Solution For Cavity Expansion Research Articles

Computation of pull-out resistance of pressure-grouted soil nails in sand using cavity expansion and contraction solutions

ABSTRACT Pressure-grouted soil nailing has been extensively used as a soil stabilization technique in transportation infrastructure projects, wherein resistance against pull-out failure is offered by shear resistance mobilized along the nail–soil interface. However, the different stages of soil nail installation significantly alter the soil properties and residual normal stress at the grout-soil interface and thereby the maximum pull-out shear stress. This article presents a computational procedure to predict the maximum pull-out shear stress of pressure-grouted soil nails in sand, incorporating the variation in soil properties and stresses throughout the installation processes and loading. The procedure is formulated within the framework of cavity expansion-contraction solutions as the entire installation and testing phases resemble either expansion or contraction of a cylindrical cavity. The proposed approach was validated using grouting and pull-out test data of soil nails in sand. The influence of various parameters on pull-out shear stress has also been examined.

Inside Back Cover

The cover image is based on the Research Article A semi-analytical solution for displacement-controlled elliptical cavity expansion in undrained MCC soil by Hang Zhou et al., https://doi.org/10.1002/nag.3302.

Undrained Elastoplastic Solution for Cylindrical Cavity Expansion in Structured Cam Clay Soil Considering the Destructuration Effects

Soil structure has significant influences on the mechanical behaviors of natural soils, although it is rarely considered in previous cavity expansion analyses. This paper presents an undrained elastoplastic solution for cylindrical cavity expansion in structured soils, considering the destructuration effects. Firstly, a structural ratio was defined to denote the degree of the initial structure, and the Structured Cam Clay (SCC) model was employed to describe the subsequent stress-induced destructuration, including the structure degradation and crushing. Secondly, combined with the large strain theory, the considered problem was formulated as a system of first-order differential equations, which can be solved in a simplified procedure with the introduced auxiliary variable. Finally, the significance and efficiency of the present solution was demonstrated by comparing with the previous solutions, and parametric studies were also conducted to investigate the effects of soil structure and destructuration on the cavity expansion process. The results show that the soil structure has pronounced effects on the mechanical behavior of structured soils around the cavity. For structured soils, a cavity pressure that is larger than the corresponding reconstituted soils when the cavity expands to the same radius is required, and the effective stresses first increase to a peak value before decreasing rapidly with soil structure degradation and crushing. The same final critical state is reached for soils with different degrees of the initial structure, which indicates that the soil structure is completely destroyed during the cavity expansion. With the increase of the destructuring index, the soil structure was destroyed more rapidly, and the stress release during the plastic deformation became more significant. Moreover, the present solution was applied in the jacking of a casing during the sand compact pile installation and in situ self-boring pressuremeter (SBPM) tests, which indicates that the present solution provides an effective theoretical tool for predicting the behavior of natural structured soils around the cavity.

Interpretation of state parameter in partially drained tailings: a case history examination

Estimating state parameter in tailings storage facilities (TSFs) is a key component to assessing their stability. The cone penetrometer test (CPT) forms the key tool to all current methods to enable rapid assessment of in situ state parameter. Methods to estimate state parameter from the CPT in common use range from screening-level techniques to drained and undrained cavity expansion methods. Importantly, there is no comprehensive method, such as a cavity expansion-based approach, for partially drained CPT soundings. This paper outlines further investigation of a recent study where state parameter had been estimated using screening methods and through direct comparison of in situ void ratio (through water content) to the critical state line measured on reconstituted samples. In the current study, the state parameter was estimated on the basis of both drained and undrained cavity expansion solutions. This was done as although the sounding in question was partially drained, the drained and undrained cavity expansion solutions represent accepted leading practice in TSF investigations. The results of this comparison indicate that the use of drained and undrained cavity expansion tools appears to over- and under-estimate state parameter, respectively. Implications for tailings engineering practice, and ways forward for this issue, are discussed.

