软土地基上分期施工的路堤沉降预测方法

Settlement prediction of embankments with stageconstruction on soft groundLIU Song-yu，JING FeiInstitute of Geotechnical Engineering, Southeast University,Nanjing210096,China；软土地基上分期施工的路堤沉降预测方法刘松玉，经绯岩土工程研究所210096期，中国南京东南大学摘要沉降量和沉降速率控制是软土地基上路堤工程设计的关键问题，由于固结理论的局限性和参数的不确定性，理论预测的精度较低，而基于现场实测数据的观测法则显示出了较高的精度。

本文在Asaoka观测法的基础上,形成了一种软土路基上分期施工时路堤沉降预测的方法，结合江苏海相软土上的高速公路工程进行了沉降预测分析。

关键词：沉降；路堤；观测法；分期施工；江苏海相软土1.简介对于软土地基上的路堤设计来说，沉降和稳定性是需要考虑的两个关键性因素。

现有的评估路堤稳定性的方法基本上能满足设计要求。

因此，沉降便成了设计分析路堤长久性的关键参数。

换句话说，对沉降的分析是路堤分析的最合适的方法。

软土地基上路堤的沉降主要是由于路堤的固结和侧向流动所引起的。

对于软土地基上的路堤，人们做了很多这方面的研究。

很多实验已经得出了对于预估沉降量和沉降率的实际值的理论，同时，实验也解释了一些涉及精确预估沉降量的问题。

Duncan于1993年、Olson于1998年分别对预估沉降量在现有条件下所引起缺陷的不确定性因素进行了分析。

这些不确定性因素使得估算路堤沉降量和沉降速率有时特别困难甚至是无法进行估算。

尽管数值分析法能提高计算的精确性，但是土的本构模型涉及到很多不能被确定的参数。

然而，随着数值分析法的计算化，这使得我们可以获得更多的土的本构模型和相应的程序代码，从而使计算得以简化得以更精确。

因此，人们非常渴望发展这样一种观测方法——只要记录足够的沉降参数，通过计算机就能得到精确的沉降值。

很多研究人员在现场观测的基础上发展了沉降预估法。

该方法不仅能够得到精确解，还被认可为估算最终沉降量和沉降速率的方法。

分期施工对于软土地基上的路堤来说是一个特殊的程序。

随着每一个施工期路堤的固结，路堤的安全性会逐渐提高，竣工后的沉降量也会减少。

施工时期的沉降—时间（s-t）曲线可能会比瞬时荷载的曲线更为复杂。

尽管竣工后的沉降量会减少，但是施工时期路堤在稳定的最终荷载作用下的初始的固结期会明显增加。

为了加快沉降速率，减小软土层的竣工后的二次沉降，实际中我们经常采用超载，也就是在竣工时期加临时荷载，然后卸载。

对于软土层上路堤的施工期的沉降分析的问题有如下几种：(1)预估施工时期由于钻孔测试而引起的变形。

(2)预估在永久荷载作用下由于第一施工期所引起的最终沉降。

(3)预估在永久荷载和相应的超载下由于超载所引起的竣工后的沉降。

第一个问题主要依赖于设计时的理论。

其余两个问题需要以经验为根据而不是靠理论方法。

因为它们是靠观测的数据而得来的。

在任何情况下，第二个和第三个从现场观测到的预估沉降量比理论算得的沉降量都可靠。

Leroueil et al 提出了有效应力路径，分析了施工时期竖向沉降和横向沉降之间的关系。

Stamatopoulos 和Kotzias 发展了在永久荷载下确定最终沉降的方法，但这种方法是基于弹性理论的，而且它很难用来计算沉降率。

而双曲线模型的方法又是依据总的荷载—沉降关系来预估最终沉降量，这种方法对于在初始天然荷载下的沉降很不灵敏。

本文在Asaoka 观测法的基础上，提出了一种软土地基上分期施工时在永久荷载作用下的预估最终沉降的方法。

2. 分期观测法Asaoka 建议采取一个“观测过程”，利用现场观测的数据来估算最终沉降量和原位固结系数。

这种方法因为其简单性和有效性而变得越来越受欢迎。

该方法是基于单向固结沉降量S 0 , S 1 , S 2 , …… ，S j 在时间0 ，∆t ，2∆t ，…… ，j ∆t 时能被作为第一近似值，公式如下：S j =0β+1βS j-1 (1) 在时间S j - S j-1图里它代表了一条直线。

