軟土地基上分期施工的路堤沉降預(yù)測(cè)方法

1、Settlement prediction of embankments with stageconstruction on soft groundLIU Song-yu，JING Fei Institute of Geotechnical Engineering, Southeast University,Nanjing 210096,China； 軟土地基上分期施工的路堤沉降預(yù)測(cè)方法 劉松玉，經(jīng)緋 巖土工程研究所210096期，中國(guó)南京東南大學(xué)摘 要沉降量和沉降速率控制是軟土地基上路堤工程設(shè)計(jì)的關(guān)鍵問(wèn)題，由于固結(jié)理論的局限性和參數(shù)的不確定性，理論預(yù)測(cè)的精度較低，而基于現(xiàn)場(chǎng)實(shí)測(cè)數(shù)據(jù)的觀測(cè)法則

2、顯示出了較高的精度。本文在Asaoka觀測(cè)法的基礎(chǔ)上,形成了一種軟土路基上分期施工時(shí)路堤沉降預(yù)測(cè)的方法，結(jié)合江蘇海相軟土上的高速公路工程進(jìn)行了沉降預(yù)測(cè)分析。關(guān)鍵詞： 沉降； 路堤； 觀測(cè)法； 分期施工； 江蘇海相軟土1. 簡(jiǎn)介對(duì)于軟土地基上的路堤設(shè)計(jì)來(lái)說(shuō)，沉降和穩(wěn)定性是需要考慮的兩個(gè)關(guān)鍵性因素?，F(xiàn)有的評(píng)估路堤穩(wěn)定性的方法基本上能滿足設(shè)計(jì)要求。因此，沉降便成了設(shè)計(jì)分析路堤長(zhǎng)久性的關(guān)鍵參數(shù)。換句話說(shuō)，對(duì)沉降的分析是路堤分析的最合適的方法。軟土地基上路堤的沉降主要是由于路堤的固結(jié)和側(cè)向流動(dòng)所引起的。對(duì)于軟土地基上的路堤，人們做了很多這方面的研究。很多實(shí)驗(yàn)已經(jīng)得出了對(duì)于預(yù)估沉降量和沉降率的實(shí)際值的理論

3、，同時(shí)，實(shí)驗(yàn)也解釋了一些涉及精確預(yù)估沉降量的問(wèn)題。Duncan于1993年、Olson于1998年分別對(duì)預(yù)估沉降量在現(xiàn)有條件下所引起缺陷的不確定性因素進(jìn)行了分析。這些不確定性因素使得估算路堤沉降量和沉降速率有時(shí)特別困難甚至是無(wú)法進(jìn)行估算。盡管數(shù)值分析法能提高計(jì)算的精確性，但是土的本構(gòu)模型涉及到很多不能被確定的參數(shù)。然而，隨著數(shù)值分析法的計(jì)算化，這使得我們可以獲得更多的土的本構(gòu)模型和相應(yīng)的程序代碼，從而使計(jì)算得以簡(jiǎn)化得以更精確。因此，人們非?？释l(fā)展這樣一種觀測(cè)方法只要記錄足夠的沉降參數(shù)，通過(guò)計(jì)算機(jī)就能得到精確的沉降值。很多研究人員在現(xiàn)場(chǎng)觀測(cè)的基礎(chǔ)上發(fā)展了沉降預(yù)估法。該方法不僅能夠得到精確解，還

4、被認(rèn)可為估算最終沉降量和沉降速率的方法。分期施工對(duì)于軟土地基上的路堤來(lái)說(shuō)是一個(gè)特殊的程序。隨著每一個(gè)施工期路堤的固結(jié)，路堤的安全性會(huì)逐漸提高，竣工后的沉降量也會(huì)減少。施工時(shí)期的沉降時(shí)間（s-t）曲線可能會(huì)比瞬時(shí)荷載的曲線更為復(fù)雜。盡管竣工后的沉降量會(huì)減少，但是施工時(shí)期路堤在穩(wěn)定的最終荷載作用下的初始的固結(jié)期會(huì)明顯增加。為了加快沉降速率，減小軟土層的竣工后的二次沉降，實(shí)際中我們經(jīng)常采用超載，也就是在竣工時(shí)期加臨時(shí)荷載，然后卸載。對(duì)于軟土層上路堤的施工期的沉降分析的問(wèn)題有如下幾種：(1)預(yù)估施工時(shí)期由于鉆孔測(cè)試而引起的變形。(2)預(yù)估在永久荷載作用下由于第一施工期所引起的最終沉降。(3)預(yù)估在永久

