Weightless Soil Research Articles

A stable CS-FEM for the static and seismic stability of a single square tunnel in the soil where the shear strength increases linearly with depth

A numerical procedure using a stable cell-based smoothed finite element method (CS-FEM) is presented for estimation of stability of a square tunnel in the soil where the shear strength increases linearly with depth. The kinematically admissible displacement fields are approximated by uniform quadrilateral elements in conjunction with the strain smoothing technique, eliminating volumetric locking issues and the singularity associated with the Mohr–Coulomb model. First, a rich set of simulations was performed to compute the static stability of a square tunnel with different geometries and soil conditions. The presented results are in excellent agreement with the upper and lower bound solutions using the standard finite element method (FEM). The stability charts and tables are given for practical use in the tunnel design, along with a newly proposed formulation for predicting the undrained stability of a single square tunnel. Second, the seismic stability number was computed using the present numerical approach. Numerical results reveal that the seismic stability number reduces with an increasing value of the horizontal seismic acceleration (αh), for both cases of the weightless soil and the soil with unit weight. Third, the link between the static and seismic stability numbers is described using corrective factors that represent reductions in the tunnel stability due to seismic loadings. It is shown from the numerical results that the corrective factor becomes larger as the unit weight of soil mass increases; however, the degree of the reduction in seismic stability number tends to reduce for the case of the homogeneous soil. Furthermore, this advanced numerical procedure is straightforward to extend to three-dimensional (3D) limit analysis and is readily applicable for the calculation of the stability of tunnels in highly anisotropic and heterogeneous soils which are often encountered in practice.

Spudcan Penetration Simulation Using the Coupled Eulerian-Lagrangian Method with Thermo-Mechanical Coupled Analysis

A novel modeling technique based on the coupled Eulerian-Lagrangian (CEL) method is provided to solve the geotechnical problems with large deformations. The technique is intended to solve the update problem of soil mechanical properties during spudcan penetration in normally consolidated clay soil. In the CEL model, the normal method of assigning an increasing shear strength profile with depth (NA) is defective due to its Eulerian framework. In this paper, a new technique is proposed to update soil material properties by introducing thermo-mechanical coupled analysis (TMCA) to the CEL models. During establishment of the CEL models, the optimal penetration velocity and minimum mesh size are determined through parametric studies. Reasonability and accuracy are then verified through comparison of the preliminary results with the soil flow configuration and penetration resistance (Fv) of a centrifuge test, and the results of the proposed method are compared with those of the remeshing and interpolation technique with small strain (RITSS) method. To achieve a CEL model with satisfactory accuracy, the NA and TMCA methods implemented in the CEL models and the RITSS method are first adopted in weightless soil. Comparison of the findings with those obtained in previous studies shows that the TMCA method can update material properties and predict Fv. The TMCA method is then applied to soils with self-weight and different shear strength profiles. Results show that the proposed method is capable of accurately modeling the large deformation problem of spudcan penetration in non-homogeneous clay.

The ultimate bearing capacity of shallow strip footings using slip-line method

Based on the limit equilibrium theory, an accurate approach is proposed to solve the ultimate bearing capacity of shallow strip footings under general conditions. The foundation soil is considered to be an ideal elastic-plastic material, which obeys the Mohr-Coulomb yield criterion, and is assumed to be an ideal continuous medium which is isotropic, homogeneous and incompressible or non-expansive. Through analyzing the relative motion and interaction between the footing and soil, the problem of the ultimate bearing capacity of shallow strip footings is divided into two categories. A minimum model with the total vertical ultimate bearing capacity as its objective function is established to solve the ultimate bearing capacity using the slip-line method with no need to make any assumptions on the plastic zone and non-plastic wedge in advance. A convenient and practical simplified method is also proposed for practical engineering purposes. Furthermore, the first category of the problem in the case of the same uniform surcharges on both sides of footings is the focus of the study: the applicable conditions of Terzaghi’s ultimate bearing capacity equation as well as the theoretical exact solutions to its three bearing capacity factors are derived, and a new bearing capacity equation is put forward as a replacement for Terzaghi’s equation. The geometric and mechanical similarity principle is proposed by a dimensionless analysis. The results show that for perfectly smooth footings, the total vertical ultimate bearing capacity obtained by the present method is in good agreement with those by existing methods, whereas the existing methods underestimate the ultimate bearing capacity in the case of perfectly rough footings. The classic Prandtl mechanism is not the plastic failure mechanism of the ultimate bearing capacity problem of perfectly smooth footings on weightless soil.

