成比例,我么可以将K f 的值从其实际值(Pa 9 102?)减少,利用上面得表达式瞧瞧其产生的误差。 流动体积模量还会影响无流动但就是有空隙压力产生的模型的收敛速率(见1、7节流动与力学的相互作用)。如果K f 就是一个通过比较机械模型得到的值,则由于机械变形将会产生孔隙压力。如果K f 远比k 大,则压缩过程就慢,但就是一般有可能K f 对其影响很小。例如在土体中,孔隙水中还会包含一些尚未溶解的空气,从而明显的使体积模量减小。 在无流动情况下,饱与体积模量为: n K K K f u + = (7、5) 不排水的泊松比为: ） G 3K (22G 3K u u u +-= ν (7、6) 这些值应该与排水常量k 与ν作比较,来估计压缩的效果。重要的就是,在FLAC 3D 中,
岩石力学习题 第一章绪论 1.1 解释岩石与岩体的概念，指出二者的主要区别与联系。 1.2 岩体的力学特征是什么？ 1.3 自然界中的岩石按地质成因分类可分为几大类，各有什么特点？ 1.4 简述岩石力学的研究任务与研究内容。 1.5 岩石力学的研究方法有哪些？ 第二章岩石的物理力学性质 2.1 名词解释：孔隙比、孔隙率、吸水率、渗透性、抗冻性、扩容、蠕变、松弛、弹性后效、长期强度、岩石的三向抗压强度 2.2 岩石的结构和构造有何区别？岩石颗粒间的联结有哪几种？ 2.3 岩石物理性质的主要指标及其表示方式是什么？ 2.4 已知岩样的容重=22.5kN/m3，比重，天然含水量，试计算该岩样的孔隙率n，干容重及饱和容重。 2.5 影响岩石强度的主要试验因素有哪些？ 2.6 岩石破坏有哪些形式？对各种破坏的原因作出解释。 2.7 什么是岩石的全应力－应变曲线？什么是刚性试验机？为什么普通材料试 验机不能得出岩石的全应力－应变曲线？ 2.8 什么是岩石的弹性模量、变形模量和卸载模量？
2.9 在三轴压力试验中岩石的力学性质会发生哪些变化？ 2.10 岩石的抗剪强度与剪切面上正应力有何关系？ 2.11 简要叙述库仑、莫尔和格里菲斯岩石强度准则的基本原理及其之间的关系。 2.12 简述岩石在单轴压力试验下的变形特征。 2.13 简述岩石在反复加卸载下的变形特征。 2.14 体积应变曲线是怎样获得的？它在分析岩石的力学特征上有何意义？ 2.15 什么叫岩石的流变、蠕变、松弛？ 2.16 岩石蠕变一般包括哪几个阶段？各阶段有何特点？ 2.17 不同受力条件下岩石流变具有哪些特征？ 2.18 简要叙述常见的几种岩石流变模型及其特点。 2.19 什么是岩石的长期强度？它与岩石的瞬时强度有什么关系？ 2.20 请根据坐标下的库仑准则，推导由主应力、岩石破断角和岩石单轴抗压强度给出的在坐标系中的库仑准则表达式，式中。 2.21 将一个岩石试件进行单轴试验，当压应力达到100MPa时即发生破坏，破坏面与大主应力平面的夹角(即破坏所在面与水平面的仰角)为65°，假定抗剪强度随正应力呈线性变化(即遵循莫尔库伦破坏准则)，试计算： 1)内摩擦角。 2)在正应力等于零的那个平面上的抗剪强度。
常见岩层力学参数
11 细砂岩2800 28.85 16.04 12.02 0.20 3.47 43 4.96 5-2煤1410 2.12 1.73 0.82 0.30 0.18 20 0.2 细砂岩2597 27.00 15.28 11.2 0.21 3.1 42 3.48 5-1煤1410 2.12 1.73 0.82 0.30 0.18 20 0.2 细砂岩2586 33.40 18.02 14.02 0.19 3.8 43 5.13 砂质泥岩2520 7.88 4.9 3.2 0.23 1.18 35 1.8 泥岩2567 6.90 4.3 2.8 0.23 0.7 30 1.68 4-1煤1460 2.43 2.12 0.93 0.31 0.5 24 0.35 泥岩2463 6.39 3.94 2.6 0.23 0.68 30 0.98 底板岩层2463 6.39 3.94 2.6 0.23 0.68 30 0.98 砂岩2650 4.35 2.9 1.74 0.25 9.5 41 4.21 7煤1400 1.49 2.08 0.54 0.38 1.2 20 0.64 砂质泥岩2550 3.45 2.61 1.35 0.28 7.6 30 3.0 砂岩2690 5.61 3.35 2.3 0.22 10.7 41 4.96 9煤1400 1.49 2.08 0.54 0.38 1.2 20 0.64 砂岩2650 4.76 3.05 1.92 0.24 10.2 40 4.8 砂质泥岩2600 3.84 2.91 1.5 0.28 7.8 32 3.65 石灰岩2800 10.69 5.57 4.53 0.18 11.4 38 6.7 砂质泥岩2600 3.84 2.91 1.5 0.28 7.8 32 3.65 石灰岩2800 10.69 5.57 4.53 0.18 11.4 38 6.7