5、荷載和相應(yīng)的超載下由于超載所引起的竣工后的沉降。第一個(gè)問(wèn)題主要依賴于設(shè)計(jì)時(shí)的理論。其余兩個(gè)問(wèn)題需要以經(jīng)驗(yàn)為根據(jù)而不是靠理論方法。因?yàn)樗鼈兪强坑^測(cè)的數(shù)據(jù)而得來(lái)的。在任何情況下，第二個(gè)和第三個(gè)從現(xiàn)場(chǎng)觀測(cè)到的預(yù)估沉降量比理論算得的沉降量都可靠。Leroueil et al提出了有效應(yīng)力路徑，分析了施工時(shí)期豎向沉降和橫向沉降之間的關(guān)系。Stamatopoulos和Kotzias發(fā)展了在永久荷載下確定最終沉降的方法，但這種方法是基于彈性理論的，而且它很難用來(lái)計(jì)算沉降率。而雙曲線模型的方法又是依據(jù)總的荷載沉降關(guān)系來(lái)預(yù)估最終沉降量，這種方法對(duì)于在初始天然荷載下的沉降很不靈敏。本文在Asaoka觀測(cè)法的基礎(chǔ)上

6、，提出了一種軟土地基上分期施工時(shí)在永久荷載作用下的預(yù)估最終沉降的方法。2. 分期觀測(cè)法Asaoka建議采取一個(gè)“觀測(cè)過(guò)程”，利用現(xiàn)場(chǎng)觀測(cè)的數(shù)據(jù)來(lái)估算最終沉降量和原位固結(jié)系數(shù)。這種方法因?yàn)槠浜?jiǎn)單性和有效性而變得越來(lái)越受歡迎。該方法是基于單向固結(jié)沉降量S0 , S1 , S2 , ，Sj在時(shí)間0 ，t ，2t ， ，jt時(shí)能被作為第一近似值，公式如下： Sj =+Sj-1 (1)在時(shí)間Sj- Sj-1圖里它代表了一條直線。這里是直線的截距，是直線的傾角。當(dāng)達(dá)到最終沉降時(shí)：Sj= Sj-1=Sf ，因此，最終沉降Sf可以由如下公式求得： Sf = (2) ln= - （兩面排水時(shí)） (3) ln=

7、- （頂部排水時(shí)） (4)常數(shù)和固結(jié)系數(shù)CV有關(guān)：Magnan和Deroy認(rèn)為對(duì)于橫向排水： Ch = (5)對(duì)于豎向排水： Cv = (6)這里De ，H分別是排水路徑的長(zhǎng)度。Asaoka觀測(cè)法也表明，Sj- Sj-1圖中的直線在多級(jí)荷載作用下會(huì)改變位置，而且，當(dāng)沉降相對(duì)較小而粘土層相對(duì)較厚時(shí)，移動(dòng)的直線基本上和初始直線是平行的。但是，該方法并沒(méi)有討論給出如何確定從一個(gè)直線段到下一個(gè)直線段的移動(dòng)距離。在表達(dá)式(1)中，當(dāng)j = 0時(shí)，t = 0，S(t=0) = S0 ,這里t是荷載的工作時(shí)間。如果在荷載卸載的瞬間將t設(shè)置為0，那么Sj-1就變?yōu)?。因此S0 = =瞬時(shí)沉降Se (7)這就意

8、味著Asaoka觀測(cè)法能被擴(kuò)展為求固結(jié)沉降，其值等于Sj- Sj-1圖里的 直線的截距，這里t = 0是在荷載加上之后。此外，這種瞬時(shí)沉降也是分期施工期平行線的移動(dòng)距離。事實(shí)上，根據(jù)Asaoka觀測(cè)法的最初土層的沉降值能由下式求得： St = (8) (9)這里T和F是兩個(gè)未知的時(shí)間系數(shù)。 在豎向排水的底部和土層的頂部，=T=(t , z=0) 。如果t = 0，那么=(t=0 , z=0) =初始彈性應(yīng)變。因此，S(t=0)=S0就能得到瞬時(shí)沉降Se 。Se也能由如下彈性原理的公式求解： S0=Se= (10)上式清楚地表明Asaoka觀測(cè)法能夠被擴(kuò)展到估算施工期路堤的沉降。也就是說(shuō)，下一個(gè)

9、施工期的路堤的狀況可由上一個(gè)施工期的，進(jìn)行估算。上一個(gè)施工期的路堤的沉降測(cè)量值越多，下一個(gè)施工期的估算值就越精確。分期觀測(cè)法包括以下幾個(gè)步驟： (1)觀察時(shí)間沉降曲線的草圖(2)選擇時(shí)間間隔t，通常是10到100天之間。在tj 時(shí)刻讀取曲線上的沉降Sj 。(3)在相應(yīng)的坐標(biāo)系里以Sj- Sj-1為軸，從0開始標(biāo)出沉降Sj- Sj-1的點(diǎn)。(4)用直線將標(biāo)出的點(diǎn)連起來(lái)，直線相應(yīng)的傾角是，在Sj軸上的截距為，與45o直線的交點(diǎn)是第一工期的最后固結(jié)沉降量。(5)利用第一工期的通過(guò)(10)式反求不排水壓縮模量。(6)通過(guò)已知的Eu來(lái)確定下一工期的路堤沉降，從而確定直線段的移動(dòng)距離。(7)假設(shè)CV在分期