An elastoplastic solution for cylindrical cavity expansion under constant water content conditions in anisotropic unsaturated soils

In this paper, an elastoplastic solution is developed for cylindrical cavity expansion in anisotropic unsaturated soils under constant water content conditions. The most prominent features of the solution can be attributed to 1) the stress–strain behaviour of unsaturated soil is subtly coupled with the saturation-suction behaviour; 2) both the mechanical and hydraulic behaviours are modelled as elastoplastic processes; and 3) an anisotropic critical state soil model for saturated soil is extended to an unsaturated situation to consider the effects of the initial stress anisotropy and stress-induced anisotropy of the natural unsaturated soils. The problem is formulated as a system of first-order differential equations and solved as an initial value problem. A numerical code that can judge the hydraulic yield condition of soil particles during the cavity expansion process is developed based on the Runge-Kutta algorithm to solve the governing equations. Parametric analyses, which cover a wide range of suctions, overconsolidation ratios, degrees of initial stress anisotropy, are conducted to investigate the effects of these important factors on the expansion responses in unsaturated soils. The proposed solution could potentially be applied to interpret pressuremeter tests and model pile installation effects in anisotropic unsaturated soils.

Spherical cavity expansion in porous rock considering plasticity and damage

AbstractIn rock engineering, damage evolution upon loading imposes significant impacts on the stiffness of rock mass and its deformation characteristics. In order to investigate the influence of both damage and plasticity on cavity expansion, a plastic damage solution is derived for undrained spherical cavity expansion in rock medium. For the consideration of plasticity‐damage, Modified Cam‐Clay (MCC) model is selected as the plasticity driver, a damage evolution criterion is adopted and coupled with MCC. The coupled damage MCC model is validated against experimental data in the literature. The proposed cavity expansion solution with the consideration of plasticity damage is verified through a classic solution in literature. The role of damage in undrained spherical cavity expansion is investigated by studying the spatial variations of effective stress, pore pressure and damage for cases with different stress ratios. Distribution of cavity expansion induced plastic and damage zones for cases with different stress ratios are also reproduced and discussed. Cavity expansion results show that, the damage zone should be considered for engineering application as the plastic zone is affected due to the damage evolution. In addition, the stability (e.g., radial stress) of rock mass is overestimated in classical solution without the consideration of damage zone.

Undrained solution of cylindrical cavity expansion for unsaturated soils with modified Cam-clay model

This paper develops a new semi-analytical approach for undrained cylindrical cavity expansions in unsaturated soils. The unsaturated soil behavior is described within a simple, yet effective, critical state-based elastoplastic framework with suction being treated as a hardening parameter. Different from its saturated counterpart, the cavity expansion problem in unsaturated soils involves five basic variables, namely, the three stress components, specific volume, and suction. A constitutive equation for the water phase, in addition to the soil elastoplastic constitutive relationship plus the radial equilibrium condition, is therefore required to construct a set of coupled, self-contained differential equations for the solution of the cavity boundary value problem. With the introduction of an auxiliary variable, all these governing equations can be expressed in terms of the Lagrangian formulation and then simultaneously solved through the standard numerical procedure. The numerical example results show that the suction has significant hardening effects on the overall cavity expansion responses and, in particular, the stress trajectories calculated for a representative soil element at the cavity surface. It is also interesting to observe that the shear dilation phenomenon, developed during the course of cavity expansion, usually occurs in relatively dense unsaturated soils with high unsaturated suction.

A unified and rigorous solution for quasi-static cylindrical cavity expansion in plasticity constitutive models

This paper presents a unified and rigorous solution for the quasi-static cylindrical cavity expansion problem in all existing plasticity constitutive models. Rigorous three-dimensional definitions of p’ and q are used as proposed by Chen & Abousleiman. Then, the p-q stress space is transformed to the three stress components in a cylindrical coordinate system. The governing partial differential equations (PDEs) for cylindrical cavity expansion, including the stress equilibrium equation, the constitutive equation, the consistency equation, the continuity equation, and the drainage conditions, are written with respect to the three stress components in a cylindrical coordinate system. The PDEs are subsequently reduced to ordinary differential equations (ODEs), which can be summarized in unified matrix form by means of a similarity transformation. A rigorous semi-analytical solution can immediately be obtained by numerically solving the ODEs using commercial ODE solvers, such as MATLAB. The proposed solution procedure is general and can be applied to both the drained and undrained conditions in all plasticity constitutive models. Finally, the partially drained effect was discussed through numerical analysis, and empirical equations considering the partially drained effect were proposed for calculating the limit effective radial stress and excess pore pressure at the cavity wall.