几种常见岩石力学参数汇总 2010年9月2日 参考资料：《构造地质学》，谢仁海、渠天祥、钱光谟编，2007年第2版，P25-P37。 1.泊松比的变化范围： 2.弹性模量的变化范围：
3.常温常压下强度极限： 4.内摩擦角和内聚力的变化范围： 一、课程名称：中国戏曲介绍课时：2个学时 二、背景分析：戏曲是中国文化的瑰宝，同学们对中国戏曲 还不够了解，不能经常接触戏曲。 三、教学内容：中国戏曲 四、教学目标：初步了解中国戏曲的相关知识，并学会哼唱具有代表性的戏曲，简要说出
他们的起源 五、教学过程： 【引入课程】1、先介绍董永和七仙女的故事，然后放[天仙配]，为讲戏曲作铺垫，将同学们带入戏曲的氛围中 【初步了解】1、介绍戏曲相关知识中国戏曲主要是由民间歌舞、说唱和滑稽戏三种不同艺术形式综合而成。它起源于原始歌舞，是一种历史悠久的综合舞台艺术样式。经过汉、唐到宋、金才形成比较完整的戏曲艺术，它由文学、音乐、舞蹈、美术、武术、杂技以及表演艺术综合而成，约有三百六十多个种类。它的特点是将众多艺术形式以一种标准聚合在一起，在共同具有的性质中体现其各自的个性。[1]中国的戏曲与希腊悲剧和喜剧、印度梵剧并称为世界三大古老的戏剧文化，经过长期的发展演变，逐步形成了以“京剧、越剧、黄梅戏、评剧、豫剧”五大戏曲剧种为核心的中华戏曲百花苑。[2-5]中国戏曲剧种种类繁多，据不完全统计，中国各民族地区地戏曲剧种约有三百六十多种，传统剧目数以万计。其它比较著名的戏曲种类有：昆曲、粤剧、淮剧、川剧、秦腔、晋剧、汉剧、河北梆子、河南坠子、湘剧、黄梅戏、湖南花鼓戏等。放[刘海砍樵] 2、戏曲行当 生、旦、净、丑各个行当都有各自的形象内涵和一套不同的程式和规制；每个都行当具有鲜明的造型表现力和形式美。 3、艺术特色 综合性、虚拟性、程式性，是中国戏曲的主要艺术特征。这些特征，凝聚着中国传统文化的美学思想精髓，构成了独特的戏剧观，使中国戏曲在世界戏曲文化的大舞台上闪耀着它的独特的艺术光辉。 4、唱腔 第一种是抒情性唱腔，其特点为速度较缓慢，曲调婉转曲折，字疏腔繁，抒情性强。它宜于表现人物深沉而细腻的内心感情。许多剧种的慢板、大慢板、原板、中板均厉于这-类。放[女驸马] 第二种是叙事性唱腔，其特点为速度中等，曲调较平直简朴，字密腔简，朗诵性强。它常用于交代情节和叙述人物的心情。许多剧种的二六、流水等均属于这一类。放[花木兰] 第三种是戏剧性唱腔，其特点为曲调的进行起伏较大，节奏与速度变化较为强烈，唱词的安排可疏可密。它常用于感情变化强烈和戏剧矛盾冲突激化的场合。各戏剧中的散板、摇板等板式曲调都属于这一类。 5、国五大戏曲剧种
岩爆发生条件的基本分析 张志强关宝树翁汉民 ( 提要 , 得出了判断岩爆发生的基本条件 , I I 线出口段已发生岩 , . 2 U 458. 1 Basic Analysis of Rock Bursti ng Occurrence Cond ition Zhang Zh iqiang Guan B ao shu W en H anm ing (D ep t . of U nderground and Geo technical Engineering , Southw est J iao tong U niversity , Chengdu 610031, Ch ina Abstract B ased on the statistics , analysis and inducti on of the cases of rock bu rsting occu r 2rence in tunneling engineering at hom e and ab road , the basic conditi on s