A macroelement framework for shallow foundations including changes in configuration

Macroelement plasticity models are being increasingly applied to study non-linear soil–foundation interaction (SFI) problems. Macroelement models are particularly appealing from a computational standpoint, as they can capture the essence of SFI by means of a few degrees of freedom. However, all the macroelement formulations available in the literature suffer from the same limitation, that is the incapability of accounting for changes in both geometry and loading/boundary conditions. Accordingly, macroelement models are usually calibrated to analyse a given boundary value problem, with no chance of handling situations with significant variations in embedment, lateral surcharge and/or phreatic level. The present work shows how standard soil modelling concepts can be exploited to reproduce relevant ‘configurational features’ of non-linear SFI. A macroelement framework is here proposed to simulate the drained load–settlement response of shallow footings on sand in the presence of varying surface/body forces. As a first step, the ideal case of a weightless soil layer is exclusively considered. The macroelement constitutive equations are conceived/calibrated on a minimal set of finite-element results; the satisfactory predictive capabilities of the macroelement model are finally demonstrated by retrospectively simulating selected finite-element tests.

Finite element analysis of the plastic limit load and the collapse mechanism of strip foundations with non-associated Drucker-Prager model

This paper is devoted to the numerical study of the influence of the non-associativity of the Drucker–Prager model on the plastic limit load and the failure mechanism of the strip footings. The attention is mainly focused on the determination (estimation) of the mechanical fields and geometric characteristics of the collapse mechanism. Rough and smooth contact between the punch and the substrate are considered. Analyses were performed by incremental finite element simulations by using of the object oriented computer code Cast3m. The code is first validated against analytical solutions for two problems available in the literature. It is worth noting that during this validation, we provide new numerical results concerning the ultimate load of a pressurised pore with non-associate matrix. Then, the limit plastic load of the weightless soil is computed and the post-treatment of the numerical results permits one to select the relevant mechanical fields. The main result is that, for the Prandtl mechanism associated to the rough footing, the angle base of the triangular wedge under the footing is independent of the dilatancy angle. This property appears to be very interesting and useful when constructing analytical bounds of the plastic limit load within the framework of limit analysis.

Numerical study of pull-out capacities of dynamically embedded plate anchors

Dynamically embedded plate anchors (DEPLAs) are a type of offshore anchor that combine the capacity advantages of vertically loaded plate anchors with the installation benefits of dynamically installed anchors. DEPLA capacity under monotonic loading conditions in clay has been investigated through centrifuge and field tests. In this paper, the monotonic capacity of DEPLAs in normally consolidated clay was studied using a three-dimensional large deformation finite element approach based on frequent mesh regeneration. Results from the numerical simulations were validated by comparison with centrifuge test data and existing numerical and analytical solutions for circular and rectangular plates. The effect of anchor embedment depth, anchor roughness, fluke (or plate) thickness, plate inclination, and DEPLA geometry were investigated in a parametric study where soil was prescribed to remain attached to the DEPLA base. The findings indicate that for a horizontal anchor subjected to vertical loading, most DEPLA geometries exhibit deep behaviour at an embedment ratio of 2.5, but that this embedment ratio is dependent upon the plate inclination, with vertical plates requiring the highest embedment depth for a deep localized failure mechanism. At a shallow embedment depth equal to one plate diameter, the reduction in capacity factor as the plate inclination changes from horizontal to vertical is 23.4%, compared with 1.3% at an embedment depth equal to four plate diameters. Plate roughness and fluke thickness are shown to have a minimal effect on the anchor capacity factor for vertical loading. Analyses that considered the breakaway (no tension) at the DEPLA base demonstrated that the anchor capacity factor approaches the no breakaway value as the embedment depth increases and as the soil strength (relative to the effective unit weight of the soil) decreases. The paper proposes a simple means of approximating the anchor capacity factor for breakaway conditions, by summing the capacity factor in weightless soil (which is unique for a given DEPLA geometry) and the normalized overburden pressure.

