土的壓縮性及固結理論

1、第4章土的壓縮性及固結理論基本內(nèi)容這是本課程的重點。在學習土的壓縮性指標確定方法的基礎上，掌握地基最終沉降量計算原理和地 基固結問題的分析計算方法。學習要求：1 .掌握土的壓縮性與壓縮性指標確定方法；2 .掌握有效應力原理；3 .掌握太沙基一維固結理論； 4.1 概述(outline)土在自重應力或附加應力作用下，地基土要產(chǎn)生附加變形，包括體積變形和形狀變形。對于土來說，體積變形通常表現(xiàn)為體積縮小。我們把這種在外力作用下土體積縮小得特性稱為土的壓縮性(compressibility) 。It is well recognized that the deformations will be in

2、duced in ground soil under self-weight or net contact pressure. The load-induced soil deformations can be divided into volumetric deformation and deviatoric deformation (namely, angular distortion or deformation in shape). The volumetric deformation is mainly caused by the normal stress, which compa

3、ct the soil, resulting in soil contraction instead of soil failure. The deviatoric deformation is caused by the shear stress. When the shear stress is large enough, shear failure of the soil will be induced and soil deformation will develop continuously. Usually shear failure over a large area is no

4、t allowed to happen in the ground.土的壓縮性主要有兩個特點：(1)土的壓縮性主要是由于孔隙體積減少而引起的；(2)由于孔隙水的排出而引起的壓縮對于飽和粘土來說需要時間，將士的壓縮隨時間增長的過程 稱為土的固結。在建筑物荷載作用下，地基土主要由于壓縮而引起的豎直方向的位移稱為沉降。研究建筑物沉降包含兩方面的內(nèi)容：一是絕對沉降量的大小，亦即最終沉降；二是沉降與時間的關系，主要介紹太沙基的一維固結理論土體產(chǎn)生體積縮小的原因：(1) 固體顆粒的壓縮；(2) 孔隙水和孔隙氣體的壓縮，孔隙氣體的溶解；孔隙水和孔隙氣體的排出。由于純水的彈模約為2X106kPa,固體顆粒的彈

5、模為 9Xl 0 7kPa, 土粒本身和孔隙中水的壓縮量，在工程壓力 (100 600kPa)范圍內(nèi)，不到土體總壓縮量的1/400,因此?？陕圆挥?。所以，土體壓縮主要來自孔隙水和土中孔隙氣體的排出?？紫吨兴蜌怏w向外排出要有一個時間過程。因此土的壓縮亦要一段時間才能完 成。把這一與時間有關的壓縮過程稱為固結。土體的變形計算，需要取得土的壓縮性指標，可以通過室內(nèi)側限壓縮試驗和現(xiàn)場原位試驗得到。室內(nèi)壓縮試驗亦稱固結試驗，是研究土壓縮性最基本的方法?，F(xiàn)場載荷試驗是在工程現(xiàn)場通過千斤頂逐級對置于地基土上的載荷板施加荷載，觀測記錄沉降隨時 間的發(fā)展以及穩(wěn)定時的沉降量s,并繪制成p-s曲線，即獲得地基土載

6、荷試驗的結果。反映土的壓縮性的指標主要有壓縮系數(shù)、壓縮模量、壓縮指數(shù)和變形模量。土的壓縮性的高低，常 用壓縮性指標定量表示，壓縮性指標，通常由工程地質(zhì)勘察取天然結構的原狀土樣進行Characteristic of soil compression(1) Compression of soil is mainly due to the decrease of void volume.(2) The compression for a clay increases with the times (consolidation)Ground soil will deform vertically du

7、e to structure load. The contents on studying structure settlement include1 The absolute settlement final settlement)2 Relationship between settlement and time. Introducing terzaghi s 1D consolidation theory Reasons of volumetric reduction of soil mass1 The compressive deformation of the soil partic

8、les.2 The compressive deformation of the pore water and air. The partial discharge of the pore water and air.The consolidation process of saturated soils is in effect a process of discharge of the pore water and corresponding reduction of the pore volume. For saturated sands, pore water is apt to di

