Analytic Solution for Finite Transversely Isotropic Circular Cylinders under the Axial Point Load Test

An exact solution for stress distributions within a finite transversely isotropic cylinder for the axial point load strength test (PLST) is analytically derived. Lekhnitskii’s stress function is first used to uncouple the equations of equilibrium. Two different kinds of solutions corresponding to the real and the complex characteristic roots of the governing equation of the stress function are derived. The solution type to be used for stress analysis depends on the anisotropic parameters of the cylinder. The solution for isotropic cylinders under the axial PLST is recovered as a special case. Numerical results show that the pattern of stress distribution along the line joining the point loads does not depend on the degree of anisotropy of the cylinder, but the magnitude of the stress distributions does. In particular, the local maximum tensile stress, which is located near the point loads, may be either larger or smaller than that of isotropic cylinders. In general, the maximum tensile stress inside the cylinder increases with the ratio of Young’s moduli, but decreases with both the ratio of Poisson’s ratio and the ratio of the shear moduli. If anisotropy of the cylinder is ignored, the point load strength index may be overestimated when the ratio of Young’s moduli is greater than one, or when the ratios of Poisson’s ratio or of the shear moduli is smaller than one.     

Numerical Analysis of One-Dimensional Consolidation in Layered Clay Using Interface Boundary Relations in Terms of Infinitesimal Strain

The interface boundary relations are derived in this study for the numerical analysis of one-dimensional consolidation in multilayered clay profiles. The finite difference solutions are formulated based on Mikasa’s consolidation equation with infinitesimal strains and constant consolidation parameters under the same fundamental assumptions and limitations of the classic Terzaghi equation. Numerical examples are presented for multilayer clay profiles under single and double drainage conditions that validate the predicted excess pore pressures, strains, settlements, and rates of consolidation using interface boundary relations in terms of infinitesimal strains that are equivalent to those expressed in terms of excess pore pressures.     

Consolidation of a Geosynthetic Clay Liner under Isotropic States of Stress

The consolidation behavior of a geosynthetic clay liner (GCL) was evaluated by consolidating duplicate specimens of the GCL in a flexible-wall cell to a final effective stress, σ′, of 241 kPa (35.0 psi). The hydraulic conductivity, k, also was measured at the end of each loading increment. The results indicated that the GCL was normally consolidated for values of σ′ greater than 34.5 kPa (5.0 psi), which correlates well with limited consolidation data reported in the literature for GCLs based on confined compression using oedometers. Values of the coefficient of consolidation, cv, for the GCL ranged from 5.2×10?10?m2/s to 2.1×10?9?m2/s, and generally decreased with increasing σ′, albeit only slightly. Values of the measured k, kmeasured, for the GCL were low ( ? 5.0×10?9?cm/s) due to the sodium bentonite content of the GCL, and were within a factor of about two of the values of k calculated on the basis of classic (Terzaghi) small-strain consolidation theory, ktheory (i.e., 0.5 ? ktheory/kmeasured ? 2.0), suggesting that the theory is appropriate for describing the consolidation behavior of the GCL. The results also are consistent with the results of previous studies based on one-dimensional consolidation of sodium montmorillonite, suggesting that there would be little difference in the consolidation behavior of the GCL under confined compression.     

Forced Vertical Vibration of Rigid Circular Disc on a Transversely Isotropic Half-Space

Vertical vibration of a rigid circular disc attached to the surface of a transversely isotropic half-space is considered in such a way that the axis of material symmetry is normal to the surface of the half-space and parallel to the vibration direction. By using Hankel integral transforms, the mixed boundary-value problem is transformed to a pair of integral equations termed dual integral equations in the literature, which generally can be reduced to a Fredholm integral equation of the second kind. With the aid of complex variable or contour integration the governing integral equation is numerically solved in the general dynamic case. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure, and the static impedance/compliance function are explicitly solved. The dynamic contact pressure under the disc and the impedance function are numerically evaluated, and it is shown that the singularity that exists at the edge of the disc is the same as the one obtained for the static case. In addition, the impedance functions evaluated here are identical to the solution given by Luco and Mita for the isotropic domain. To show the effect of different material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared.     

