Numerical Analysis For Consolidation And Modeling Of Vertical Drains Beneath Embankments On Foundations With Cohesive Soil Layers

Vertical drains is available to expedite the consolidation of cohesive soil and extensivelyapplied over the world in construction engineering of ports, buildings and roadways to reinforcesoft foundations. Sand Drain, is the most representative one in the group of vertical drains. It issuggested to call the foundation with cohesive soil layers improved by sand drains CohesiveSoil-Sand Drained Foundation (CSDF). It is important to research the behavior of sand drains in preloading processing for design andanalysis of ground improving programs. As a typical problem of consolidation process, theinvestigation of seepage and transformation of CSDF is involved with a set of basic questions toconsolidation, such as the models and solutions of consolidation for cohesive soil. Numericalmethod is one of the significant techniques for these problems and has been applied to modelingthe CSDF. In resent years, the reinforcement technique of CSDF, preloading under embankment,vacuum or coupled vacuum-embankment, has been deeply developed in China for constructionof highways. However, the engineers still do their work mainly with experience and classicalanalytical methods since the absence of new efficacious solutions and, the programs are alwaysled to some difficult situations. They help the conditions could be changed.So, it's valuable to develop scientific technique for simulation of CSDF and helpful to dealwith complex conditions for engineers. Here the purposes are presented for the paper: to analysis the normal consolidation behavior ofcohesive soil with numerical methods and abstract new points of view;to develop the modelsand numerical solutions of CSDF. Research results have been established in the dissertation forthese purposes. Uniform model in nonlinear is suggested to be combined with nonlinear constitutive modeland nonlinear seepage model. The basic nonlinear model of consolidation is shown in thediagram as following:In which H-V is the elasto-plastic element, H|N is the visco-elastic element and V|H is thevisco-plastic element for the soil framework, and W is the pore water with Darcy flow ornon-Darcy flow. A common formula is proposed to describe the volume strain speed in onedimensional condition:bPbucccdtautaPttvpvve??ε v =??εz=1 ??+2??+1+2+1εv+2εv+1ε+In which P is the loading on soil column and u is the excess pore pressure, a1,a2,b1,b2,c1,c2,c3,d are parameters involved to the state of effective stress and strain.It is also suggested to write the differential equations of Biot consolidation in matrix form asfollowing:[ K ]δ ? [C]u=F? [C ]T δ& +[G]u=nβu&+QDefinitions are:[K]=[B]T[D][B] —— stiffness matrix[G]=[C]T[H][C]/γw —— seepage matrix[C] —— coupled matrixF —— forces for equilibriumQ —— flux for equilibriumAnd δ is the displacement of soil framework, β is the coefficient for compressibility of water.The advantage of this kind of expression is that it make the analytical equations are very closeto the FEM equations of Biot consolidation.A new theoretical model of consolidation for single sand drain is developed and called as oneDimensional Dual-medium Model (DDM). Rigorous solution is given for fully penetrating sanddrain with the new model as a normal solution for the case of equal vertical strain. DDM hassome advantages related to the theory developed before: the area of soil around sand drain is notsimply marked as smear zone and non-smear zone and the model is available for any distributionof soil permeability;the number of uncertain parameters is decreased from two to only one. Themore important characteristic of DDM, is reducing mostly of the modeling dimensions forCSDF.The consolidation of CSDF is simulated firstly with one dimensional finite differencemodeling based on the DDM and curves of consolidated degree U for non-fully penetrating sanddrain is obtained. According to the comparing of results, systemic error is found in approximatedformulations proposed before for non-fully penetrating sand drain. The U calculated by China'sand Xie's(1987) methods are too great and the Hart's method is suitable at the beginning ofconsolidation and much too small at last. The errors of Xie's(1987) method increases withdecreases of length of sand drains.The commonly used technique for numerical modeling of sand drains, replacing sand drainsby equivalent sand grooves or named as sand walls, is modified based on DDM. Equivalence ofdifferential equations is strictly satisfied in the modified method and the distance betweenvertical drains is not magnified yet done in the others. Also the modified method is available fornon-fully penetrating sand drains.Difference format of non-linear consolidation equations is developed in the case of onedimension and microcomputer code NLCL is established for modeling process.This program is applied to analysis non-linear effects in K0 consolidation, including Davis'smodel, non-Darcy model and rheological model.For Davis's model, the non-linear dimensionless consolidation equation is simulated:vcTUZUUUZk??? [ ? ??]=1?with conditions:①Tv=0, U=1;②Z=0, U=1+P/σ′z0 = n +1;③Z=1,U=n+1In which ck is the attenuation index of conductivity with increase of effective stress and n=P/σ′z0is the degree of loading related to initial effective stress。