9、scharge under pressure due to high permeability; hence the consolidation process completes in a short length of time. For saturated clays, pore water discharges slowly under pressure due to low permeability; hence the consolidation process completes in a long length of time.To calculate the deformat

10、ion of the soil mass, it is necessary to know the compression indexes. These indexes can be obtained from laboratory compression test (consolidation test) and field load tests.4.2 土的壓縮性 (soil compressibility charateristic)4.2.1 固結試驗及壓縮性指標 (Oedometer test , Consolidation test and Compression indexes

11、) 側限壓縮試驗亦稱固結試驗。所謂側限就是使土樣在豎向壓力作用下只能發(fā)生豎向變形，而無側向變形。室內(nèi)壓縮試驗采用的試驗裝置為壓縮儀或固結儀(參照圖4-1)。試驗時將切有土樣的環(huán)刀置于剛性護環(huán)中，由于金屬環(huán)刀及剛性護環(huán)的限制，使得土樣在豎向壓力作用下只能發(fā)生豎向變形，而無側向 變形。在土樣上下放置的透水石是土樣受壓后排出孔隙水的兩個界面。壓縮過程中豎向壓力通過剛性 板施加給土樣，土樣產(chǎn)生的壓縮量可通過百分表量測。常規(guī)壓縮試驗通過逐級加荷進行試驗，常用的分級加荷量 p 為：50kPa,100kPa,200kPa,300kPa,400kPa。Compression test with zero la

12、teral strain is also called Oedometer test. In test, there is vertical deformation but no lateral deformation under vertical load.The characteristic of a soil during one-dimensional compression can be determined by means of the oedometer test (see Fig.4-1). The test specimen (2 cm high and a diamete

13、r to height ratio of 2.5) is in the form of a disc, held inside a metal ring and lying between two porous stones. The upper porous stone, which can move inside the ring with a small clearance, is fixed below a metal loading cap through which pressure can be applied to the specimen. The whole assembl

14、y sits in an open cell of water to which the pore water in the specimen has free access. The ring confining the specimen may be either fixed (clamped to the body of the cell) or floating (being free to move vertically): the inside of the ring should have a smooth polished surface to reduce side fric

15、tion. The confining ring imposes a condition of zero lateral strain on the specimen, the ratio of lateral to vertical effective stress being K0, the coefficient of lateral earth pressure at rest. The compression of the specimen under pressure is measured by means of a dial gauge operating on the loa

16、ding cap. Usually the specimen is gradually loaded, and the load grades are often set as p50kPa, 100kPa, 200kPa, 300kPa, 400kPa。It should be noted that the relationship between the void ratio and the effective pressure shown in fig. is not fixed for the same soil. It depends on the magnitude of the

17、applied load and the length of the loading period in the standard oedometer test, each load is normally maintained for a period of 24 hours for a 2 cm thick clay to complete the compression.如下圖，為求得土樣穩(wěn)定后的孔隙比，利用土粒子體積不變和土截面不變的兩個條件，可得出：The soil compression characteristic has been discussed in the last s

18、ection. This section discusses further the calculation method of the magnitude of the soil compression under an effective stress increment. In the current engineering practice, the widely used method for calculating the foundation settlement is the one-dimensional consolidation method, which is esta

19、blished based on the calculation formulae of soil compression under zero lateral strain condition, namely unidirectional compression. The basic assumptions made for obtaining the calculation formulae are:(1) Soil compression is fully the result of the deformation of soil skeleton due to reduction in

20、 pore volume.The compression of soil particle is omitted;(2) Deformation is only in the vertical direction, without lateral strain;(3) Stress is uniformly distributed along the height of the soil layer.Fig. shows a saturated soil specimen after compression at effective stress pi. assume the height o

21、f the soil specimen is h, the volume of soil particle V s, the corresponding void ratio ei,then the pore volume is vs and the total volume Vi is(1+ei) Vs. if the effective stress is increased to p2 equal to (pi + A p),the height of the soil specimen after compression is H2,As shown in the below figu

