土的壓縮性及固結(jié)理論

1、第4章 土的壓縮性及固結(jié)理論基本內(nèi)容這是本課程的重點(diǎn)。在學(xué)習(xí)土的壓縮性指標(biāo)確定方法的基礎(chǔ)上，掌握地基最終沉降量計(jì)算原理和地基固結(jié)問(wèn)題的分析計(jì)算方法。學(xué)習(xí)要求：1. 掌握土的壓縮性與壓縮性指標(biāo)確定方法；2掌握有效應(yīng)力原理；3掌握太沙基一維固結(jié)理論；4.1 概述(outline)土在自重應(yīng)力或附加應(yīng)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(duì)于土來(lái)說(shuō)，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 induced

2、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 compact the

3、 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 not allo

4、wed to happen in the ground.土的壓縮性主要有兩個(gè)特點(diǎn)：（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(duì)于飽和粘土來(lái)說(shuō)需要時(shí)間，將土的壓縮隨時(shí)間增長(zhǎng)的過(guò)程稱為土的固結(jié)。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(duì)沉降量的大小，亦即最終沉降；二是沉降與時(shí)間的關(guān)系，主要介紹太沙基的一維固結(jié)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；(3) 孔隙水和孔隙氣體的排出。由于純水的彈模約為2106kPa，固體顆粒的彈模為

5、9l 07kPa，土粒本身和孔隙中水的壓縮量，在工程壓力(100600kPa)范圍內(nèi)，不到土體總壓縮量的1/400，因此?？陕圆挥?jì)。所以，土體壓縮主要來(lái)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(gè)時(shí)間過(guò)程。因此土的壓縮亦要一段時(shí)間才能完成。把這一與時(shí)間有關(guān)的壓縮過(guò)程稱為固結(jié)。土體的變形計(jì)算，需要取得土的壓縮性指標(biāo)，可以通過(guò)室內(nèi)側(cè)限壓縮試驗(yàn)和現(xiàn)場(chǎng)原位試驗(yàn)得到。室內(nèi)壓縮試驗(yàn)亦稱固結(jié)試驗(yàn)，是研究土壓縮性最基本的方法?，F(xiàn)場(chǎng)載荷試驗(yàn)是在工程現(xiàn)場(chǎng)通過(guò)千斤頂逐級(jí)對(duì)置于地基土上的載荷板施加荷載，觀測(cè)記錄沉降隨時(shí)間的發(fā)展以及穩(wěn)定時(shí)的沉降量s，并繪制成p-s曲線，即獲得地基土載荷試驗(yàn)的結(jié)果。反映土

6、的壓縮性的指標(biāo)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(biāo)定量表示，壓縮性指標(biāo)，通常由工程地質(zhì)勘察取天然結(jié)構(gòu)的原狀土樣進(jìn)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 due to struc

7、ture load. The contents on studying structure settlement include 1 The absolute settlement (final settlement)2 Relationship between settlement and time. Introducing terzaghis 1D consolidation theoryReasons of volumetric reduction of soil mass1 The compressive deformation of the soil particles.2 The

8、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 discharge un

9、der 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 deformation of th

10、e 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(jié)試驗(yàn)及壓縮性指標(biāo)(Oedometer test, Consolidation test and Compression indexes) 側(cè)限壓縮試驗(yàn)亦稱固結(jié)

11、試驗(yàn)。所謂側(cè)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(wú)側(cè)向變形。室內(nèi)壓縮試驗(yàn)采用的試驗(yàn)裝置為壓縮儀或固結(jié)儀(參照?qǐng)D4-1)。試驗(yàn)時(shí)將切有土樣的環(huán)刀置于剛性護(hù)環(huán)中，由于金屬環(huán)刀及剛性護(hù)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(wú)側(cè)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(gè)界面。壓縮過(guò)程中豎向壓力通過(guò)剛性板施加給土樣，土樣產(chǎn)生的壓縮量可通過(guò)百分表量測(cè)。常規(guī)壓縮試驗(yàn)通過(guò)逐級(jí)加荷進(jìn)行試驗(yàn)，常用的分級(jí)加荷量p為：50kPa,100kPa,200kPa,300kPa,400kPa。Compression test with zero lateral strain is

12、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 diameter to height rat

13、io 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 assembly sits in an op

14、en 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 friction. The confi

15、ning 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 loading cap. Usual

16、ly the specimen is gradually loaded, and the load grades are often set as p=50kPa, 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 applied load a

17、nd 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(gè)條件，可得出：The soil compression characteristic has been discussed in the last section. This s

18、ection 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 established based

19、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 pore volume.

