Analytical and Numerical Modeling of Soft Soil Stabilized by Prefabricated Vertical Drains Incorporating Vacuum Preloading

This paper describes the analytical formulation of a modified consolidation theory incorporating vacuum pressure, and numerical modeling of soft clay stabilized by prefabricated vertical drains, with a linearly distributed (trapezoidal) vacuum pressure for both axisymmetric and plane strain conditions. The effects of the magnitude and distribution of vacuum pressure on soft clay consolidation are examined through average time-dependent excess pore pressure and consolidation settlement analyses. The plane strain analysis was executed by transforming the actual vertical drains into a system of equivalent parallel drain walls by adjusting the coefficient of permeability of the soil and the applied vacuum pressure. The converted parameters are incorporated in the finite element code ABAQUS, employing the modified Cam-clay theory. Numerical analysis is conducted to study the performance of a full-scale test embankment constructed on soft Bangkok clay. The performance of this selected embankment is predicted on the basis of four different vacuum pressure distributions. The predictions are compared with the available field data. The assumption of distributing the vacuum pressure as a constant over the soil surface and varying it linearly along the drains seems justified in relation to the field data.     

Analytical and Numerical Modeling of Consolidation by Vertical Drain beneath a Circular Embankment

In the analysis of axisymmetric problems, it is often imperative that aspects of geometry, material properties, and loading characteristics are either maintained as constants or represented by continuous functions in the circumferential direction. In the case of radial consolidation beneath a circular embankment by vertical drains (i.e., circular oil tanks or silos), the discrete system of vertical drains can be substituted by continuous concentric rings of equivalent drain walls. An equivalent value for the coefficient of permeability of the soil is obtained by matching the degree of consolidation of a unit cell model. A rigorous solution to the continuity equation of radial drainage towards cylindrical drain walls is presented and verified by comparing its results with the existing unit cell model. The proposed model is then adopted to analyze the consolidation process by vertical drains at the Sk?-Edeby circular test embankment (Area II). The calculated values of settlement, lateral displacement, and excess pore-water pressure indicate good agreement with the field measurements.     

Finite-Element Parametric Study of the Consolidation Behavior of a Trial Embankment on Soft Clay

The paper presents a case study for numerical analysis of the consolidation behavior of an instrumented trial embankment constructed on a soft soil foundation. Details are given to the geological profile, field instrumentation, laboratory test results, and determination of soil parameters for numerical modeling. Embankment settlement is estimated based on one-dimensional consolidation analysis and nonlinear finite-element analysis following Biot’s consolidation theory. Finite-element results are calibrated against the measured field data for a period of more than 3?years. Development and dissipation of excess pore pressure, long-term settlement, and horizontal displacement are predicted and discussed in light of sensitivity of embankment performance to some critical factors through a parametric study.     

Estimation of Degree of Consolidation for Vacuum Preloading Projects

The degree of consolidation is usually used as one of the criteria for assessing the effectiveness of soil improvement work using the fill surcharge or vacuum preloading method. It is also often used as a design specification in a soil improvement contract. Degree of consolidation is normally calculated using settlement data. However, as the effect of vacuum preloading is controlled largely by pore water pressure changes, it is necessary to analyze the pore water pressure variations and to assess the degree of consolidation using pore water pressures. In this paper, the problems involved in the estimation of degree of consolidation using settlement data are discussed. A method to estimate the average degree of consolidation using pore water pressure data is suggested. Two case studies are presented to examine the characteristics of the pore water pressure variation of soil under vacuum loading. The degree of consolidation achieved in each of the two cases is assessed using pore water pressure data and compared with that estimated using settlement data. Factors affecting the degree of consolidation assessment are discussed.     