22、res, because the volume of soil particle and the soil cross section do not change, the void ratio after compression can be calculated as follows:HoHo H1 e01eHoeo而 eoGs 1 wo w/ o 1公式中Gs,wo, o, w分別為土粒比重，初始含水量，初始密度和水的密度。因此只要測的的穩(wěn)定 s, o , o ，壓縮量就可按上式算得相應的孔隙比，從而繪制土的壓縮曲線。Where, Gs,wo, o, w are the specific

23、 gravity of solids, initial water content, initial density of soil and density of water. So that we can calculate the void ratio in stable state after compression/consolidation from the dial gauge readings and draw the compression curve.壓縮曲線可按兩種方式繪制。e-p曲線e-p曲線可確定土的壓縮系數(shù)，壓縮摸量等指標，e-logp曲線可確定土的壓縮指數(shù)等壓縮性指

24、標。壓縮系數(shù)(compression coefficient)的定義為“曲線上任意兩點割線的斜率”。From the curve e-p, the coefficient of consolidation and the compression modulus can be determined. It is defined as the change of void ratio over unit pressure increment, the slope of two points in the curve e-p.ee e2a - pp2p1式中負號表示隨著壓力 p的增加，e逐漸減少。壓

25、縮性不同 的土，其壓縮曲線的形狀是不一樣的。曲線愈陡，說明隨著壓 力的增加，土孔隙比的減小愈顯著，因而土的壓縮性愈高。a1.2 o.1MPa-1 時，低壓縮性土(low compressible soil)o.1 w a1-2o.5MPa -1 時，高壓縮性土 ( high compressible soil)X自重應力p1增加到外荷作用土中應力 p2 (自重與附加應力之和)In above equation, - means the void ratio decrease with the increase of the pressure p. For soils having differ

26、ent characteristic of compressibility, the curves of compression are different too . If the slope is large, it means the void ratio change is remarkable, and the soil is high compressible.壓縮才旨數(shù)(compression index) : e-lgp 坐標系統(tǒng)中的曲線上直線的斜率(slope of e-lgp curve)Ccig P2 ig Pi lg p2PiXCC是無量綱系數(shù)，同壓縮系數(shù) a一樣，壓縮

27、指數(shù)CC值越大，土的壓縮性越高。雖然壓縮系數(shù)a和壓縮指數(shù)CC都是反映土的壓縮性指標，但兩者有所不同。前者隨所取的初始壓力及壓力增量的大小 而異，而后者在較高的壓力范圍內(nèi)卻是常量，不隨壓力而變。X卸載段和再加載段的平均斜率稱為土的回彈指數(shù)Ce，而CeCc。一般粘性土的CC值在1.0左右，Ce 值在(0.10.2) CC 之間。Same as the coefficient of compression a, the larger the value of C c, the steeper the compression curve and the higher the soil compress

28、ibility will be. Although both the coefficient of compression a and the compression index are indicators of soil compressibility, they are actually different in the following aspects. The former varies with the initial pressure and the pressure increment applied, whereas the later is essentially a c

29、onstant within a majority range of the applied load.壓縮卞量(compression modulus): 土體在完全側限的條件下，豎向應力增量與豎向應變增量的比值。(The ratio of vertical stress increment over vertical strain increment with no lateral strain)1H且 e a p ,故有， H a p H11 eE 業(yè)Es d z 由右圖可知From the figure, HiHi H1 e11 e2Hee2H11 e1由此可推得側限條件下的應力應變模

30、量為(the compression modulus can be given as) :p 1 e 1EsH / H1 a mv土的壓縮模量越小，土的壓縮性越高。Es的倒數(shù)成為土的 體積壓縮系數(shù) mv(coefficient of volume compressibility),它表示單位壓應力變化 引起的單位體積變化(MPa-1)與土的壓縮系數(shù)，土的壓縮指數(shù)一樣，體積壓縮系數(shù)植越大，土的壓縮 性越高。The compression coefficient av, the compression index C c, the coefficient of volume compressibi