Limits on a Common Approximation for Layered Consolidation Analysis

A widely used procedure for solving the problem of vertical consolidation of layers with different properties is to transform the thicknesses of the layers in proportion to the square root of their coefficients of consolidation. However, the Gray–Barber closed-form solution shows that this procedure is not correct except under a restrictive set of conditions. The transformation method should not be used. When solutions are needed for layered systems, the Gary–Barber solution or numerical methods should be employed.     

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.     

Frequency-Dependent Amplification of Unsaturated Surface Soil Layer

This paper presents a study of the amplification of SV waves obliquely incident on a surface soil layer overlying rock formation. Special attention is placed on the influence of the saturation states of the soil layer and the bedrock on the amplification in both horizontal and vertical directions as well as on the amplitude ratios between the two directions at the surface, where the vertical and horizontal amplification and the amplitude ratios are expressed as functions of the frequency of incident waves. The analysis indicates that while the influence of the saturation state of the bedrock is insignificant, a change of the saturation state of the soil layer may have a marked impact on the vertical amplification. For typical seismic frequencies, an unsaturated soil layer can generate greater vertical amplification than a saturated layer; it can also cause larger amplitude ratios between vertical and horizontal components at the surface. The analysis further confirms the potential importance of the saturation condition of near-surface soils in site response analysis.     

Plate Load Tests on Cemented Soil Layers Overlaying Weaker Soil

This paper addresses the interpretation of plate load tests bearing on double-layered systems formed by an artificially cemented compacted top soil layer (three different top layers have been studied) overlaying a compressible residual soil stratum. Applied pressure-settlement behavior is observed for tests carried out using circular steel plates ranging from 0.30 to 0.60 m diameter on top of 0.15 to 0.60-m-thick artificially cemented layers. The paper also stresses the need to express test results in terms of normalized pressure and settlement—i.e., as pressure normalized by pressure at 3% settlement (p/p3%) versus settlement-to-diameter (δ/D) ratio. In the range of H/D (where H = thickness of the treated layer and D = diameter of the foundation) studied, up to 2.0, the final failure modes observed in the field tests always involved punching through the top layer. In addition, the progressive failure processes in the compacted top layer always initiated by tensile fissures in the bottom of the layer. However, depending on the H/D ratio, the tensile cracking started in different positions. The footing bearing capacity analytical solution for layered cohesive-frictional soils appears to be quite adequate up to a H/D value of about 1.0. Finally, for a given project, combining Vésic’s solution with results from one plate-loading test, it is possible (knowing of the demonstrated normalization of p/p3%-δ/D, where the pressure-relative settlement curves for different H/D ratios produce a single curve for all values of H/D) to estimate the pressure-settlement curves for footings of different sizes on different thicknesses of a cemented upper layer.     

Plane Strain and Axially Symmetric Consolidation in Unsaturated Soils

A method is presented for the analysis of coupled consolidation in unsaturated soils due to loading under conditions of plane strain as well as axial symmetry. The method is based on the transformation of the governing differential equations by the Fourier transform, when the soil system is deformed under plane strain conditions, or Hankel transform for problems exhibiting axial symmetry. The effect of such transformations is to simplify considerably the solution from a computational point of view. In addition, using these transformations the same differential equations can be used to analyze consolidation under both the above conditions. Results are presented to point out some aspects of the consolidation in unsaturated soils generated by the application of strip as well as circular loads.     

Vertical and Radial Consolidation Analysis of Multilayered Soil Using the Spectral Method

A new, easy to implement, solution to the consolidation of multilayered soil based on the spectral method is presented. Combined vertical and radial drainage under instantaneous or single ramp loading is considered, ignoring well resistance. Flow in the vertical direction is based on the average hydraulic gradient at a particular depth which allows smear effects to be included. The excess pore-water pressure profile across all soil layers is described by a single expression calculated with common matrix operations. Average excess pore pressures within or across any number of layers are easily calculated from the single expression. The new model is verified against other solutions from the current literature indicating that the more general spectral method model can replace the separate solutions developed for specific problems.     