Pullout behaviour of plate anchor in clay with linearly increasing strength

Plate anchors are widely adopted to provide uplift resistance for structures. For most offshore seabeds, the undrained shear strength profile can be reasonably approximated as varying linearly with depth. At present, there are two possible approximate approaches to determine uplift capacity of a square plate anchor in such a profile, but the validity of both approaches cannot be ascertained due to unavailability of a rigorous solution. This study addresses these uncertainties by establishing the capacity factors for a square anchor in a linearly increasing strength profile using a three-dimensional large-deformation finite element approach for a wide range of geometric and material combinations. It was found that both approaches give the correct solution only under specific conditions. Earlier studies on the uplift capacity of a plate anchor typically follow a classical path of deriving the solution for a weightless soil and extending this solution to a soil with self-weight. The applicability of such an approach to the uplift of a square anchor is examined in this study. A direct design method for a square plate anchor embedded in a linearly increasing strength profile, which enables the capacity factors for a square anchor to be directly obtained without any simplified assumptions, is then proposed.

Comparison of Analytical Solutions with Finite Element Solutions for Ultimate Bearing Capacity of Strip Footings

The finite element method is used to compute the ultimate bearing capacity of a fictitious strip footing resting on the surface of c-φ weightless soils and a real strip footing buried in the c-φ soils with weight. In order to compare the numerical solutions with analytical solutions, the mainly existing analytical methods are briefly introduced and analyzed. To ensure the precision, most of analytical solutions are obtained by the corresponding formulas rather than table look-up. The first example shows that for c-φ weightless soil, the ABAQUS finite element solution is almost identical to the Prandtls closed solutions. Up to date, though no closed analytical solution is obtained for strip footings buried in c-φ soils with weight, the numerical approximate solutions obtained by the finite element method should be the closest to the real solutions. Apparently, the slip surface disclosed by the finite element method looks like Meyerhofs slip surface, but there are still some differences between the two. For example, the former having an upwarping curve may be another log spiral line, which begins from the water level of footing base to ground surface rather than a straight line like the latter. And the latter is more contractive than the former. Just because these reasons, Meyerhofs ultimate bearing capacity is lower than that of the numerical solution. Comparison between analytical and numerical solutions indicates that they have relatively large gaps. Therefore, finite element method can be a feasible and reliable method for computations of ultimate bearing capacity of practical strip footings.

Influence of overburden pressure and soil rigidity on uplift behavior of square plate anchor in uniform clay

A numerical study incorporating three-dimensional Eulerian large deformation finite element analyses is performed to investigate the pullout process of horizontal square plate anchors in both hypothetical weightless soil and soil with self-weight. The validity of the numerical model is established through verification against published experimental and numerical results. The failure mechanisms during the pullout process under different conditions are then investigated. Three types of failure mechanism are observed; of which only two have been reported in the literature. The third mechanism identified in this study, which is a partially localized flow mechanism, is operative when the soil overburden ratio is not high enough to mobilize the full flow mechanism. The influence of soil self-weight is directly investigated by incorporating the density of the soil in the finite element model and maintaining the gravitational acceleration field throughout the analysis. The critical overburden ratio corresponding to the full transition to a localized plastic flow mechanism is identified in this study. The effect of the soil rigidity index (E/su) on the anchor uplift capability has not been systematically investigated in earlier studies. Contrary to the general failure mechanism and the full flow mechanism described in the literature, the capacity factor corresponding to this new mechanism increases with increasing E/su. The capacity factors for square plate anchors corresponding to different anchor embedment ratios, overburden ratios and E/su are provided in the form of design charts.