31、lity mv, the compression modulus Es, and the deformation modulus E are all indicators of the compression characteristics of soil. These parameters can be used for the settlement calculation, although they have different meanings.壓縮曲線特征：土體變形機理非常復雜，不是理想的彈塑性體，而是具 彈、粘、塑性 的自然歷史的產(chǎn)物(1)卸荷時，試樣不是沿初始壓縮曲線，而是沿曲線

32、bc回彈，可見土體的變形是由可恢復的彈性變形和不可恢復的塑性變形兩部份組成。(2)回彈曲線和再壓線曲線構成一逗滯環(huán)，土體不是完全彈性體；(3)回彈和再壓縮曲線比壓縮曲線平緩得多。(4)當再加荷時的壓力超過 b點，再壓縮曲線就趨于初始壓縮曲線的延長線.Typical plots of void ratio (e) after consolidation, against effective stress (p) for a saturated clay, are shown in the Fig., showing an initial compression followed by expan

33、sion and recompression, namely aloading-swelling-reloading sequence. During loading, the soil is compressed and becomes more dense, and therefore stiffer, so that the e-p relationship is curved and getting less steep. The shapes of the curves are related to the stress history of the clay. During com

34、pression, changes in soil structure continuously take place and the clay does not revert to the original structure during expansion. The plots show that a clay in the state represented by the recompression curve will be much less compressible than the same clay in a state represented by the virgin c

35、ompression curve. All in all, the following features can be identified from the figure:(4) during unloading or expansion, the soil specimen rebounds along the rebounding curve bc, rather than the virgin compression curve ab. This shows that the soil deformation is made up of two components, one is r

36、ecoverable elastic deformation, another is irrecoverable plastic deformation;(2)rebounding or expansion curve and recompression curve constitutes a hysteretic loop, which indicates that the soil is not a fully elastic material;(3)the slope of the rebounding curve and the recompression curve are gent

37、ler than that of the virgin compression curve;(4)the recompression curve ultimately joins the virgin compression curve: further compression then occurs along the virgin curve.4.2.2 現(xiàn)場載荷試驗及變形模量 （in-situ load test and the deformation modulus）現(xiàn)場載荷試驗是在工程現(xiàn)場通過千斤頂逐級對置于地基土上的載荷板施加荷載，觀測記錄沉降隨時p-s曲線,間的發(fā)展以及穩(wěn)定時的沉

38、降量s,將上述試驗得到的各級荷載與相應的穩(wěn)定沉降量繪制成即獲得了地基土載荷試驗的結果。In-situ load test is performed in field, the relationship between the settlement and the time are measured and find the stable settlement under a given load. Finally, as the test results, theo-s curve (load-settlement) can be drawn. From the in-situ tests,

39、the deformation modulus can be obtained.土的變形模量：土體在無側向約束條件下，豎向應力與豎向應變的比值。豎向應變中包括彈性應變 和塑性應變，稱之為變形模量。Deformation modulus: the ratio of the vertical load to the vertical strain is called as Deformation modulus . The vertical strain includes the elastic strain and the plastic strain.根據(jù)地基沉降的彈性力學公式（公式 5-23

40、）s i 2 bpi / si來反求地基土的變形模量。其計算公式為2From the elastic solution of s 1bpi / si , thedeformation modulus of the ground soil can be given as2Eo 1bpi / siE。： 土的變形模量，0.88 ,圓形板 0.79 )。:形狀系數(shù)，對剛性板，應取 r按表5-8查取（方形板 b:承壓板的邊長或直徑，pi：所取定的比例界限荷載si：與取定的比例界限荷載相對應的沉降，在 p-s曲線不出現(xiàn)起始的直線段時，可取為(0.0i0 0.0i5 ) b在深層平板載荷實驗時，土的變形模