Performance of a Geogrid-Reinforced and Pile-Supported Highway Embankment over Soft Clay: Case Study

This paper describes a case history of a geogrid-reinforced and pile-supported (GRPS) highway embankment with a low area improvement ratio of 8.7%. Field monitored data from contact pressures acting on the pile and soil surfaces, pore-water pressures, settlements and lateral displacements are reported and discussed. The case history is backanalyzed by carrying out three-dimensional (3D) fully coupled finite-element analysis. The measured and computed results are compared and discussed. Based on the field observations of contact stresses and pore-water pressures and the numerical simulations of the embankment construction, it is clear that there was a significant load transfer from the soil to the piles due to soil arching. The measured contact pressure acting on the pile was about 14 times higher than that acting on the soil located between the piles. This transfer greatly reduced excess positive pore water pressures induced in the soft silty clay. The measured excess pore water pressure ratio max in the soft silty clay was only about 0.3. For embankment higher than 2.5?m, predictions of stress reduction ratio based on two common existing design methods are consistent with the measured values and the 3D numerical simulations. During the construction of the piled embankment, the measured lateral displacement–settlement ratio was only about 0.2. This suggests that the use of GRPS system can reduce lateral displacements and enhance the stability of an embankment significantly.     

半透水边界砂井真空联合堆载预压Hansbo固结解

把砂井地基上下边界视为半透水边界,以研究顶部垫层和底部下卧层透水特性对砂井地基固结过程的影响.根据轴对称固结方程和等应变假定,利用Hansbo法获得了真空联合堆载预压下半透水边界砂井地基的固结解答,分析了上下边界透水系数对真空和堆载预压固结度和沉降的影响,比较了真空单独预压下本文解与Indraratna等解答和周琦等解答的联系和差别.研究表明,(1)不管真空预压还是堆载预压,固结时间因子相同时地基固结度随边界透水系数增大而增大.(2)对于真空预压,下边界透水系数越大,地基的最终沉降越小,固结期间时间因子相同时的沉降也越小;上边界透水系数越大,固结期间时间因子相同时的沉降越大.(3)对于堆载预压,不管上边界还是下边界,边界透水系数越大,最终沉降不变,而固结期间时间因子相同时的沉降越大.(4)当真空预压上边界透水时,周琦等解答的固结度大于本文解答的固结度大于Indraratna等解答的固结度.为了提高真空预压的最终沉降,需减少地基下边界的透水性.      

Stabilized Dredged Material. II: Geomechanical Behavior

This study presents the results of a detailed geotechnical evaluation of six stabilized dredged material (SDM) blends incorporating various combinations of lime, cement kiln dust, high alkali and slag cements, and Class F fly ash. The dredged material classified as CH/OH soil with an in situ moisture content (MC) of approximately 130% and void ratio of 3.35. Mix designs and unconfined compression strength tests were completed for each SDM blend based on 3-day mellowing characteristics. Compacted dry densities were on the order of 7.8–11.2?kN/m3 (49–71?lb/ft3), with MCs on the order of 34–73%. Peak effective friction angles ranged from 20–50° with cohesion intercepts on the order of 30–235 kPa (4–34?lb/in.2) using a maximum stress obiliquity criterion. Postpeak effective friction angles (15% axial strain) were routinely in excess of 40° with low cohesion (<40?kPa; 6?lb/in.2). One sample exhibited very strong soil-fabric effects (cohesion) having an effective friction angle of only approximately 9°, but cohesion on the order of 450 kPa (65?lb/in.2). Negligible consolidation of a 28-day cured sample was measured. Also, contrary to expectations based on the high sulfate contents (10,000–30,000 mg/kg) of the SDM blends, negligible swell (<1%) was measured in five of six SDM blends. The main finding of this research is the SDM blends exhibit the strength, compressibility, and bulking characteristics that make them favorable for large fill applications and subgrade improvement applications at costs equivalent to or less than conventional construction materials.     

Nonlinear Dynamic Properties of a Fibrous Organic Soil

The nonlinear dynamic properties of a fibrous peaty organic soil beneath a levee in the Sacramento–San Joaquin Delta in California are described herein. Thin-walled tube samples were obtained from four locations between the levee crest and the free field such that the in situ vertical effective stresses (σvo′) ranged from about 12 kPa in the free field to about 135 kPa beneath the levee crest. The peaty organic soil was very soft and highly compressible in the free field with initial water contents (wo) of 236–588% and shear wave velocities (Vs) of typically 22–27 m/s, and moderately firm beneath the levee crest with wo of 152–240% and Vs of typically 88–129 m/s. Stress–strain measurements in a cyclic triaxial device showed that the normalized secant shear modulus (G/Gmax) and equivalent damping ratio (ξ) versus cyclic shear strain amplitude (γc) relations were dependent on the consolidation stress (σvc′). Tests involving prior overstraining followed by reconsolidation showed that the effects of sample disturbance were likely small. Stress history, creep, and loading frequency effects were also examined. Tests on reconstituted specimens provided supplementary data on the functional relation between maximum shear modulus (Gmax) and consolidation stress conditions. Summary relations are provided for G/Gmax and ξ versus γc and for Gmax versus σvc′.     