这里0β是直线的截距，1β是直线的倾角。

当达到最终沉降时：S j = S j-1=S f ，因此，最终沉降S f 可以由如下公式求得：S f =101ββ- (2)ln 1β= - 26H tC V ∆（两面排水时） (3)ln 1β= - 22H tC V ∆（顶部排水时） (4)常数1β和固结系数C V 有关：Magnan 和Deroy 认为对于横向排水：C h =t FD e ∆⋅-12ln 8β (5) 对于竖向排水：C v =t H ∆⋅-12ln 125β (6) 这里D e ，H 分别是排水路径的长度。

Asaoka 观测法也表明，S j - S j-1图中的直线在多级荷载作用下会改变位置，而且，当沉降相对较小而粘土层相对较厚时，移动的直线基本上和初始直线是平行的。

但是，该方法并没有讨论给出如何确定从一个直线段到下一个直线段的移动距离。

在表达式(1)中，当j = 0时，t = 0，S(t=0) = S0 ,这里t 是荷载的工作时间。

如果在荷载卸载的瞬间将t 设置为0，那么Sj-1就变为0。

因此S0 = 0β=瞬时沉降Se (7)这就意味着Asaoka 观测法能被扩展为求固结沉降，其值等于Sj- Sj-1图里的 直线的截距0β，这里t = 0是在荷载加上之后。

此外，这种瞬时沉降也是分期施工期平行线的移动距离。

事实上，根据Asaoka 观测法的最初土层的沉降值能由下式求得：St = dz z t H ⎰0),(ε (8)+'++++'++=)(51)(31)(41)(21),(243242F C Z F C Z ZF T C Z T C Z T z t V V V V ！！！！ε (9)这里T 和F 是两个未知的时间系数。