Interface Electric Resistance of Electroosmotic Consolidation

There will be transition zones of electric current near the electrodes, if the electric conductive area of electrodes is smaller than that of soil. Electroosmosis tests show that the electric current in the transition zones follows a complicated two-dimensional path, while the electric current outside these zones is approximately one dimension. The thickness of transition zones is potty compared to the whole thickness of soil between anodes and cathodes. Conception of interface resistance on zero thickness interfaces, which is a simplified expression for finite thickness transition zones, is presented in this paper to simplify the two-dimensional problem within the transition zones into one dimension. Studies show that the interface electric resistance is inversely proportional to the ratio of electric conductive areas between electrodes and soil. A brief formula is deduced to predict the in situ interface electrical resistance, which presents a more accurate estimation of electric current and energy consumption to the design of electroosmotic consolidation engineering.     

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.     

Soil Moisture Flow Modeling with Water Uptake by Plants (Wheat) under Varying Soil and Moisture Conditions

A variably saturated soil moisture flow model is developed for planted soils with depth varying properties by incorporating a nonuniform macroscopic root water uptake function. The model includes spatial and temporal variation of the root density with dynamic root growth for simulating water uptake by plants along with the impact of soil moisture availability. The governing partial differential moisture flow equation integrated over the depth with a plant water uptake term is solved numerically by the implicit finite difference method using an iterative scheme. The model is first tested for barren soils for two profiles considering constant and depth varying soil characteristics under constant inflow condition. The results obtained are later tested with experimental data available in the literature. A nonuniform plant water uptake term is subsequently incorporated in the model and water uptake by wheat plants under different soil moisture availability conditions is studied. Finally, the moisture flow model is validated with field data of rain fed wheat (Triticum aestivum) using a dynamic root growth model for a layered root zone soil profile. The simulated soil moisture regime of the layered root zone shows a reasonably good agreement with the observed data.     

High-Pressure Isotropic Compression Tests on Fiber-Reinforced Cemented Sand

High-pressure isotropic compression tests were carried out on reconstituted sand samples that were reinforced with cement, randomly distributed fibers, or both, making comparisons with the unreinforced sand and conducting tests from a variety of initial specific volumes. The results indicated changes in the isotropic compression behavior of the sand due to the inclusion of fibers and/or cement. Cementitious bonds are sufficiently strong relative to the particles to allow the cemented samples to reach states outside the normal compression line (NCL) of the uncemented soil, but the effectiveness of cemented fiber-reinforced specimens is even larger due to the control of crack propagation in the cemented sand after the inclusion of fibers. Distinct NCLs were observed for the sand, fiber-reinforced sand, cemented sand, and fiber-reinforced cemented sand. Both fiber breakage and fiber extension were observed in fibers measured after testing indicating that fibers individually have worked under tension, even though in the macroscopic scale, isotropic compressive stresses were applied. Fiber reinforcement was found to reduce the particle breakage of both the uncemented and cemented sands.     

On the Theory of Seismic and Seismoelectric Phenomena in a Moist Soil

In this paper, Frenkel introduced the theory of wave propagation in saturated porous media. A second-type compressional wave, also known as the slow wave, was predicted for the first time, based on theoretical analysis. The seismoelectric phenomena observed in the field were explained as the result of second-type wave propagation. This paper was originally published in 1944 in the Journal of Physics, Vol. III, No. 5, pp. 230–241. It is republished with permission by the Schmidt Institute of Earth Physics, Russian Academy of Sciences, courtesy of Professor Alexander O. Gliko, Director of the Institute. The paper was prepared with typographical corrections by Alexander Cheng.     