Theoretical Solution for Cavity Expansion in Crushable Soil

Abstract This paper proposed a theoretical solution for cavity expansion in crushable soils. The constitutive relations of the crushable soils were described by the breakage mechanics model that ex...

Analysis of cylindrical cavity expansion in anisotropic overconsolidated clays using the Extended UH model

Anisotropy and overconsolidation are two important features of depositional clay and are not comprehensively addressed in current cavity expansion solutions. Aiming at better modeling the cavity expansion responses in the natural soils, this paper develops a novel and rigorous elastoplastic semi-analytical solution by implementing the advanced anisotropic unified hardening (UH) model in conjunction with incorporating the anisotropic SMP criterion. The novel incorporation of the anisotropic SMP criterion and the proper consideration of overconsolidated properties are the major contributions of the present solution. By utilizing the anisotropic stress transformation method, the initial stress-induced anisotropy, anisotropic yielding and anisotropic failure of soil are also incorporated into the proposed solution. Following the derived constitutive equations in incremental form and large strain theory, both undrained and the drained cases are reduced to boundary-value problems consisting of several first-order ordinary differential equations formed in the Lagrangian scheme. Detailed parametric analyses are presented and compared with other existing solutions to investigate the effects of anisotropy and initial overconsolidation on the cavity responses. The present solution could properly capture the cross-anisotropy and 3D strength of overconsolidated soil and hence provides a more advanced and generic approach for modeling the cavity expansion responses in wide ranges of soils.

Numerical study on undrained cone penetration in structured soil using G-PFEM

This paper presents a model for the numerical simulation of cone penetration in structured soil under undrained conditions based on the Particle Finite Element Method. An extended version of the Clay and Sand Model (CASM), allowing microstructural bonding and its degradation to be taken into account, was implemented into the application G-PFEM and compared to the analytical solution for undrained spherical cavity expansion. A robust model for cone penetration is obtained using a nonlocal stress-integration combined with the IMPLEX integration scheme. A parametric study on the shape of the yield surface – which is adaptable for the CASM – and the degree of initial bonding, as well as the rate of destructuration, was conducted to investigate the influence on the obtained normalized parameters Qt, BQ, U, and the cone factors Nkt, NΔu, Nke used for the determination of the undrained shear strength. It was found that the highest cone factors, leading to conservative estimations of the peak undrained shear strength, are obtained for unbonded material. Both, the shear strength and the tip resistance increase due to soil structure, however, Nkt and Nke are not significantly influenced as long as no destructuration takes place during penetration.

Analytical Solution for Cavity Expansion in Rate-Dependent and Strain-Softening Clay and Its Application for CPT Tests

AbstractThis paper incorporated two important characteristics of clay, namely its rate-dependent and strain-softening behavior, into a theoretical framework based on cavity expansion. The modified ...

Investigation of pile penetration in calcareous soft rock using X-ray computed tomography

Penetration of open- and closed-ended model piles into intact chalk, a soft calcareous rock, was investigated using microfocus X-ray computed tomography (XCT). Three-dimensional images of the specimens showed that the piles crushed and densified the chalk in their path, creating a crushed chalk annulus around the shaft, a region of compressed destructured chalk below the tip, and fractures across cemented regions of the specimen. Laser-diffraction particle-size analyses of the crushed chalk annulus after exhumation showed limited difference with laboratory-remoulded chalk, which suggested thorough de-cementation. Installation stresses and XCT-derived densities were paired using a simplified cylindrical cavity expansion solution to estimate effective radial stress–void ratio states at the pile tip during penetration. More complex numerical solutions could not be applied using the available data. This approach posed significant problems, as it could not suitably incorporate hardening and non-linear stiffness behaviours of chalk during pile penetration, nor account for the creation of discontinuities. However, effective radial stress–void ratio estimates were found to converge with the reconstituted critical state line of the material at high stresses and low void ratios. This partially supported the use of a critical state framework to characterise pile penetration in chalk, as proposed in recent literature.