在竖向排水的底部和土层的顶部，),(z t ε=T=ε(t , z=0) 。

如果t = 0，那么),(z t ε=ε(t=0 , z=0) =e ε=初始弹性应变。

因此，S(t=0)=S0就能得到瞬时沉降Se 。

Se 也能由如下弹性原理的公式求解：S0=Se=u E qbIV )1(2- (10)上式清楚地表明Asaoka 观测法能够被扩展到估算施工期路堤的沉降。

也就是说，下一个施工期的路堤的状况可由上一个施工期的0β，1β进行估算。

上一个施工期的路堤的沉降测量值越多，下一个施工期的估算值就越精确。

分期观测法包括以下几个步骤：(1)观察时间—沉降曲线的草图(2)选择时间间隔∆t ，通常是10到100天之间。

在tj 时刻读取曲线上的沉降Sj 。

(3)在相应的坐标系里以Sj- Sj-1为轴，从0开始标出沉降Sj- Sj-1的点。

(4)用直线将标出的点连起来，直线相应的倾角是1β，在Sj 轴上的截距为0β，与45o 直线的交点是第一工期的最后固结沉降量。

(5)利用第一工期的0β通过(10)式反求不排水压缩模量。

(6)通过已知的Eu 来确定下一工期的路堤沉降，从而确定直线段的移动距离。

(7)假设C V 在分期施工时是连续的，并且假设相对于软土的厚度来说路堤沉降非常小，这可以保证下一工期的直线段平行于第一施工期的直线段。

(8)从与45o 斜线的交点预估下一施工期的最后沉降量。

(9)利用1β的值通过式(5)、(6)分别估算C h 和C V 。

3.实例研究3.1工程地址和工程概述连云港—徐州高速公路的A段是一段长31km的高速公路，它把港口城市连云港和国家高速公路网连在一起。

该工程于1999年12月开始动工。

这其中包括104座桥和涵洞。

该高速公路路堤的底部宽40m，高从3m到7m不等。

根据设计标准，路堤和结构的沉降值必须控制在10cm以内。

竣工后的路堤沉降在建成后的15年里必须小于30cm。

很明显，路堤的沉降量和沉降速率对工程的可靠性和经济性是至关重要的。

3.2地面下的土质条件连徐高速公路的A段要经过海相沉积平原。

该平原的地基土剖面图包括0到3m厚的上层硬表层的硬粘土，其下是5.6m到13m厚的软粘土，别名江苏海相软土。

软粘土下是交替间隔的硬粘土和稠粘土，厚度从10m到20m，它们一直延伸到基岩。

3.3土层的改良和路堤的施工我们设计采用干射搅拌法和砂垫层分期施工法来减少总的沉降和竣工后的沉降。

从1999年12月开始，路堤用残积粘土填充，在第一期施工到2.5—3.5m高后，让土自然固结6个月。

固结沉降期间通过沉降板定期观测路堤的沉降，这一期间，一些观测到的沉降比相应的设计总沉降还大。

为了修改原先的设计，使得下一施工期的方案更可靠，我们有必要再次预估基于第一施工期沉降观测结果的路堤的性状。

3.4预估最终沉降从路堤填充高度和对路堤中心处砂垫层的地表沉降测试结果中，我们发现第一期和第二期的沉降曲线下降非常陡。

第二施工期后的最后沉降可以由分期观测法通过第一期的观测数据来预测。

这表明预估沉降量和测试沉降量基本上是相符的。

曲线同时也表明基于第一期观测数据的不排水弹性模量E u和C V的有效性。

E u/c u的比率为50—100，而C V（现场）/C V（室内）的比率为6—12。

这也似乎表明江苏海相粘土E u/c u在低范围内的比率符合。

Bangkok粘土和其它已经存在的粘土的比率为70—253（也就是计算数据是有效的），而实际的固结系数值大于试验测得的值，这会导致更快速率的沉降。

4. 结论基于Asaoka观测法的理论来源，结合对江苏海相粘土的研究，本文发展了一种软土路基上分期施工时路堤沉降预测的方法。

结论如下：(1)对比所有的最终沉降预测的观测方法，Asaoka观测法能够成功地扩展到预测分期施工路堤的沉降。

的。

(2)在根据Asaoka观测法绘制的S j-和S j-1图中，瞬时沉降S e被证明是等于截距0因此，在第一期观测中，我们能够得到软土层的不排水压缩模量。

它有助于我们更精确地估算下一期的瞬时沉降。

(3)假定实际的固结系数和土层厚度在分期施工期仍然保持连续，倾角1 的平行线段的移动距离等于第一分期由公式反求的瞬时沉降值。

(4)本文所介绍的这种方法的优点是下一个分期的不排水压缩模量的值和固结系数的值可由第一分期的计算分析获得。

(5)实例研究表明，江苏海相软土的E u/c u的比率从50到100不等，而实际的固结系数几乎都比实验室试验所得的数据大。

AbstractThe magnitude and rate of the settlement are the key elements subjected to design analysis of embankments on soft ground. The observational methods based onfieldmeasurement have indicated the promising results and become effective methods to predict the final settlement, while the uncertainties of parameters and theories limit significantly the accuracy of settlement estimation. This paper presents an observational method to predict the settlement performance of embankments with stage construction on soft ground based on Asaoka method. The case studies show the accordance of the predicting results with the field measured data. It is also given from the case study that the value of E u / C u ratio ranges from 50 to 100 for Jiangsu Marine clay and its actual coefficient of consolidation is almost one order of magnitude larger than the laboratory data.Key words:settlement; embankment; observational method; stage construction; Jiangsu Marine clay1. IntroductionSettlement and stability are two primary considerations systematically related to the design of an embankment on soft ground. The tools available for the stability evaluation seem to be satisfactory. The key element of long term behavior of the embankment routinely subjected to design analysis is the settlement. In other words , the settlement analysis is the most appropriate approach to the embankment analysis .The settlements of embankments on soft clays result from the consolidation and the lateral flow under the embankments. Many researches have been made on performance of embankments on soft ground.Although many experiences have shown the practical value of the theory for estimating settlements and settlements rates , they also illustrated some of the problems in volved in making accurate prediction of the settlement .Duncan (1993) and Olson (1998) analyzed the uncertainties causing the shortcomings in the current state of the art for settlement prediction respectively. These uncertainties sometimes make it difficulty or impossible to estimate the magnitude and rate of settlement for embankments . Although the numerical analysis may be possible to improve the accuracy , the soil models may involve many parameters that can not be determined economically. However , the evolution of numerical methods with computer may result in simpler models and complete codes that are increasingly becoming available.It is desirable therefore to develop observational methods based upon which the settlement can be estimated once sufficient data has been recorded. Many researchers developed the settlement prediction methods on field measurement observation , which have indicated promising results and become an accepted method to estimate final settlements and rates of settlements.Stage construction is a typical procedure for embankments on the soft ground. With a certain period of consolidation at every stage construction ,the safety factor of the embankment can be generally raised and the post construction settlement may be reduced. The settlement - time curve during stage construction may be more complicated than it is withinstantaneous loading. The period for primary consolidation at a definite final load with stage construction may be increased significantly , in spite of the fact that the post construction settlement can be reduced. In order to speed up the rate of settlement and minimize the post construction secondary settlement of soft clays , surcharge is often used in practice ,which can be taken as a type of stage construction with temporary loading and unloading stages .Problems related to the settlement analysis of stage construction for embankments on soft clays are of the following types:(1) Prediction of the deformation behavior of stage construction from the results of borings and tests .