The equation had been investigated byDavis(1965) in analytical solution while ck=1 but modeling results are obtained with any cases ofck and n in the paper.The effects of two possible types of non-Darcy flow are discussed according to modelingresults. An important new conclusion for the existence of non-Darcy flow in soil columnexperiments is presented from reviewing of the analysis given by previous researcher. Twomistakes are found in previous analysis of soil column experiments: (1) transformation of soilframework was neglected during unsteady flow of pore water;(2) the effects of observationinstruments to the results of experiment were neglected. The mistakes are associated with aviewpoint that the phenomenon in soil column experiments shows non-Darcy flow in clay.However, it's proved in this paper, with analytical solution and water pressure-tube modifiednumerical modeling, that linear theory of consolidation with Darcy flow has enough satisfiabilityto the soil column experiment presented by Feng(1995) and by contraries non-Darcy flow'ssolutions are not agree to the data observed.Finite element method (FEM) for Biot consolidation and finite difference method (FDM) forTerzaghi consolidation of soft foundations with sand grooves are studied in the paper. Modelingcode CFEM2 and CFDM2 are developed to accomplish the simulation work.It's found from repeatedly modeling test that, to ensure the convergence of iterative solutionprocedure for coupled numerical equations of consolidation, time steps should be restricted as:max2()[()]Cv?t >sω ?LWhere ?t is the length of time step, ?L is the scale of elements in network and Cv is thecoefficient of consolidation. The function s(ω) gives a value greater than zero and increasingwith increase of the acceleration factor ω.The applicability of FEM and FDM is discussed for soft foundations. Compared to the resultsof FEM, excess pore pressure is greater and settlement is smaller which given by FDM. Thedifferences of settlement on the surface arises from drains is too great with FDM. The viewpointis proposed that FEM is more reasonable than FDM since it deal with the transformation andexcess pore pressure at the same time considering coupled consolidation but settlement valuesare indirectly obtained from excess pore pressure with FDM. However, FDM is simple forapplication and available to the cases of precision demand less than 10%.Some common characteristics have been shown in modeling of soft foundations with sandgrooves such as the stiffness of shallow pre-consolidated soils do influence to the settlement offoundation remarkably.The PDSS ( Plane Deformation & Spatial Seepage) modeling method which proposed by Xiein 1987 is suggested to be the most valuable procedure for simulation of CSDF.The paper has developed Xie's PDSS model at some aspects as following:1.Distribution of sand drains is not directly treated while the grid patterns are triangular inXie's model. To solve the problem, three symmetric sections are selected to excavate themodeling space:and the space is divided into spatial elements with 6 nodes or 8 nodes.2. A sand drain is located on a series of element in column with the shape of square in Xie'smodel. It is pointed out that the procedure is not correct for radial flow around sand drains andwould bring errors of excess pore pressure at the degree of 7.3% or more. In the paper, atechnique developed in hydrogeology for well flow in numerical analysis of groundwater isintroduced to the modeling of sand drains. The modified numerical flow model in threedimensions is successful to consider the smear action and well resistance effect.3. The place of nodes in the FEM network are fixed in Xie's model. It is not proper for thestrain of soil is always larger than 10% and great settlement would reshape the foundation. So,the location of grid nodes are moveable in modified model.4. Also the effects of large and uneven settlement to actual load distribution on the surface offoundations are neglected in Xie's model and considered in the paper.xySection 1Section 2Section 3 Drains5. The model is improved to be able to accomplish inverse programs. The values of parametersinput to the model are auto-optimal adjusted by compare the modeling results with observeddata.A C++ code program FDSPACE is designed according to above modifies for FEM modelingof CSDF.The program has been successfully used to a case study of preloading project for softfoundation beneath highway embankment in Guangdong province, China. The foundation wasdrained by sand drains 21.5 m long and preloaded by combined vacuum and embankment. Largesettlement more than 3.0m had been observed in about 2.5 years.Liner elastic model, Duncan-Chang's model and Cambridge Clay model and models forsecondary compression are introduced to clay layers in the ground. The optimal values of 54parameters are obtained from inverse procedure. It is indicated that Cambridge Clay model is themost satisfactory one among the models. Liner elastic model is not able to simulate the plasticpatterns of cohesive soils.It has been predicted that the post-construction subsidence of the foundation would be over to0.5m in 10 years.The development of seepage fields and stress fields in the foundation are investigatedaccording to the modeling results and flux of pore water in the sand drains are analyzed.The actions of some factors to consolidation of CSDF under vacuum and embankmentcombined preloading, such as length and interval of sand drains, depth and thickness of sandylayers, are studied in the paper. It's indicated that the sand drains have functions at large depthmore than 20m in the ground. Compared to preloading by embankment only, preloading bycombined vacuum and embankment is beneficial to shorten construction period of embankmentfilling and decrease the post-construction subsidence without failing on steady of the foundation.The research results presented above have advantages for studies of numerical methods in soilmechanics and for practices of soft ground improvement techniques.