fo r deter m in ing the po ssib ility of rock bu rsting occu rrence are p ropo sed in th is p aper . Fu rther m o re , the basic con 2diti on s are tested and verified th rough analysing the rock bu rsting occu rrence regi on in the II line of the Q in ling T unnel and reach ing a better resu lt . Keywords rock bu rsting ; in itial stress ; tunnel excavati on 岩爆是岩体中聚集的高弹性应变能 , 因开挖而产生的一种具有代表性的应力释放现象。岩 爆是突发性的 , 岩体急剧破坏 , 岩片由岩体表面上突发性地飞出 , 而且大都发生在隧道掌子面附近及侧壁上 , 与塌顶和坍方有明显区别。随着我国铁路、公路、水电建设的不断发展 , 隧道已经向长大、深埋方向发展。近几年来 , 长度超过 10km 以上的隧道工程不断涌现 , 例如 18. 4km 的秦岭西康线铁路隧道 , 12km 的长粱山铁路隧道 , 10km 左右的太平驿水工隧洞等 , 这些隧道的埋置深度大多在800~1000m 以上 , 有些甚至超过 2000m 。此外 , 由于地质活动的影响 , 隧道可能穿
岩石的强度理论与本构关系 朱浮声 (东北大学土木系,沈阳110006) 朱浮声,1948年6月生于黑龙江齐齐哈尔11976年毕业于东北大学,1983年 获中国矿业大学工学硕士学位,1991年获东北大学博士学位11988年曾在 美国南伊利诺大学作访问学者,1993年在瑞典皇家工学院任客座教授1现 任东北大学土木工程系教授,辽宁省力学学会理事1主要研究方向为计算岩 土力学和岩土加固技术1在国内外学术刊物上发表论文50余篇,出版5锚 喷加固设计方法6等学术专著2部,译著1部1 摘要本文简要介绍了岩石强度理论和本构关系的发展和现状,讨论了它们不同的特点与适用条件1 关键词岩石,岩体,强度理论,本构关系 1前言 随着电子计算机的飞速发展和计算技术的逐步完善,对岩石强度理论和本构关系提出了更高要求,以便更真实描述岩石和岩体力学特征,求解复杂的工程岩石力学问题1 由于岩石材料力学性质的某些相似性和其它历史原因,岩石强度理论和本构关系的早期研究曾大量引用了土力学成果,并提出了一些适用于岩土介质的强度理论和本构关系1随着岩石力学的发展,人们认识到,岩石和岩体的物理力学性质不仅有别于其它非摩擦工程材料,而且,与土或混凝土等摩擦材料也存在较明显差异1例如,岩石破坏包括脆性、延性及由脆性向延性转化等复杂类型;岩体的力学特性受控于岩块和不连续面的力学特性;岩石工程的稳定性通常受主要不连续面控制等1因此,近年来又提出了适用于岩石、不连续面和岩体的强度理论或本构方程式1本文旨在介绍这些理论研究的最新进展,并对已有岩土强度理论和本构关系的适用条件和局限性加以简要评价1 限于篇幅,本文仅涉及与时间无关的各向同性和等向强化模型1 2岩土共用的强度理论和本构关系 211弹性 均质、各向同性或横观各向同性模型曾被广泛用于描述岩土力学特征,特别是峰值强度前的应力-应变关系,并得到了大量解析解和实用近似解1考虑到应力-应变曲线的明显非线性特性,曾将非线性弹性理论与计算机技术相结合,提出了一批数值算法,并在60~70年代的岩土力学分析中不断被引用1例如,以曲线各点的割线模量取代弹性常数,构成了各种超弹性模型[1],或以增量形式描述非线性弹性应力-应变关系,形成了亚弹性模型[2]等1但是,由于这些模型只考虑到岩土材料的弹性特征,并且,随着模型阶次增高,待定常数的数目往往过多,因而,限制了它们的广泛应用1