(2) Prediction of the final settlement at permanent load from the behavior of the first stage construction.(3) Prediction of the post construction settlement at the permanent load and corresponding time of surcharge removed from the behavior of the surcharge.The first of these problems is heavily dependent on the theory , which is necessary in design. The other two predictions require empirical rather than theoretical methods because they are based on observational data. In any case , the fact that the second and third predictions are derived from field observations makes them more reliable than the theoretical predictions .Leroueil et al revealed the effective stress path and analyzed the relationship between vertical settlement and lateral displacement during stage construction. Stamatopoulos and Kotzias developed a method to determine the final settlement at permanent load from the behavior of surcharge, but it is based on the elastic theory and difficult to calculate the rate of the settlement . The hyperbolic method is based on the total load - settlement relationship to predict the final settlement , which is not sensitive to the nature of the initial loading condition.This paper presented a method for the prediction of the final settlement at permanent load from the behavior of the first stage construction based on the Asaoka method.2. Stage observational methodAsaoka proposed an ‘observational procedure ’to estimate the final settlement and in2situ coefficient of consolidation from the field observational data. This method is becoming increasing popular because of its simplicity and effectivity.The method is based on the fact that one dimensional consolidation settlements S 0 , S 1 ,S 2 , … ，Sj at times 0 ，∆t ，2∆t ，… ，j ∆t can be expressed as a first order approximationbySj =0β+1βSj-1 (1)which represents a straight line in a Sj vs Sj-1 plot , where 0β is the intercept and 1β is the slope of the line. When the ultimate settlement has been reached : Sj= Sj-1=Sf , therefore ,the ultimate settlement Sf can be given bySf =101ββ- (2)andln 1β= -26H t C V ∆ (both top and bottom drainage) (3) ln 1β= - 22H t C V ∆ (top drainage) (4) The constant 1β has been suggested by Magnan and Deroy to be related to the coefficient of consolidation Cv as follows: for horizontal radial drainage onlyC=tF D e ∆⋅-12ln 8β (5) for vertical drainage onlyC v =tH ∆⋅-12ln 125β (6) where D e , H are the drainage path length respectively.Asaoka method also stated that the straight line in S j - S j-1 space would moved up in the case of multi-staged loading , moreover , the shifted lines become almost parallel to the initial when the settlement is relatively small compared to the thickness of clay layer. However , it is not discussed and provided how to determine the shift distance from the line of first stage to the line of the next stage.In the expression (1) ,when j = 0 that is : t = 0 and S (t=0) = S 0 ,where t can be taken as 0 from any time after loading works . If t is set as 0 at the exact time once the load is exerted , then , S j-1 becomes 0 , therefore ,S 0=0β= immediate settlement S e . (7) This means that Asaoka method can be extended to obtain the construction settlement , which equals to the intercept 0β of the liner line in the space S j - S j-1, where t = 0 is set just after loading. Moreover , this immediate settlement contributes the shift distance of the parallel lines during stage construction.In fact , from the derivation of the Asaoka method , the settlement of soil layers can be expressed asS t = dz z t H ⎰0),(ε (8) And +'++++'++=)(51)(31)(41)(21),(243242F C Z F C Z ZF T C Z T C Z T z t VV V V ！！！！ε (9) where T and F are two unknown function of time.With the vertical drainage boundary conditions and at the ground surface ,),(z t ε=T =ε(t , z=0) . If t = 0 , ),(z t ε=ε(t=0 , z=0) =e ε= initial elastic strain. Therefore , S(t=0)=S 0 gives the immediate settlement S e , which can also be estimated from the elastic method by the equation :S 0=S e =uE qbI V )1(2- (10) It is clearly shown that the Asaoka method has been extended to predict the settlement of embankments with stage construction. In other words , the behavior of next stage construction can be predicted with the 0β ,1β from the last stage construction. The more the previous stages with settlement measurement , the higher the accuracy of next stage prediction. The stage observational method includes following steps :(1) Sketch observed time settlement curve .(2) Choose a time interval ∆t , which usually ranges from 10 to 100 days , read the settlements S j from the curve at times t j ( = ∆t j , j = 1 ,2 ,3, …).(3) Plot the settlements S j , S j-1 in a coordinate system with axis S j , S j-1 originated from 0.(4) Fit the plotted points by a straight line , of which corresponding slope is read as 1β. The intercept at the S j axis gives 0β , while the point of intersection with the 45o line , gives the final consolidation settlement of the first stage.