Observations on Mohr-Coulomb Plasticity under Plane Strain

Linear elastic-perfect plasticity using the Mohr-Coulomb yield surface is one of the most widely used pressure-sensitive constitutive models in engineering practice. In the area of geotechnical engineering, a number of problems, such as cavity expansion, embankment stability, and footing bearing capacity, can be examined using this model together with the simplifying assumption of plane strain. This paper clarifies the situation regarding the direction of the intermediate principal stress in such an analysis and reveals a unique relationship between hydrostatic pressure and the principal stress ratio for Mohr-Coulomb and Tresca perfect plasticity under those plane-strain conditions. The rational relationship and direction of the intermediate principal stress are illustrated through both material-point and finite-element simulations. The latter involves the analysis of a rigid strip footing bearing onto a weightless soil and the finite-deformation expansion of a cylindrical cavity.

Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion

SUMMARYA probabilistic model is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a spatially varying soil. The soil cohesion and friction angle were considered as two anisotropic cross‐correlated non‐Gaussian random fields. The deterministic model was based on numerical simulations. An efficient uncertainty propagation methodology that makes use of a non‐intrusive approach to build up a sparse polynomial chaos expansion for the system response was employed. The probabilistic numerical results were presented in the case of a weightless soil. Sobol indices have shown that the variability of the ultimate bearing capacity is mainly due to the soil cohesion. An increase in the coefficient of variation of a soil parameter (c or φ) increases its Sobol index, this increase being more significant for the friction angle. The negative correlation between the soil shear strength parameters decreases the response variability. The variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random fields, the increase being more significant for the cohesion parameter. The decrease in the autocorrelation distances may lead to a smaller variability of the ultimate bearing capacity. Finally, the probabilistic mean value of the ultimate bearing capacity presents a minimum. This minimum is obtained in the isotropic case when the autocorrelation distance is nearly equal to the footing breadth. However, for the anisotropic case, this minimum is obtained at a given value of the ratio between the horizontal and vertical autocorrelation distances. Copyright © 2012 John Wiley & Sons, Ltd.

Limit loads for a shallow anchor/trapdoor embedded in a non-associative Coulomb soil

A theoretical methodology for determining the range of possible plane-strain limit loads acting on an anchor or trapdoor buried within a non-associative Coulomb soil is presented. Solutions are given for shallow anchors and trapdoors underlying both weightless soil with surface load and soil possessing self-weight with no surface load. A method for determining limit loads for combined scenarios is additionally outlined. Solutions are shown to correlate favourably with experimental and finite-element data in the literature.

Error Analysis of Superposition Method in Bearing Capacity Calculation

Duo to non-linearity of ground material’s behavior, the error will be introduced using traditional superposition method to calculate bearing capacity. The main cause of superposition error is that bearing capacity factors based on failure mechanism of weightless soil is not applicable for weight soil. Based on slip line method, variation trend of error introduced by superposition method is investigated. The investigation of this paper showed that, bearing capacity calculated by traditional superposition method is conservative, and the error increased with increasing of internal fractional angle.