3.2 侏罗系煤岩层物理力学性质测试 3.2.1试验仪器及原理 本试验采用电子万能压力试验机(图3.24)对侏罗系、石炭系岩石试样进行抗压强度、抗拉强度以及抗剪强度的测定。 (a) 电子万能压力试验机 (b) 单轴抗压强度测试 (c) 抗拉强度测试 (d) 抗剪强度测试 图3.24 岩石力学电子万能压力试验机及试验过程 (1) 岩石抗压强度测定： 单轴抗压强度的测定：将采集的岩块试件放在压力试验机上，按规定的加载速度(0.1mm/min)加载至试件破坏。根据试件破坏时，施加的最大荷载P ，试件横断面A 便可计算出岩石的单轴抗压强度S 0，见式(3.1)。 S 0= P A (3.1) 一般表面单轴抗压强度测定值的分散性比较大，因此，为获得可靠的平均单轴抗压强度值，每组试件的数目至少为3块。 (2) 岩石抗拉强度的测定： 做岩石抗拉试验时，将试件做成圆盘形放在压力机上进行压裂试验，试件受集中荷载的作用，见式(3.2)。
S t = 2P DT π (3.2) 式中：S t ——岩石抗拉强度 MPa ； P ——岩石试件断裂时的最大荷载，KN ； D ——岩石试件直径； T ——岩石试件厚度。 为使抗拉强度值较准确，每种岩石试件数目至少3块。 (3) 岩石抗剪强度测定： 将岩石试件放在两个钢制的倾斜压模之间，然后把夹有试件的压模放在压力实验机上加压。当施加荷载达到某一值时，试件沿预定的剪切面剪断，见式(3.3)。 sin cos n T P A A N P A A τασα? = =? ??? ==?? (3.3) 式中：P ——试件发生剪切破坏时的最大荷载； T ——施加在破坏面上的剪切力； N ——作用在破坏面上的正压力； A ——剪切破坏面的面积； τ——作用在破坏面上的剪应力； n σ——作用在破坏面上的正应力； α——破坏面上的角度。 每组取3块试件，变换不同的破坏角，根据所得的数值，便可在στ-坐标系上画出反映岩石发生剪切破坏的强度曲线。并可求出反映岩石力学性质的另外两个参数：粘聚力c 及内摩察角?。 3.2.2 标准岩样加工 根据需要和所在矿的条件，在晋华宫矿12#煤层2105巷顶板钻取岩样，钻孔长度约22m ，在。根据各段岩心长度统计结果，晋华宫矿顶板岩层的RQD 值为72.4%，围岩质量一般。 岩心取出后，随即贴上标签，用透明保鲜袋包好以防风化，之后装箱，托运到实验室，经切割、打磨、干燥制成标准的岩石试样，岩样制作过程见图3.25。
第三章岩体的变形与破坏 变形：不发生宏观连续性的变化，只发生形、体变化。 破坏：既发生形、体变化、也发生宏观连续性的变化。 1．岩体变形破坏的一般过程和特点 （1）岩体变形破坏的基本过程及发展阶段 ①压密阶段（OA段）： 非线性压缩变形—变形对应力的变化反应明显； 裂隙闭合、充填物压密。 应力-应变曲线呈减速型（下凹型）。 ②弹性变形阶段（AB段）： 经压缩变形后，岩体由不连续介质转变为连续介质； 应力-应变呈线性关系； 弹性极限B点。 ③稳定破裂发展阶段（BC段）： 超过弹性极限（屈服点）后，进入塑性变形阶段。 a．出现微破裂，随应力增长而发展，应力保持不变、破裂则停止发展； b.应变：侧向应变加速发展，轴向应变有所增高，体积压缩速率减缓（由于微破裂的出现）；
④不稳定破裂发展阶段（CD段）： 微破裂发展出现质的变化： a.破裂过程中的应力集中效应显著，即使是荷载应力保持不变，破裂仍会不断地累进性发展； b. 最薄弱部位首先破坏，应力重分布导致次薄弱部位破坏，直至整体破坏。“累进性破坏”。 c. 应变：体积应变转为膨胀，轴向及侧向应变速率加速增大； ※结构不均匀；起始点为“长期强度”； ⑤强度丧失、完全破坏阶段（DE段）： 破裂面发展为宏观贯通性破坏面，强度迅速降低， 岩体被分割成相互分离的块体—完全破坏。 （2）岩体破坏的基本形式 ①张性破坏（图示）； ②剪切破坏（图示）：剪断，剪切。 ③塑性破坏（图示）。 破坏形式取决于：荷载条件、岩体的岩性及结构特征； 二者的相互关系。 ①破坏形式与受力状态的关系： a.与围压σ3有关： 低围压或负围压—拉张破坏（图示）； 中等围压—剪切破坏（图示）； 高围压（150MN/m2=1500kg/cm2）—塑性破坏。 的关系： b.与σ 2 σ2/σ 3 <4（包括σ 2 =σ3），岩体剪断破坏，破坏角约θ=25°； σ2/σ 3 >8（包括σ 2 =σ1）：拉断破坏，破坏面∥σ1，破坏角0°; 4≤σ2/σ3≤8：张、剪性破坏，破坏角θ=15°。 ②破坏形式与岩体结构的关系： 完整块体状—张性破坏； 碎裂结构、碎块结构—塑性破坏； 裂隙岩体—取决于结构面与各主应力之间的方位关系。