10、施工時(shí)是連續(xù)的，并且假設(shè)相對(duì)于軟土的厚度來(lái)說(shuō)路堤沉降非常小，這可以保證下一工期的直線段平行于第一施工期的直線段。(8)從與45o斜線的交點(diǎn)預(yù)估下一施工期的最后沉降量。(9)利用的值通過(guò)式(5)、(6)分別估算Ch和CV 。3. 實(shí)例研究3.1 工程地址和工程概述連云港徐州高速公路的A段是一段長(zhǎng)31km的高速公路，它把港口城市連云港和國(guó)家高速公路網(wǎng)連在一起。該工程于1999年12月開始動(dòng)工。這其中包括104座橋和涵洞。該高速公路路堤的底部寬40m，高從3m到7m不等。根據(jù)設(shè)計(jì)標(biāo)準(zhǔn)，路堤和結(jié)構(gòu)的沉降值必須控制在10cm以內(nèi)?？⒐ず蟮穆返坛两翟诮ǔ珊蟮?5年里必須小于30cm。很明顯，路堤的沉降量和

11、沉降速率對(duì)工程的可靠性和經(jīng)濟(jì)性是至關(guān)重要的。3.2 地面下的土質(zhì)條件連徐高速公路的A段要經(jīng)過(guò)海相沉積平原。該平原的地基土剖面圖包括0到3m厚的上層硬表層的硬粘土，其下是5.6m到13m厚的軟粘土，別名江蘇海相軟土。軟粘土下是交替間隔的硬粘土和稠粘土，厚度從10m到20m，它們一直延伸到基巖。3.3 土層的改良和路堤的施工我們?cè)O(shè)計(jì)采用干射攪拌法和砂墊層分期施工法來(lái)減少總的沉降和竣工后的沉降。從1999年12月開始，路堤用殘積粘土填充，在第一期施工到2.53.5m高后，讓土自然固結(jié)6個(gè)月。固結(jié)沉降期間通過(guò)沉降板定期觀測(cè)路堤的沉降，這一期間，一些觀測(cè)到的沉降比相應(yīng)的設(shè)計(jì)總沉降還大。為了修改原先的設(shè)計(jì)

12、，使得下一施工期的方案更可靠，我們有必要再次預(yù)估基于第一施工期沉降觀測(cè)結(jié)果的路堤的性狀。3.4 預(yù)估最終沉降從路堤填充高度和對(duì)路堤中心處砂墊層的地表沉降測(cè)試結(jié)果中，我們發(fā)現(xiàn)第一期和第二期的沉降曲線下降非常陡。第二施工期后的最后沉降可以由分期觀測(cè)法通過(guò)第一期的觀測(cè)數(shù)據(jù)來(lái)預(yù)測(cè)。這表明預(yù)估沉降量和測(cè)試沉降量基本上是相符的。曲線同時(shí)也表明基于第一期觀測(cè)數(shù)據(jù)的不排水彈性模量Eu和CV的有效性。Eu/cu的比率為50100，而CV（現(xiàn)場(chǎng)）/CV（室內(nèi)）的比率為612。這也似乎表明江蘇海相粘土Eu/cu在低范圍內(nèi)的比率符合。Bangkok粘土和其它已經(jīng)存在的粘土的比率為70253（也就是計(jì)算數(shù)據(jù)是有效的），

13、而實(shí)際的固結(jié)系數(shù)值大于試驗(yàn)測(cè)得的值，這會(huì)導(dǎo)致更快速率的沉降。4. 結(jié)論基于Asaoka觀測(cè)法的理論來(lái)源，結(jié)合對(duì)江蘇海相粘土的研究，本文發(fā)展了一種軟土路基上分期施工時(shí)路堤沉降預(yù)測(cè)的方法。結(jié)論如下：(1)對(duì)比所有的最終沉降預(yù)測(cè)的觀測(cè)方法，Asaoka觀測(cè)法能夠成功地?cái)U(kuò)展到預(yù)測(cè)分期施工路堤的沉降。(2)在根據(jù)Asaoka觀測(cè)法繪制的Sj-和Sj-1圖中，瞬時(shí)沉降Se被證明是等于截距的。因此，在第一期觀測(cè)中，我們能夠得到軟土層的不排水壓縮模量。它有助于我們更精確地估算下一期的瞬時(shí)沉降。(3)假定實(shí)際的固結(jié)系數(shù)和土層厚度在分期施工期仍然保持連續(xù)，傾角的平行線段的移動(dòng)距離等于第一分期由公式反求的瞬時(shí)沉降值