Equal Strain Consolidation by Vertical Drains

This paper shows the development of a series of closed-form solutions of equal strain consolidation in the presence of a vertical drain with smear and well resistance. Using an approach that considers the effects of both the radial and vertical drainage in a fully coupled fashion, solutions are obtained for the excess pore pressure and the degree of consolidation in the compressible soil subjected to a step- or ramp-loading situation. The closed-form solutions in the present paper may be evaluated in an electronic spreadsheet on a standard personal computer.     

Probabilistic Analysis of Coupled Soil Consolidation

Coupled Biot consolidation theory was combined with the random finite-element method to investigate the consolidation behavior of soil deposits with spatially variable properties in one-dimensional (1D) and two-dimensional (2D) spaces. The coefficient of volume compressibility (mv) and the soil permeability (k) are assumed to be lognormally distributed random variables. The random fields of mv and k are generated by the local average subdivision method which fully takes account of spatial correlation, local averaging, and cross correlations. The generated random variables are mapped onto a finite-element mesh and Monte Carlo finite-element simulations follow. The results of parametric studies are presented, which describe the effect of the standard deviation, spatial correlation length, and cross correlation coefficient on output statistics relating to the overall “equivalent” coefficient of consolidation. It is shown that the average degree of consolidation defined by excess pore pressure and settlement are different in heterogeneous soils. The dimensional effect on the soil consolidation behaviors is also investigated by comparing the 1D and 2D results.     

Solution Charts for Finite Strain Consolidation of Normally Consolidated Clays

This paper presents graphical solution charts for 1D consolidation of a single homogeneous layer of normally consolidated clay under a surcharge load. Cast in dimensionless form, the charts include the effects of vertical strain, self-weight, and decreasing compressibility and hydraulic conductivity during the consolidation process. To estimate total settlement, the user must specify the initial layer thickness, compression index, initial void ratio at the midheight of the layer, and initial and final effective stress conditions at the top of the layer. To estimate the rate of settlement and distribution of excess pore pressure, boundary drainage conditions and the initial hydraulic conductivity at the midheight of the layer are also required. As a design tool, the charts can be used to make preliminary estimates of settlement and excess pore pressure with fewer restrictive assumptions than for conventional theory. The charts can also be used to verify solutions obtained from numerical analyses. Furthermore, the charts are educational in that they illustrate the effect of different variables on the consolidation process. Using the solution charts, estimated values for settlement are in good agreement with field measurements for a well-documented case study. Estimated and measured values for excess pore pressure are in reasonable agreement during the middle stages of consolidation but are in lesser agreement during the early and later stages.     

Simplified Plane-Strain Modeling of Stone-Column Reinforced Ground

The acceleration of consolidation rate by stone columns was mostly analyzed within the framework of a basic unit cell (i.e., a cylindrical soil body around a column). A method of converting the axisymmetric unit cell into the equivalent plane-strain model would be required for two-dimensional numerical modeling of multicolumn field applications. This paper proposes two simplified conversion methods to obtain the equivalent plane-strain model of the unit cell, and investigates their applicability to multicolumn reinforced ground. In the first conversion method, the soil permeability is matched according to an analytical equation, whereas in the second method, the column width is matched based on the equivalence of column area. The validity of these methods is tested by comparison with the numerical results of unit-cell simulations and with the field data from an embankment case history. The results show that for the case of linear-elastic material modeling, both methods produce reasonably accurate long-term consolidation settlements, whereas for the case of elastoplastic material modeling, the second method is preferable as the first one gives erroneously lower long-term settlements.     