第35卷第3期岩石力学与工程学报V ol.35 No.3 2016年3月Chinese Journal of Rock Mechanics and Engineering March，2016评价岩石脆性指标对滚刀破岩效率的影响 刘泉声1，2，刘建平1，时凯3，潘玉丛1，黄兴1，刘学伟1，魏莱1 (1. 中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室，湖北武汉 430071；2. 武汉大学土木建筑工程学院 岩土与结构工程安全湖北省重点实验室，湖北武汉 430072；3. 碧桂园控股有限公司营销中心，广东广州 528000) 摘要：脆性是岩石重要的力学性质之一。岩石脆性与滚刀破岩效率密切相关，但目前还没有统一的用于评价滚刀 破岩效率的岩石脆性指标。总结现有的35种脆性指标，将其分为基于强度、应变、应变能、硬度、莫尔包络线、特殊试验和其他等7种类型。为研究岩石脆性与滚刀破岩效率之间的关系，通过滚刀贯入试验，引入归一化比能 概念，提出表征岩石脆性的新指标，重点研究基于强度和贯入试验的脆性指标与归一化比能之间的关系。试验结 果表明：(1) 滚刀更难贯入高强度岩石；(2) 脆性指标B2和B4与归一化比能之间呈强烈的指数函数关系，随着脆 性的增高，归一化比能降低，滚刀破岩效率增高，应优先选用脆性指标B2来评价滚刀破岩效率，其次是脆性指标 B4；(3) 将单轴抗压强度约20 MPa定义为单轴抗压强度过渡值，滚刀不适宜切削单轴抗压强度小于20 MPa的软 岩。试验结果对评价滚刀破岩效率时岩石脆性指标的选取具有一定的指导意义。 关键词：岩石力学；脆性指标；盘形滚刀；贯入试验；破岩效率 中图分类号：TU 45 文献标识码：A 文章编号：1000–6915(2016)03–0498–13 Evaluation of rock brittleness indexes on rock fragmentation efficiency by disc cutter LIU Quansheng1，2，LIU Jianping1，SHI Kai3，PAN Yucong1，HUANG Xing1，LIU Xuewei1，WEI Lai1 (1. State Key Laboratory of Geomechanics and Geotechnical Engineering，Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，Wuhan，Hubei 430071，China；2.Key Laboratory of Safety for Geotechnical and Structural Engineering of Hubei Province，School of Civil Engineering，Wuhan University，Wuhan，Hubei 430072，China；3. Marketing Center of Country Garden Holdings Company Limited，Guangzhou，Guangdong 528000，China) Abstract：Brittleness is one of the most important mechanical properties of rock. The fragmentation efficiency of rock is closely related to the rock brittleness. No unified brittleness index of rock is confirmed in evaluating rock fragmentation efficiency by disc cutter. The existing 35 different brittleness indices were summarized and classified into seven categories with respect to strength，strain，strain energy，hardness，Mohr envelope，special tests，etc. In order to study the relations between the rock brittleness and the rock fragmentation