A semi-analytical solution to spherical cavity expansion in unsaturated soils

This paper presents a rigorous solution for spherical cavity expansion in unsaturated soils under constant suction condition. The hydraulic behavior that describes the saturation-suction relationship is modeled by a void ratio-dependent soil-water characteristic curve, which allows the hydraulic behavior to fully couple with the mechanical behavior that is described by an extended critical state soil model for unsaturated soil through the specific volume. Considering the boundary condition and introducing an auxiliary coordinate, the problem is formulated to a system of first-order differential equations with three principal stress components and suction as basic unknowns, which is solved as an initial value problem. Parameter analyses are conducted to investigate the effects of suction and the overconsolidation ratio on the overall expansion responses, including the pressure-expansion response, the distribution of the stress components around the cavity, and the stress path of the soil during cavity expansion. The results reveal that the expansion pressures and the distribution of the stress components in unsaturated soils are generally higher than those in saturated soils due to the existence of suction.

Load-displacement behaviour of tapered piles: Theoretical modelling and analysis

This paper presents a simplified analytical approach for evaluating the load-displacement response of single tapered pile and pile groups under static axial compressive loads. The response of the tapered pile shaft is considered elastically in the initial stage, whereas the increase in stresses due to slippage along the pile-soil interface is obtained from a developed undrained cylindrical cavity expansion solution based on the K0-based anisotropic modified Cam-clay (K0-AMCC) model. An effective iterative computer program is developed to calculate the load-displacement behaviour of a single tapered pile. Regarding the response analysis of tapered pile groups, a finite-difference method is employed to calculate the interaction between tapered pile shaft, and the linear elastic model to simulate the interaction developed at the pile base. A reduction coefficient is introduced into the analysis of pile shaft interaction to clarify the reinforcing effect between tapered piles. Therefore, the settlement calculation methods of pile groups are proposed for different pile cap stiffness. The calculation methods of single tapered pile and pile groups are validated using two 3D Finite Element (FE) programs, and the comparison results show that reasonable predictions can be made using the method proposed in this paper. Parametric studies are conducted to investigate the effects of taper angle, soil anisotropy, pile spacing, and pile number on the load-displacement behaviour of single tapered pile and tapered pile groups.

Undrained cylindrical cavity expansion in modified cam-clay soil: A semi-analytical solution considering biaxial in-situ stresses

This paper presents a semi-analytical solution for undrained cylindrical cavity expansion in modified Cam-clay soils under biaxial in-situ stresses based on the small strain and large strain assumptions in the elastic and plastic regions, respectively. The cylindrical cavity expansion problem is treated as a boundary value problem and formulated by solving a system of first-order differential equations with four stress components as basic unknown variables. The validity of the proposed solution is examined by comparing with the existing solution, where the in-situ stress is uniform. Extensive parametric studies are conducted to investigate the effects of biaxial in-situ stresses on the stress distribution, the expansion process and the shape and size of elastic-plastic boundary. The results indicate that the elastic-plastic boundary is in the shape of an ellipse due to the shear stress induced by biaxial in-situ stresses. The major axis of the elliptical elastic-plastic boundary is in accordance with the direction of the larger in-situ stress. The present solution is free of the limitation that the cavity expands under the uniform in-situ stress, therefore it is expected to provide a more general method for practical geotechnical and petroleum problems.