14、。(4)本文所介紹的這種方法的優(yōu)點(diǎn)是下一個(gè)分期的不排水壓縮模量的值和固結(jié)系數(shù)的值可由第一分期的計(jì)算分析獲得。(5)實(shí)例研究表明，江蘇海相軟土的Eu/cu的比率從50到100不等，而實(shí)際的固結(jié)系數(shù)幾乎都比實(shí)驗(yàn)室試驗(yàn)所得的數(shù)據(jù)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 onfield measurement have

15、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

16、 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 Eu / Cu ratio ranges from 50 to 100 for Jiangsu Marine clay and its actual coefficient o

17、f consolidation is almost one order of magnitude larger than the laboratory data.Key words: settlement; embankment; observational method; stage construction; Jiangsu Marine clay1. Introduction Settlement and stability are two primary considerations systematically related to the design of an embankme

18、nt 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 a

19、nalysis .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 settlement

20、s 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 uncertainti

21、es 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 n

22、umerical 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 s

23、ettlement 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 consolida

24、tion 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 with instantaneous loading. The period for primary consolidation

25、 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

26、 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

27、 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 f

28、irst 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 obse

29、rvations 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 set

30、tlement 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

31、 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 method Asaoka proposed anobservational procedureto estimate the final settlem

32、ent 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 S0 , S1 , S2 , ，Sj at times 0 ，t ，2t ， ，jt can be expres

33、sed as a first order approximation by Sj =+Sj-1 (1)which represents a straight line in a Sj vs Sj-1 plot , where is the intercept and 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 = (2) and ln= - (both

34、top and bottom drainage) (3) ln= - (top drainage) (4)The constant has been suggested by Magnan and Deroy to be related to the coefficient of consolidation Cv as follows: for horizontal radial drainage only C= (5)for vertical drainage onlyCv = (6)where De , H are the drainage path length respectively

35、.Asaoka method also stated that the straight line in Sj- Sj-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 a

36、nd 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) = S0 ,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 , th

37、en , Sj-1 becomes 0 , therefore ,S0= immediate settlement Se . (7) This means that Asaoka method can be extended to obtain the construction settlement , which equals to the intercept of the liner line in the space Sj- Sj-1, where t = 0 is set just after loading. Moreover , this immediate settlement

38、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 asSt = (8)And (9)where T and F are two unknown function of time.With the vertical drainage boundary conditions and at the

39、 ground surface , =T=(t , z=0) . If t = 0 , =(t=0 , z=0) = initial elastic strain. Therefore , S(t=0)=S0 gives the immediate settlement Se , which can also be estimated from the elastic method by the equation :S0=Se= (10)It is clearly shown that the Asaoka method has been extended to predict the set

40、tlement of embankments with stage construction. In other words , the behavior of next stage construction can be predicted with the , from the last stage construction. The more the previous stages with settlement measurement , the higher the accuracy of next stage prediction. The stage observational

41、method includes following steps :(1) Sketch observed time settlement curve .(2) Choose a time intervalt , which usually ranges from 10 to 100 days , read the settlements Sj from the curve at times t j ( = t j , j = 1 ,2 ,3, ).(3) Plot the settlements Sj , Sj-1 in a coordinate system with axis Sj , S

42、j-1 originated from 0.(4) Fit the plotted points by a straight line , of which corresponding slope is read as . The intercept at the Sj axis gives , while the point of intersection with the 45o line , gives the final consolidation settlement of the first stage.(5) From the of the first stage constru

43、ction to determine the undrained modulus Eu by inverse analysis (10) .(6) Determine the next stage construction settlement with the above known Eu (10) , thus resulting in the shift distance of line.(7) Assume the CV remains constant during stage construction and settlement is small compared with th

44、e thickness of soft soils , this makes the line of next stage construction parallel to the first stage with the slope.(8) Predicting the final settlement of next stage construction from the intersection of the shifted line with the 45o line.(9) Estimate the Ch and CV from the value of with the equat

45、ion (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 i

46、n 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 constru

47、ction settlements of embankments 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

48、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 extendin

49、g 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.

50、After the first stage construction of 2.53.5 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

51、 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 se

52、ttlementThe 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

53、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 Eu and coefficient of consolidation Cv based on the first stage observational data , giving ranges of Eu / cu ratio of 50100 and CV (field) /CV (lab) ratio of 612. It seems to be in the lower range of the Eu / cu ratio for Jiangsu Marine clay compared with the ratio of 70253 for Bangkok clay and othe