41、量的計算公式為：2E0I ibpi /siI :承壓板埋深z時的修正系數(shù)，當zb時，I=0.5+0.23b/z ,其余符號與上式同。WhereE0： deformation modulus:coefficient of shape, for a rigid plate, the values of r are as shown in table 5-8 (square: 0.88, circle:0.79)。b: the length or the diameter of the plate, pi: the given limit loadsi： the settlement accordi

42、ng to pi, if in the curve p-s, the beeline cannot be seen, the value is considered as (0.0i0-0.0i5) bFor the deep plate loading tests the deformation modulus is given as:2E0I 1 bp1 /s1I:承壓板埋深z時的修正系數(shù)，當zb時，I=0.5+0.23b/z,其余符號與上式同。I ： Modification coefficient of depth of plate , when zb, I=0.5+0.23b/z.變

43、形模量與壓縮模量的關系(Relationship between the deformation modulus and thecompression modulus)zE0K0zE0yE0xE01E02 K0z zEsE0Es(1)EsUnder laterally confined conditionThe relationship between the deformation modulus and the compression modulus is given as此公式的推導過程要求學生參照p.99-p.100的內(nèi)容自行推倒，并安排 4.2.3為自學內(nèi)容，從而達到理解土內(nèi)部的應力

44、間的特性，掌握變形模量與壓縮模量兩者之間的關系，為學習以后的章節(jié)奠定基 礎。4.3 飽和土中的有效應力4.3.1 飽和土中的有效應力原理作用于飽和土體內(nèi)某截面上總的正應力s由兩部分組成：一部分為孔隙水壓力u,它沿著各個方向均勻作用于土顆粒上，其中由孔隙水自重引起的稱為靜水壓力，由附加應力引起的稱為超靜孔隙水壓 力(孔隙水壓力)；另一部分為有效應力s,它作用于土的骨架(土顆粒)上，其中由土粒自重引起 的即為土的自重應力，由附加應力引起的稱為附加有效應力。飽和土中總應力與孔隙水壓力、有效應 力之間存在如下關系。The resistance or a reaction to the total st

45、ress in a saturated soil is provided by a combination of the stresses from the solids(effective stress) and water in pores(pore water pressure), the relationship between the total stress , the pore water pressure and the effective stress is u或 u1)任一平面上受到的總應力等于有效應力加孔隙水壓力之和；2) 土的強度的變化和變形只取決于土中有效應力的變化。

46、如下圖，根據(jù)有效應力原理，C點處的豎向有效應力為(as shown in the below figure, from theeffective principle, the vertical effective stress at point C is),u1h1sath2wh21h1h2 ( 為浮重度)。這與第3章地下水位以下水對土柱體有浮力作用的概念是一致的。hi4.3.2 水中水滲流時的土中有效應力(soil effective stress when seepage occurs)當?shù)叵滤疂B流時，土中水將對土顆粒作用著滲流力，如下圖所示的兩種情況。Under seepage cond

47、ition, the seepage force to the soil particle will occurs, as shown in the below figures.BA-hih2sat不同情況水滲流時土中總應力的分布是相同的，土中水的滲流不影響總應力植。水滲流時產(chǎn)生滲 流力，致使土中有效應力及孔隙水壓力發(fā)生變化。土中水自上向下滲流時，滲流力方向與重力方向相 同，有效應力增加，孔隙水壓力減少。反之，土中水自下向上滲流時，滲流力方向與重力方向相反， 有效應力減少，孔隙水壓力增加。The distribution of total stress is same even under d

48、ifferent seepage condition. The seepage can not influence the total stress. Due to the seepage force, the effective stress and the pore water stress will change. When the water seepage upward, the seepage force is opposite to the gravity, the effective stress will decrease. On the contrary, when the

49、 water seepage downward, the direction of the seepage force is same as the gravity, the effective stress will increase.4.3.3 毛細水上升時的土中有效應力土的毛細性是指能夠產(chǎn)生毛細現(xiàn)象的性質(zhì)，土的毛細現(xiàn)象是指土中水在表面張力作用下，沿著細的 孔隙向上及其它方向移動的現(xiàn)象。毛細現(xiàn)象在以下四個方面對工程有影響：(1)毛細水的上升是引起路基凍害因素之一；(2)對建筑毛細水上升引起地下室過分潮濕；(3)毛細水的上升可能引起土地的沼澤化和鹽漬化；(4)當?shù)叵滤薪g性時，毛細水上升對