Lateral Force Induced by Rectangular Surcharge Loads on a Cross-Anisotropic Backfill

This article presents approximate but analytical-based solutions for computing the lateral force (force per unit length) and centroid location induced by horizontal and vertical surcharge surface loads resting on a cross-anisotropic backfill. The surcharge loading types include: point load, finite line load, and uniform rectangular area load. The planes of cross-anisotropy are assumed to be parallel to the ground surface of the backfill. Although the presented solutions have never been proposed in existing literature, they can be derived by integrating the lateral stress solutions recently addressed by the author. It is clear that the type and degree of geomaterial anisotropy, loading distances from the retaining wall, and loading types significantly influence the derived solutions. An example is given for practical applications to illustrate the type and degree of soil anisotropy, as well as the loading types on the lateral force and centroid location in the isotropic/cross-anisotropic backfills caused by the horizontal and vertical uniform rectangular area loads. The results show that both the lateral force and centroid location in a cross-anisotropic backfill are quite different from those in an isotropic one. The derived solutions can be added to other lateral pressures, such as earth or water pressure, which are necessary in the stability and structural analysis of a retaining wall. In addition, they can be utilized to simulate more realistic conditions than the surcharge strip loading in geotechnical engineering for the backfill geomaterials are cross-anisotropic.     

Rapid Construction and Settlement Behavior of Embankment Systems on Soft Foundation Soils

The I-15 Reconstruction Project in Salt Lake City, Utah required rapid embankment construction in an urban environment atop soft lacustrine soils. These soils are compressible, have low shear strength, and require significant time to complete primary consolidation settlement. Because of this, innovative embankment systems and foundation treatments were employed to complete construction within the approved budget and demanding schedule constraints. This paper evaluates and compares the construction time, cost, and performance of three embankment/foundation systems used on this project: (1) one-stage mechanically stabilized earth (MSE) wall supported by lime cement columns; (2) expanded polystyrene (geofoam) embankment with tilt-up panel fascia walls; and (3) two-stage MSE wall with prefabricated vertical drain installation and surcharging. Of the technologies evaluated, the geofoam embankment had the best performance based on settlement and rapid construction time considerations, but is more costly to construct than a two-stage MSE wall with PV drain foundation treatment. The one-stage MSE wall with lime cement treated soil was the most costly, and did not perform as well as expected; thus, it had only limited use on the project.     

Dynamic Properties of Highly Organic Soils from Montezuma Slough and Clifton Court

The nonlinear dynamic properties of highly organic soils from two levee sites in the Sacramento-San Joaquin Delta in California are described. Cyclic triaxial, resonant column and torsional shear tests were performed on thin-walled tube samples obtained from beneath levee crests, beneath adjacent berms, and in the free field such that the in situ vertical effective stresses (σvo′) ranged from about 16?to?67?kPa. These highly organic soils had considerably different organic characteristics from those used in previous studies of dynamic properties. The tested samples had organic contents of 14 to 61%, initial water contents (wo) of 88 to 496%, shear wave velocities (Vs) of 20?to?130?m/s, and organic components that ranged from highly fibrous to highly decomposed and amorphous. Secant shear modulus (G), normalized secant shear modulus (G/Gmax), and equivalent damping ratio (ξ) versus cyclic shear strain amplitude (γc) relations are presented, and their dependence on variables such as consolidation stress, organic content, prior loading history, testing device, and loading frequency are illustrated. Findings are compared to previously published results.     

3D FE Analyses of Buried Pipeline with Elbows Subjected to Lateral Loading

This study investigates the interaction between soil and pipeline in sand subjected to lateral ground displacements with emphasis on the peak force exerted to a bended elbow-pipe. A series of three-dimensional (3D) finite-element (FE) analyses were performed in both opening and closing modes of the elbow section for different initial pipe bending angles. To model the mechanical behavior of sands, two soil models were adopted: Mohr-Coulomb and Nor-Sand soil model. Investigations also included the effects of pipe embedment depth and soil density. Results show that the opening mode exhibits higher ultimate forces and greater localized deformations than the closing mode. Nondimensional charts that account for pipeline location, bending angle, and soil density are developed. Soil-spring pipeline analyses of an elbow-pipe were performed using modified F-δ soil-spring models based on the 3D FE results and were compared to the findings of conventional spring model analyses using the standard two-dimensional soil-spring model. Results show that the pipe strain does not change in the closing mode case. However, in the opening mode case, the pipe strain computed by the modified analysis is larger than that by the conventional analysis and the difference is more pronounced when the pipe stiffness is stiffer.     