Three-Dimensional Large Deformation FE Analysis of Square Footings in Two-Layered Clays

In strong over soft two-layered clays, there is a potential for the footing to experience a punch-through failure, where the footing penetrates a large distance at a short time after the initial peak resistance is reached. Three-dimensional (3D) large deformation finite-element analyses using 3D RITSS method were conducted to simulate the penetration responses of square footings in strong over soft clays. The effects of surface soil heave and soil layer interface deformation during footing penetration were studied in weightless soils. Fitted equations were proposed to express the footing capacity response against the penetration depth. Based on the fitted equations, formulas to calculate footing peak bearing factor and the corresponding penetration depth were developed. The peak footing capacity factor and the corresponding penetration depth increases with the increasing of soil layer strength ratio, relative top soil layer thickness and soil weight factor, thus the potential of punch-through failure was reduced accordingly. It was also found that the soil weight effect can be a simple surcharge based on the formula developed in the weightless soil. Design charts for the peak footing capacity factor and the corresponding penetration depth were developed.

Undrained Bearing Capacity of Two-Strip Footings on Spatially Random Soil

A probabilistic study on the interference of two parallel rough rigid strip footings on a weightless soil with a randomly distributed undrained shear strength performed. The problem is studied using the random finite element method, where nonlinear finite element analysis is merged with random field theory within a Monte Carlo framework. The variability of undrained shear strength is characterized by a lognormal distribution and an exponentially decaying spatial correlation length. The estimated bearing capacity statistics of isolated and two footings cases are compared and the effect of footing interference discussed. Although interference between footings on frictionless materials is not very great, the effect is shown to be increased by soil variability and spatial correlation length.

Numerical stability of implicit integration schemes in nonassociated viscoplasticity

The analytical numerical stability of existing implicit integration schemes in nonassociated viscoplasticity when the finite element method is used as the discretization method is presented. This is done first by generalization of existing implicit numerical techniques to integrate the nonsymmetric system of equations obtained if nonassociated flow rules are used. Then the stability of the numerical process is analyzed for any smooth yield function and for both associated and nonassociated flow rules. The conclusions of the analytical stability study are verified using one numerical example and both associated and nonassociated flow rules. The Drucker-Prager yield function is used to study the stability behavior of the steady-state solution of a uniform strip footing on a weightless soil. Here both flow rules are used with varying degrees of nonassociativity. Both explicit and implicit numerical integration schemes are used. Two cases of implicit methods are specifically examined, which include the fully implicit and the trapezoidal methods.

On the effect of base friction on bearing capacity

INTRODUCTION IN THE classic Prandtl solution for the bearing capacity of weightless soils, the bearing stresses are perpendicular to the loaded surface [1]. This implies that the base of the footing is perfectly smooth (8 = 0). Terzaghi [2] recognized the effect of base friction on bearing capacity and proposed that for perfectly rough (8 = q~) bases the angle a of the active zone be taken as equal to q~ instead of 45 + q0/2, as in the Prandtl solution. Meyerhof [3] proposed an approximate formula for the consideration of the roughness of the base of footing in bearing capacity calculations. Hu [4] and Assad Abdul-Baki and L. A. Beik [5] assumed ct to be variable and proposed to define the bearing capacity factors as minimum values for variable a; the latter authors related 8 at the edge of the footing to ~ by the appropriate equations of the theory of plasticity. Straight line boundaries of the active zones assumed by these authors suggest a uniform 8 across the base of the footing. The logarithmic spirals assumed in the radial zone are valid for weightless soil only; therefore, the proposed bearing capacity factors can be considered as only approximations. Negre and Stutz [6] obtained numerical solutions of the differential equations of plasticity for the case where 8 = q~ at the edge of the footing and decreases gradually toward the center. In this paper, the effect of base friction on the geometry of slip line fields and the distribution of bearing stresses is analyzed in both the two-dimensional and the axially symmetric case by theory of plasticity methods.

On certain plasticity solutions in soil mechanics

The ultimate bearing capacity of a general type of rigid foundation, supported by a weightless soil which exhibits both cohesion and internal friction, is found by integrating the Kötter equations. Several particular cases, including both smooth and rough interface conditions and the case of an embedded rough foundation, are considered, and values of the bearing capacity factors N c and N q as a function of φ are given in equation and graphical form. Certain special cases of the resulting solutions are shown to be consistent with various commonly used expressions.