Effect of the Smear and Transition Zones around Prefabricated Vertical Drains Installed in a Triangular Pattern on the Rate of Soil Consolidation

Soil disturbance caused by the installation of prefabricated vertical drains (PVDs) has a large impact on the rate of consolidation. It is essential in design to quantify this effect. In this paper, we investigate the consolidation rate of soils with PVDs installed in a triangular pattern using two-dimensional finite-element analysis with full consideration of disturbance effects. This is done by accounting for the transition zone that exists between the highly disturbed smear zone and the undisturbed zone. The hydraulic conductivity in the transition zone is assumed to increase linearly from a low value in the smear zone to the original in situ value in the undisturbed zone. The actual band shape of the PVD and hexagonal zone of influence around it are used in the analysis. In addition to soil disturbance effects, the influence on consolidation rate of the size of the smear and the transition zones, the PVD spacing, and the mandrel size and shape is also investigated. Guidelines are given for using an equivalent system, where the transition zone is replaced by an expanded smear zone producing the same effect. This equivalent-system approach allows use of existing analytical solutions that consider only the smear zone in analysis and design.     

Three-Dimensional Nonlinearly Varying Rectangular Loads on a Transversely Isotropic Half-Space

In engineering situations, loads applied to the four corners of a rectangle might have different values and might not be uniformly or linearly distributed. A configuration of linearly or nonlinearly varying loads with different contact pressures at each corner can be represented as a superposition of various loading types. The loading types include uniform, linearly varying in the x direction, linearly varying in the y direction, nonlinearly varying in the x direction, and nonlinearly varying in the y direction. This work newly presents the first and second loading solutions, and derives the others therefrom. These solutions are directly obtained by integrating the point load solutions in a transversely isotropic half-space. The presented solutions are concise and easy to use; they specify that the type and degree of material anisotropy, the dimensions of the loaded region, and the loading types decisively affect the displacements and stresses in a transversely isotropic half-space. The proposed solutions can simulate realistically the actual loading problem in many engineering situations.     

New Fast Convolution Algorithm in Boundary-Element Methods for Two- and Three-Dimensional Linear Soil Consolidation Analysis

Over the last 25?years, the time domain boundary element formulations for the linear consolidation theory of Biot involving fully coupled governing differential equations of flow through porous media and those of elastic deformation of porous skeleton have been fully developed and implemented for both single-region and multiregion two-dimensional plane strain, axisymmetric and three-dimensional problems. However, this storage-based convolution method used in those developments was not found to be suitable for solving large practical problems because of the substantial computer disk space requirements. In order to find a better alternative, an accurate integration-based scheme was developed by the present writers and co-workers, in which, the storage was eliminated by accurately recalculating the summation (involved in the time convolution) of the right-hand side at each step during the time marching process. Although this work was not published in any literature, by using this type of approach, solving large scale problems became possible in an accurate manner, but the computational cost was significantly high, and there was a further need to develop a more practical and efficient time stepping algorithm. In the present work, an efficient and simplified integration-based fast convolution algorithm for two- and three-dimensional soil consolidation analysis has been subsequently developed. In this new algorithm, all of the time convolution steps have been calculated by assuming an equivalent spatial and temporal averaged value of the variables over each element to represent the total effect. The number of Gauss points used has been calculated in an efficient manner based on time-embedded distance criteria to accurately capture the past effects. The efficiency and accuracy of this newly developed fast convolution algorithm are compared with the accurate integration-based convolution approach and also with the analytical and other available solutions. Examples of applications involving two- and three-dimensional practical soil consolidation problems are presented to demonstrate the usefulness of the developed algorithm.     

Consolidation of Soft Clay Foundations Reinforced by Stone Columns under Time-Dependent Loadings

This paper presents an analytical solution for the consolidation of soft soil foundations reinforced by stone columns under time-dependent loadings. The differential equations of the foundations reinforced by stone columns are obtained including smear and well resistance under arbitrary applied loadings. The closed-form solutions of pore pressure and the overall average degree of consolidations are obtained for some common types of loadings, such as step loading, ramp loading, and cyclic trapezoidal loading. By solving the equations using a semianalytical method, the comparisons agree very well with the existing analytical solutions, which verify the correctness and accuracy of the proposed methods. Using the solutions obtained, some selected charts are presented and the relevant consolidation behavior is investigated and discussed.