efficiency by disc cutter，the normalized specific energy concept was introduced after carrying out the indentation tests with disc cutter，and a new index of rock brittleness was proposed. In addition，the relations between the normalized specific energy and brittleness indexes based on strength and indentation test were mainly studied. The results show that it 收稿日期：2015–05–04；修回日期：2015–07–22 基金项目：国家重点基础研究发展计划(973)项目(2014CB046903，2015CB058102)；湖北省自然科学基金重点项目(2011CDA119) Supported by the National Key Basic Research and Development Program of China(973 Program)(Grants No. 2014CB046903 and 2015CB058102) and Key Program of Natural Science Foundation of Hubei Province(Grant No. 2011CDA119) 作者简介：刘泉声(1962–)，男，博士，1983年毕业于山东矿业学院矿井建设专业，现任研究员、博士生导师，主要从事岩土与地下工程方面的教学与研究工作。E-mail：liuqs@https://www.doczj.com/doc/906583573.html, DOI：10.13722/https://www.doczj.com/doc/906583573.html,ki.jrme.2015.0569
岩石物理学及岩石性质 一、矿物 1.1矿物 矿物是单个元素或若干个元素在一定地质条件下形成的具有特定理化性质的化合物，是构成岩石的基本单元。矿物多数是在地壳（地球）物理化学条件下形成的无机晶质固体，也有少数呈非晶质和胶体。 1.2矿物的主要物理特性 1.2.1光学特性 （1）颜色：矿物的颜色由矿物对入射光的反映呈现出来。一般来说矿物的颜色是矿物对入射光吸收色的补色。 （2）条痕:条痕色指矿物经过在不涂釉的瓷板上擦划，在瓷板上留下的矿物粉粒的颜色。 （3）光泽:光泽是矿物表面对入射光所射的总光量。根据光泽有无金属感，将光泽分为金属光泽与非金属光泽。矿物光泽特性既与矿物组成和结构有关，又与矿物表面特征有关。 （4）透明度:透明度与矿物对矿物透射光的多少有关。 1.2.2力学性质 （1）硬度： 矿物的硬度是指矿物的坚硬程度。一般采用摩氏硬度法鉴别矿物硬度。即采用标准矿物的硬度对未知矿物进行相对硬度的鉴别。摩氏硬度中选取十种矿物作为标准矿物，将矿物分为10级，称为摩氏硬度计。这十种矿物硬度由1级到10级的顺序是：①滑石，②石膏，③方解石，④磷灰石，⑤萤石，⑥正长石，⑦石英，⑧黄玉，⑨刚玉，⑩金刚石。 （2）解理与断口： 矿物受力后产生破裂出现的没有一定方向的不规则的断开面，谓之断口。当晶质体矿物受力断开时，出现一系列平行的、平整的裂面时，称为解理。断口出现的程度跟解理的完善程度相互消长，解理程度越低的矿物越容易形成断口。因此，断口具有了非晶质体的基本含义。解理与晶质体内质点间距有明显的关系，
解理常出现在质点密度较大的方向上。 （3）延展性： 矿物的延展性，也可以称为矿物的韧性。其特征是表现为矿物能被拉成长丝和辗成薄片的特性。这是自然金属元素具有的基本特性。 1.3重要矿物 （1）自然元素矿物：这类矿物较少，其中包括人们所熟知的矿物，如金、铂、自然铜、硫磺、金刚石（见图1）、石墨等。 图1金刚石 （2）硫化物类矿物：本类是金属元素与硫的化合物，大约200多种，Cu、Pb、Mo、Zn、As、Sb、Hg等金属矿床多有此类矿物富集而称，具有很大的经济价值。 方铅矿PbS。闪锌矿ZnS。黄铁矿FeS2（见图2） 图2黄铁矿 （3）氧化物及氢氧化物类矿物：本类矿物分布相当广泛，共约180多种，包括重要的造盐矿物如石英及Fe、Al、Mn、Cr、Ti、Sn、U、Th等的氧化物或氢