20、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 p1. assume the height of the soil sp

21、ecimen is h, the volume of soil particle Vs, the corresponding void ratio e1,then the pore volume is vs and the total volume V1 is(1+e1) Vs. if the effective stress is increased to p2 equal to (p1+p),the height of the soil specimen after compression is H2,As shown in the below figures, because the v

22、olume of soil particle and the soil cross section do not change, the void ratio after compression can be calculated as follows:H0H0/（1+e0）Hi/（1+ei）HidHVs=1Vs=1Vv=e0Vv=eipi而 公式中分別為土粒比重，初始含水量，初始密度和水的密度。因此只要測(cè)的的穩(wěn)定壓縮量就可按上式算得相應(yīng)的孔隙比，從而繪制土的壓縮曲線。Where, are the specific gravity of solids, initial water conten

23、t, 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-logp曲線e-p曲線可確定土的壓縮系數(shù)，壓縮摸量等指標(biāo)，e-logp曲線可確定土的壓縮指數(shù)等壓縮性指標(biāo)。壓縮系數(shù)(compression coefficien

24、t)的定義為“曲線上任意兩點(diǎn)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.式中負(fù)號(hào)表示隨著壓力p的增加，e逐漸減少。壓縮性不同的土，其壓縮曲線的形狀是不一樣的。曲線愈陡，說(shuō)明隨著壓力的增加，土孔隙比的減小

25、愈顯著，因而土的壓縮性愈高。a1-2-1時(shí)，低壓縮性土(low compressible soil)a1-2b時(shí)，I=0.5+0.23b/z，其余符號(hào)與上式同。Where E0：deformation modulus：coefficient of shape, for a rigid plate, the values of are as shown in table 5-8（square: 0.88，circle:0.79）。b：the length or the diameter of the plate, p1：the given limit loads1： the settlement

26、 according to p10.015）bFor the deep plate loading tests，the deformation modulus is given as：I：承壓板埋深z時(shí)的修正系數(shù)，當(dāng)zb時(shí)，I=0.5+0.23b/z，其余符號(hào)與上式同。I：Modification coefficient of depth of plate變形模量與壓縮模量的關(guān)系(Relationship between the deformation modulus and the compression modulus) Under laterally confined condition

27、 The relationship between the deformation modulus and the compression modulus is given as此公式的推導(dǎo)過(guò)程要求學(xué)生參照p.99-p.100的內(nèi)容自行推倒，并安排4.2.3為自學(xué)內(nèi)容，從而達(dá)到理解土內(nèi)部的應(yīng)力間的特性，掌握變形模量與壓縮模量?jī)烧咧g的關(guān)系，為學(xué)習(xí)以后的章節(jié)奠定基礎(chǔ)。4.3 飽和土中的有效應(yīng)力作用于飽和土體內(nèi)某截面上總的正應(yīng)力s由兩部分組成：一部分為孔隙水壓力u，它沿著各個(gè)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(yīng)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

28、應(yīng)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(yīng)力，由附加應(yīng)力引起的稱為附加有效應(yīng)力。飽和土中總應(yīng)力與孔隙水壓力、有效應(yīng)力之間存在如下關(guān)系。The resistance or a reaction to the total stress 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

29、total stress , the pore water pressure and the effective stress is1）任一平面上受到的總應(yīng)力等于有效應(yīng)力加孔隙水壓力之和；2）土的強(qiáng)度的變化和變形只取決于土中有效應(yīng)力的變化。如下圖，根據(jù)有效應(yīng)力原理，C點(diǎn)處的豎向有效應(yīng)力為(as shown in the below figure, from the effective principle, the vertical effective stress at point C is)，（為浮重度）。這與第3章地下水位以下水對(duì)土柱體有浮力作用的概念是一致的。ABCh1h24.3.2 水

30、中水滲流時(shí)的土中有效應(yīng)力(soil effective stress when seepage occurs) 當(dāng)?shù)叵滤疂B流時(shí)，土中水將對(duì)土顆粒作用著滲流力，如下圖所示的兩種情況。Under seepage condition, the seepage force to the soil particle will occurs, as shown in the below figures.ABCh1h2ABCh1h2hh不同情況水滲流時(shí)土中總應(yīng)力的分布是相同的，土中水的滲流不影響總應(yīng)力植。水滲流時(shí)產(chǎn)生滲流力，致使土中有效應(yīng)力及孔隙水壓力發(fā)生變化。土中水自上向下滲流時(shí)，滲流力方向與重力方向相同

31、，有效應(yīng)力增加，孔隙水壓力減少。反之，土中水自下向上滲流時(shí)，滲流力方向與重力方向相反，有效應(yīng)力減少，孔隙水壓力增加。The distribution of total stress is same even under different 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 upwa

32、rd, the seepage force is opposite to the gravity, the effective stress will decrease. On the contrary, when the water seepage downward, the direction of the seepage force is same as the gravity, the effective stress will increase.土的毛細(xì)性是指能夠產(chǎn)生毛細(xì)現(xiàn)象的性質(zhì)，土的毛細(xì)現(xiàn)象是指土中水在表面張力作用下，沿著細(xì)的孔隙向上及其它方向移動(dòng)的現(xiàn)象。毛細(xì)現(xiàn)象在以下四個(gè)方面對(duì)