(5) From the 0β of the first stage construction to determine the undrained modulus E u by inverse analysis (10) .(6) Determine the next stage construction settlement with the above known E u (10) , thus resulting in the shift distance of line.(7) Assume the C V remains constant during stage construction and settlement is small compared with the thickness of soft soils , this makes the line of next stage construction parallel to the first stage with the slope 1β.(8) Predicting the final settlement of next stage construction from the intersection of the shifted line with the 45o line.(9) Estimate the C h and C V from the value of 1β with the equation (5) or (6) .3. Case study3. 1 Site and project descriptionSection A of Lianxu highway is a 31 km long high standard expressway connecting the port city Lianyugang to the national highway system of China. It was began to construction from Dec. 1999. There are 104 bridges or culverts or passways in this 31 km long section designed to connect embankments . The bottom width of the embankment is 40 m , while the height of embankment changes from 3 to 7 m.Based on the design code , the differential settlements between embankments and structures have to be controlled less than 10 cm. Post construction settlements ofembankments have to be less than 30 cm during the post construction period of 15 years . It is clear that the magnitude and rates of the embankment settlements are the extremely important problem to make the project reliable and economical .3. 2 Subsurface conditionsThe section A of Lianxu highway passes over the marine deposit plain. The typical subsoil profile consists of 0 to 3m think upper crust of stiff clay underlain by a 5.6 to 13m thick soft clay ,which is named Jiangsu Marine clay. Blow this soft clay , lies alternating layers of stiff clay and dense sand extending to badrock with the varied thickness of 10 to 20m.3. 3 Soil improvement and embankment constructionDry Jet Mixing and stage construction with sand blanket have been designed to reduce the total settlement and post construction settlement . The embankment filled with residual clay from Dec. 1999. After the first stage construction of 2.5～3.5 m high , about 6 months were left along for soil consolidation. The settlements are observed regularly by settlement plates . During the period of the first stage consolidation , some observational settlements are found to be larger than the corresponding designed total settlement . It is necessary to re-predict the behavior of the embankments based on the settlement observational results of the first stage construction , in order to modify the original design and make the reliable decision for next stage construction.3. 4 Prediction of the final settlementThe typical fill heights with time and measured ground surface settlements at the center of embankments with sand blankets are shown. It can be seen that the settlement curve drops significantly between the first stage and second stage construction. The final settlements of the second stage construction are predicted from the first stage observational data by the stage observational method. It indicates that the predicted settlements are basically consistent with the measured settlement . Table 1 also shows the bake analyzed values of undrained elastic modulus E u and coefficient of consolidation C v based on the first stage observational data , giving ranges of E u / c u ratio of 50～100 and C V (field) /C V (lab) ratio of 6～12. It seems to be in the lower range of the E u / c u ratio for Jiangsu Marine clay compared with the ratio of 70～253 for Bangkok clay and other clays existing in the different literature. The actual coefficient of consolidation appears one order of magnitude larger than the laboratory value , this resulting in the faster rate of measured settlement .4. ConclusionsOn the basis of theoretical derivation of Asaoka method and case study of Jiangsu Marine clay , this paper presented a Stage Observational Method for settlement prediction of embankments on soft ground with stage construction. The following conclusions can begiven:(1) Considering the available observational methods for ultimate settlement prediction , the Asaoka method may be successfully extended to make the settlement prediction for stage construction embankments .βin the S j and(2) The immediate settlement S e is verified to be equal to the interceptS j-1space of the Asaoka method , therefore , the undrained modulus of soft ground can be obtained from the first stage construction measurements , this contributing to the more accurate estimation of immediate settlement of the next stage construction.(3) Assuming the actual coefficient of consolidation and the thickness of the soft ground remain constant during stage construction , the shifting distances of the parallel lines with the βis equaled to the immediate settlements , which can be calculated with the inverse slope of1modulus from the first (last) stage construction.(4) The distinct advantage of the recommended method is that the values of undrained modulus and coefficient of consolidation for next stage construction are inversely analyzed from the first (last) stage construction.(5) From the case study , the value of E u / c u ratio ranges from 50 to 100 for Jiangsu Marine clay , while the actual coefficient of consolidation is almost one order of magnitude larger than the laboratory data.。