Consolidation of a Finite Transversely Isotropic Soil Layer on a Rough Impervious Base

A semianalytical solution to axisymmetric consolidation of a transversely isotropic soil layer resting on a rough impervious base and subjected to a uniform circular pressure at the ground surface is presented. The analysis uses Biot’s fully coupled consolidation theory for a transversely isotropic soil. The general solutions for the governing consolidation equations are derived by applying the Hankel and Laplace transform techniques. These general solutions are then used to solve the corresponding boundary value problem for the consolidation of a transversely isotropic soil layer. Once solutions in the transformed domain have been found, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore-water pressure and fluid discharge can finally be obtained by direct numerical inversions of the integral transforms. The accuracy of the present numerical solutions is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Further, some numerical results are presented to show the influence of the nature of material anisotropy, the surface drainage condition, and the layer thickness on the consolidation settlement and the pore pressure dissipation.     

Procedures for Determining Maximum Emitter Discharge in Subsurface Drip Irrigation

One problem associated with subsurface drip irrigation (SDI) is the reduction in discharge resulting from soil-water back-pressure at the emitter outlets. An experimental setup was made to measure emitter discharge and pressure at the emitter outlet in different soils. Experiments were carried out with 2–24??L/h noncompensating and compensating emitters, operating at a constant lateral pressure of 10?m. Emitter discharge was reduced to a range of 2–10% for noncompensating models and to less than 1% for compensating models. Soil pressure ranged from 0.15–2.07?m. Laboratory conditions were simulated with HYDRUS-2D/3D. Experimental values of discharge and soil pressure showed good agreement with estimated values. Finally, maximum emitter discharge to limit the decrease of discharge was determined for an operating pressure of 10?m. For a 10% decrease, considering a constant radius of the spherical cavity in the soil, maximum emitter discharge was 2.35??L/h for loamy soil and 12.44??L/h for sandy soil for noncompensating emitters, and 10.73 and 54.51??L/h, respectively for compensating emitters. These values increased when considering a cavity radius variable with emitter discharge.     

某堆场试验区软基处理工程效果分析

试验区采用真空联合堆载法进行软基处理,室内土工试验表明,地基的力学性质有一定的提高,处理后淤泥层含水率、孔隙比及压缩系数分别下降了9.32%、6.59%和2.68%;而湿密度、φ、c及压缩模量分别提高了1.09%、40.48%、10.02%和13.53%;现场十字板抗剪强度试验结果表明,埋深15m以上淤泥不排水十字板抗剪强度平均增长了25.9%。通过现场沉降监测和孔隙水压力监测的试验数据,试验区经110d的真空联合堆载法处理,理论估算地基平均固结度≤90%。处理措施需要进一步优化。     

Class A Prediction of the Behavior of Soft Estuarine Soil Foundation Stabilized by Short Vertical Drains beneath a Rail Track

In Australia, very few rail tracks have been constructed directly on deep estuarine deposits. In recent years, Kooragang Island has become a major export terminal and most coal trains need to cross the main lines at Sandgate to enter Kooragang Island. In this study, a rail track built on up to 30 m of thick soft estuarine soil was stabilized with relatively short vertical drains to consolidate the soil just beneath the track, and no additional preloading surcharge was provided, except the weight from the trains. The initial soil compression was caused by the passage of trains with a speed restricted at 40 km/h. From this study, it is shown that prefabricated vertical drains significantly decrease the buildup of excess pore-water pressure during cyclic loading, and also continue to dissipate excess pore-water pressure during the rest period. A preliminary finite-element analysis was employed to examine the performance of vertical drains, and a Class A prediction was obtained in terms of lateral and vertical displacements. The monitored settlement and lateral displacement results are presented and discussed. The study shows that relatively short vertical drains are sufficient for providing stability for rail tracks, without the need for driving deep vertical drains through the entire soft soil depth.