33、工程有影響：（1）毛細(xì)水的上升是引起路基凍害因素之一；（2）對(duì)建筑毛細(xì)水上升引起地下室過(guò)分潮濕；（3）毛細(xì)水的上升可能引起土地的沼澤化和鹽漬化；（4）當(dāng)?shù)叵滤薪g性時(shí)，毛細(xì)水上升對(duì)建筑物和構(gòu)筑物的基礎(chǔ)中的混凝土、鋼筋等形成浸蝕作用。ABCh1h2 其全應(yīng)力，有效應(yīng)力的分布形式如下圖。 4.4 土的單向固結(jié)理論(1 dimensional consolidation theory)4.4.1 飽和土體的滲透（流）固結(jié)(Consolidation of saturated soil) 定義：飽和土體在壓力作用下，孔隙中水隨時(shí)間的增長(zhǎng)逐漸被排出，同時(shí)孔隙體積也隨之減少的過(guò)程稱為飽和土體的滲透（流）

34、固結(jié)過(guò)程。 The compression of a saturated soil is a result of drainage of pore water and the corresponding contract of the void volume. The process of the drainage of the pore water is called the process of consolidation of saturated soil壓縮固結(jié)過(guò)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

35、漸轉(zhuǎn)移到土骨架來(lái)承受，成為有效應(yīng)力。以上三方面為飽和土體固結(jié)作用，即排水、壓縮和壓力轉(zhuǎn)移，飽和土體的滲透固結(jié)，可以用彈簧活塞模型來(lái)說(shuō)明：以彈簧模擬土骨架，圓筒中的水模擬孔隙中水；活塞模擬土的透水性，活塞上作用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

36、includes: drainage, compression, pressure transition. 4.4.2 太沙基一維固結(jié)里論。(Terzaghis theory of one dimensional consolidation)基本假設(shè)：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(dá)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(shí)施加。7土體變形完全是孔隙水壓力消散引起的。Assumptions in the theory 1 The soil is homo

37、genous and saturated. 2 The solid particles and water are incompressible. 3 Compression and flow are one-dimensional (vertical, i.e., in the direction of the applied pressure). 4 Strains are small 5 Darcys law is valid at all hydraulic gradient 6 The coefficient of permeability k and the coefficient

38、 of volume compressibility mv remain constant throughout the process. 7 There is a unique relationship, independent of time, between void ratio and effective stress.單位單元體的流入水量(Flow in the unit element) 流出水量(Flow out the unit element)水量變化為(Volume change of water) 單位單元體中孔隙體積變化率（減少）為 , 根據(jù)固結(jié)滲流的連續(xù)條件，單元體在

39、某一時(shí)間的水量變化應(yīng)等于單元體中孔隙體積的變化，并考慮到單元體內(nèi)土粒體積為不變的常數(shù)，因此可知： The rate of the void volume change of the unit element (Contraction) is . Since the volume change of water is equal to the void volume change, and the soil particle volume is constant, the follow equation can be obtained.* （4-22） 再根據(jù)土的應(yīng)力應(yīng)變關(guān)系的側(cè)限條件，有： 并

40、將此公式代入上式，則有 From the stress-strain relationship under confined condition, , and substitute it into equation （4-22）, （4-24） 根據(jù)全應(yīng)力與有效應(yīng)力的關(guān)系，且有單元體中的孔隙水壓力為 以和 代入4-24式即可得到一維固結(jié)的微分方程是4-25From the relationship of the total stress and the effective stress, and the pore water pressure is , substitute , into eq

41、uation 4-24, we can obtain the differential equation 4-25 of one-dimensional consolidation. 4-25a 4-25b 4-25c ：稱為土的豎向固結(jié)系數(shù)(coefficient of consolidation)。在如下初始條件和邊界條件如下(under the follow initial and boundary conditions):t = 0和 0 z H 時(shí), u =u0=p0 t 和 z = 0 時(shí), u = 00 t 和 z = H 時(shí), t = 和 0 z H 時(shí), u=0式中 Cv：

42、固結(jié)系數(shù), , a ： 土的壓縮系數(shù)，k ：土的滲透系數(shù)采用分離變量法，可求得滿足初始條件和邊界條件的解答如下(The solution for the excess pore water pressure at depth z after time t is) (4-26)：時(shí)間因素(time factor).H土層最遠(yuǎn)的排水距離，當(dāng)土層為單面(上面或下面)排水時(shí)，H取土層厚度；雙面排水時(shí)，水由土層中心分別向上下兩方向排出，此時(shí)H應(yīng)取土層厚度之半。 H: the longest drainage distance. When the free drainage can only take p

43、lace at one boundary surface, (i.e., one-way drainage), the layer is said to be half-closed layer, and the length of the drainage path equal the thickness of the layer. If free drainage takes place on its upper and lower surfaces (i.e., two-way drainage), the layer is said to be an open layer and the length of the drainage path is equal to half the thickness of the layer.4.4.3 土的固結(jié)系數(shù) 土的固結(jié)系數(shù)是反映土體固結(jié)快慢的一個(gè)重要指標(biāo)。在地基土層的固結(jié)沉降計(jì)算中，土的豎向固結(jié)系數(shù)cv是一個(gè)控制性指標(biāo)，式（4-25c）表明cv與固結(jié)過(guò)程中孔隙水壓力消散的速度成正比。Cv值越大，在其