50、建筑物和構筑物的基礎中的混凝土、鋼筋等形成浸蝕作用。 其全應力，有效應力的分布形式如下圖。4.4 土的單向固結理論 (1 dimensional consolidation theory)4.4.1 飽和土體的滲透(流)固結 (Consolidation of saturated soil) 定義：飽和土體在壓力作用下，孔隙中水隨時間的增長 逐漸被排出，同時孔隙體積也隨之減少的過程稱為飽和土體的滲透(流)固結過程。The compression of a saturated soil is a result of drainage of pore water and the correspon

51、ding contract of the void volume. The process of the drainage of the pore water is called the process of consolidation of saturated soil 壓縮固Z過程(process of consolidation): a) 土體孔隙中自由水逐漸排出；b) 土體體積逐漸減少； c)孔隙水壓力逐漸轉移到土骨架來承受，成為有效應力。 以上三方面為飽和土體固結作用，即 排水、壓縮和壓力轉 移，飽和土體的滲透固結，可以用彈簧活塞模型來說明：以彈簧模擬土骨架，圓筒中的水模擬孔隙中 水

52、；活塞模擬土的透水性，活塞上作用b A壓力。a) The free water gradually outflow. b) The volume of soil is gradually reduced. c) The pore water pressure is gradually transferred to soil fabric, changed as effective stress. The procedure includes: drainage, compression, pressure transition.4.4.2 太沙基一維固結里論。(Terzaghi s theor

53、y of one dimensional consolidation)基本假設：1 . 土層是均質(zhì)、各向同性和完全飽和的；2 . 土的壓縮完全是由于孔隙體積的減少，土粒和水是不可壓縮的；3 .水的滲流和土層的壓縮僅在豎向發(fā)生；4 .水的滲流遵從達西定律；5 .滲透系數(shù)k和壓縮系數(shù)a保持不變。6 .外荷載一次瞬時施加。7 . 土體變形完全是孔隙水壓力消散引起的。Assumptions in the theory1 The soil is homogenous and saturated.2 The solid particles and water are incompressible.3 Co

54、mpression and flow are one-dimensional (vertical, i.e., in the direction of the applied pressure).4 Strains are small5 Darcys law is valid at all hydraulic gradient6 The coefficient of permeability k and the coefficient of volume compressibility mv remain constant throughout the process.7 There is a

55、 unique relationship, independent of time, between void ratio and effective stress.h .流出水量(Flow out the unit element) q k2h zdz dxdy水量變化為(Volume change of water) q q k-hdxdydz z單位單元體中孔隙體積變化率 （減少）為一Vwte- dxdydz ,根據(jù)固結滲流的連續(xù)條件,t 1 e單位單兀體白勺流入水重 (Flow in the unit element) q kiA k dxdy z單元體在某一時間的水量變化應等于單元體

56、中孔隙體積的變化，并考慮到單元體內(nèi)土粒體積1dxdydz為不變的吊數(shù)，因此可知：The rate of the void volume change of the unit element (Contraction) isSince the volume change of water is equal to the void volume change,Vw t and thetsoiledxdydz .1 eparticle volume1 ，一dxdydz1 e*八 k zis constant, the follow equation can be obtained.(4-22 )再根

57、據(jù)土的應力應變關系的側限條件，有： de adpFrom the stress-strain relationship under confined condition, equation (4-22),adde并將此公式代入上式，則有adp ad , and substitute it intok 1 e 2h, 1Tk a zmv2h(4-24)根據(jù)全應力與有效應力的關系,t且有單元體中的孔隙水壓力為wh和tu代入4-24式即可得到一維固結的微分方程是4-25tFrom the relationship of the total stress and the effective stress, and the pore water pressure is u wh ,2hsubstitute z1_2u w z2 , tu; into equation 4-2