(E , ν) 与(K , G )的转换关系如下： ) 1(2ν+= E G （） 当ν值接近的时候不能盲目的使用公式，因为计算的K 值将会非常的高，偏离实际值很多。最好是确定好K 值(利用压缩试验或者P 波速度试验估计)，然后再用K 和ν来计算G 值。 表和分别给出了岩土体的一些典型弹性特性值。 岩石的弹性（实验室值）（Goodman,1980） 表 土的弹性特性值（实验室值）（Das,1980） 表 各向异性弹性特性——作为各向异性弹性体的特殊情况，横切各向同性弹性模型需要5中弹性常量：E 1, E 3, ν12,ν13和G 13；正交各向异性弹性模型有9个弹性模量E 1,E 2,E 3, ν12,ν13,ν23,G 12,G 13和G 23。这些常量的定义见理论篇。 均质的节理或是层状的岩石一般表现出横切各向同性弹性特性。一些学者已经给出了用各向同性弹性特性参数、节理刚度和空间参数来表示的弹性常数的公式。表给出了各向异性岩石的一些典型的特性值。 横切各向同性弹性岩石的弹性常数（实验室） 表
流体弹性特性——用于地下水分析的模型涉及到不可压缩的土粒时用到水的体积模量K f ，如果土粒是可压缩的，则要用到比奥模量M 。纯净水在室温情况下的K f 值是2 Gpa 。其取值依赖于分析的目的。分析稳态流动或是求初始孔隙压力的分布状态（见理论篇第三章流体-固体相互作用分析），则尽量要用比较低的K f ，不用折减。这是由于对于大的K f 流动时间步长很小，并且，力学收敛性也较差。在FLAC 3D 中用到的流动时间步长,? tf 与孔隙度n ，渗透系数k 以及K f 有如下关系： ' f f k K n t ∝ ? （） 对于可变形流体（多数课本中都是将流体设定为不可压缩的）我们可以通过获得的固结系数νC 来决定改变K f 的结果。 f 'K n m k C + = νν （） 其中 其中，' k ——FLAC 3D 使用的渗透系数 k ——渗透系数，单位和速度单位一样（如米/秒） f γ——水的单位重量 考虑到固结时间常量与νC 成比例，我么可以将K f 的值从其实际值（Pa 9 102?）减少，利用上面得表达式看看其产生的误差。 流动体积模量还会影响无流动但是有空隙压力产生的模型的收敛速率（见节流动与力学的相互作用）。如果K f 是一个通过比较机械模型得到的值，则由于机械变形将会产生孔隙压力。如果K f 远比k 大，则压缩过程就慢，但是一般有可能K f 对其影响很小。例如在土体中，孔隙水中还会包含一些尚未溶解的空气，从而明显的使体积模量减小。 在无流动情况下，饱和体积模量为： n K K K f u + = （） 不排水的泊松比为： ） G 3K (22G 3K u u u +-= ν （） 这些值应该和排水常量k 和ν作比较，来估计压缩的效果。重要的是，在FLAC 3D 中，排水特性是用在机械连接的流变计算中的。对于可压缩颗粒，比奥模量对压缩模型的影响比例与流动。 固有的强度特性 在FLAC 3D 中，描述材料破坏的基本准则是摩尔-库仑准则，这一准则把剪切破坏面看作直线破坏面： s 13N f φσσ=-+ （） 其中 )sin 1/()sin 1(N φφφ-+=
（E, v与（K, G）的转换关系如下: 3(1 2 ) (7.2) 当v值接近0.5的时候不能盲目的使用公式 3.5，因为计算的K值将会非常的高，偏离 实际值很多。最好是确定好K值（利用压缩试验或者P波速度试验估计），然后再用K和v 来计算G值。 表7.1和7.2分别给出了岩土体的一些典型弹性特性值。 各向异性弹性特性一一作为各向异性弹性体的特殊情况，横切各向同性弹性模型需要 中弹性常量：E1, E3, V2, V3和G13；正交各向异性弹性模型有9个弹性模量E1,E2,E3, V2, V3 , V3 ,G12,G 13和G23。这些常量的定义见理论篇。 均质的节理或是层状的岩石一般表现出横切各向同性弹性特性。一些学者已经给出了用 各向同性弹性特性参数、节理刚度和空间参数来表示的弹性常数的公式。表 3.7给出了各向异性岩石的一些典型的特性值。
流体弹性特性一一用于地下水分析的模型涉及到不可压缩的土粒时用到水的体积模量 K f ,如果土粒是可压缩的，则要用到比奥模量 M 。纯净水在室温情况下的 K f 值是2 Gpa 。 其取值依赖于分析的目的。 分析稳态流动或是求初始孔隙压力的分布状态 （见理论篇第三章 流体-固体相互作用分析），则尽量要用比较低的 K f ，不用折减。这是由于对于大的 K f 流动 时间步长很小，并且，力学收敛性也较差。在 FLAC 3D 中用到的流动时间步长,tf 与孔隙度 n ，渗透系数k 以及K f 有如下关系： 丄 n t f ' （7.3） K f k 对于可变形流体（多数课本中都是将流体设定为不可压缩的） 我们可以通过获得的固结 系数C 来决定改变K f 的结果。 (7.4) 其中 1 m K 4G/3 k k f 其中，k '—— FLAC 3D 使用的渗透系数 k —渗透系数，单位和速度单位一样（如米 /秒） f ――水的单位重量 9 考虑到固结时间常量与 C 成比例，我么可以将K f 的值从其实际值（2 10 Pa ）减少, 利用上面得表达式看看其产生的误差。 流动体积模量还会影响无流动但是有空隙压力产生的模型的收敛速率 （见1.7节流动与 力学的相互作用）。如果K f 是一个通过比较机械模型得到的值， 则由于机械变形将会产生孔 隙压力。如果K f 远比k 大，则压缩过程就慢，但是一般有可能 K f 对其影响很小。例如在土 体中，孔隙水中还会包含一些尚未溶解的空气，从而明显的使体积模量减小。 在无流动情况下，饱和体积模量为： (7.5) 不排水的泊松比为: n K f K f
岩爆发生条件的基本分析 作者：张志强关宝树翁汉民隧道技术来源：本站原创点击数：156 更新时间：2005-6-9 提要通过对国内外隧道工程施工中所发生岩爆实例的统计、分析与归纳，得出了判断岩爆发生的基本条件，并以此对目前正在施工中的西康线秦岭隧道II线出口段已发生岩爆区段进行了验证，效果很好。 关键词岩爆地应力隧道开挖 岩爆是岩体中聚集的高弹性应变能，因开挖而产生的一种具有代表性的应力释放现象。岩爆是突发性的，岩体急剧破坏，岩片由岩体表面上突发性地飞出，而且大都发生在隧道掌子面附近及侧壁上，与塌顶和坍方有明显区别。随着我国铁路、公路、水电建设的不断发展，隧道已经向长大、深埋方向发展。近几年来，长度超过10 km以上的隧道工程不断涌现，例如18.4 km的秦岭西康线铁路隧道，12 km的长粱山铁路隧道，10 km左右的太平驿水工隧洞等，这些隧道的埋置深度大多在800～1 000 m以上，有些甚至超过2 000m。此外，由于地质活动的影响，隧道可能穿过高地应力区等，在隧道施工过程中发生岩爆的可能性大为增加。为减小岩爆造成的损失，安全而经济地施工，研究岩爆发生的基本条件是很有必要的。 1 从工程实例看岩爆的发生 表1列出国内外曾经发生岩爆的一些隧道工程的概况，从中对岩爆发生的条件或许可以找出一些可供参考的规律。表1中参数σc表示岩石单轴抗压强度；Is表示点荷载强度；σmin、σmax分别表示地应力的最小值和最大值。
国内外隧道工程发生岩爆的统计 表1 隧道名称埋深/m断面积/m2 地质条件σc/MPaIs/MPaσmin/MPaσmax/MPa 挪威赫古拉公路隧道最大70038.6前寒武纪片麻岩100～2504.5～1118.925.0 挪威兰峡湾公路隧道200～1 50050.0片麻岩、花岗片麻岩、片麻闪长岩60～2002.7～9.09.034.0 挪威西玛水电站地下厂房700800花岗岩、花岗片麻岩1808.319.548.8 瑞典维泰斯引水隧洞250——粉砂岩、石英岩803.66.850.0～70.0 瑞典Headrace 隧道30067石英岩2008.82.0～8.028.0 南非金矿1 437～2 404——石英岩198～2309.037.0～60.065.0 美国Galena金矿1 200 ——石英岩1757.752.052.0 南非Hoist地下洞室1 450130石英岩198～2309.039.044.3 挪威Eikesdal公路隧道80036片麻岩(坚硬)2008.821.230.6 日本关越公路隧道750～1 05085石英闪长岩、页岩23610.716.289.0 瑞典捷克坦水工隧洞400——花岗岩1808.350.0125.0 挪威Sewage隧道1307花岗岩1808.33.535.0 日本新清水隧道1 000——石英闪长岩1838.027.089.0