Expansion responses of a cylindrical cavity in overconsolidated unsaturated soils: A semi-analytical elastoplastic solution

This paper presents a semi-analytical elastoplastic solution for cylindrical cavity expansion in overconsolidated (OC) unsaturated soils under constant water content condition, in which both the OC features and the coupled hydro-mechanical behaviour of soils are properly addressed. The unified hardening model for OC unsaturated soil is further coupled with a void ratio-dependent soil-water characteristic curve to model the coupled hydro-mechanical soil responses during expansion. With the aid of an auxiliary variable, the coupled hydro-mechanical constitutive matrix for the investigated problem is finally formulated as a set of first-order ordinary differential equations in terms of Lagrangian description, with the three net stress components, the suction, and the void ratio as the basic unknowns. The governing differential equations are solved as an initial value problem with the code developed based on the Runge-Kutta algorithm. Parametric studies show that both the overconsolidation ratio and the suction have remarkable impacts on the expansion responses, including the distribution of stress components, the change of degree of saturation as well as the expansion pressures. The proposed solution could provide a reasonable tool for interpretation of the pressuremeter tests and prediction of pile installation effects in overconsolidated unsaturated soils.

Undrained cylindrical and spherical cavity expansion in elastic–viscoplastic soils

Various undrained cavity expansion solutions for elastic–plastic soil have been proposed previously. However, no solution has been presented for elastic–viscoplastic (EVP) soil until now. This paper presents a general solution method for solving the classical one-dimensional (1D) boundary value problem (BVP) for undrained cylindrical or spherical cavity expansion in EVP soil with an emphasis on the rate effect of soil. The solution method is summarized as three standard procedures: (i) obtaining the soil displacement and strain under incompressible conditions, (ii) calculating the effective stress of soil through a suitable constitutive law, and (iii) obtaining the pore pressure by numerically solving the stress equilibrium equation through the finite difference method (FDM) or other numerical solution techniques. The numerical algorithms for calculating the effective stress and pore pressure are very simple, without any complex iteration processes, and they require little calculation time but provide high computational accuracy. In addition, some numerical results are given to investigate the influence of the cavity expansion velocity on the cavity expansion response. The proposed solution procedure is general and can be applied not only for the EVP model but also for other plasticity models, and the given EVP solution can be applied to interpret the rate effect of the cone penetration test and pile penetration.

Solution for spherical cavity expansion in state-dependent soils

This work presents a spherical cavity expansion solution aimed at linking soil constitutive behavior with quantities that bear direct engineering meanings for practicing engineers (e.g., foundation bearing capacity). For this purpose, we derive the solution based on the state-dependent, critical state constitutive model proposed by Li and Dafalias (Geotechnique 50(4): 449–460, 2000), whose ability to realistically represent the actual mechanical behavior of sand has been extensively verified in the literature. To ensure the reliability of the solution, we verify it against an independent finite element analysis of spherical cavity expansion in solid governed by the same constitutive model. In this validation, we also highlight the dependence of cavity expansion response on the current state of granular materials relative to critical state. The application of the proposed solution in solving engineering problems is demonstrated in predicting the resistance of cone penetration and the ground movements associated with static pipe bursting in sand. We show that, based on the soil parameters determined from laboratory triaxial tests, the proposed solution can reasonably represent the dependence of cone penetration resistance on the density and pressure level of sand, as revealed from centrifuge testing. By comparing with finite element analysis, we demonstrate that the proposed solution can provide useful estimations for soil displacements caused by pipe bursting operation. These archetypal examples suggest that the proposed cavity expansion solution can form a theoretical basis for linking fundamental soil properties with quantities that have direct implications for geotechnical engineering practice.

Elasto-plastic solutions for expanding cavities in strain-hardening and/or softening soils

This paper presents an analytical finite strain solution for cavity expansion in strain-hardening and/or softening Mohr-Coulomb soil subjected to a non-associated flow rule. The evolutions of material parameters, i.e. deformation and strength parameters, are totally considered. The finite strain is applied to describe the plastic behavior with the logarithmic strain. By assuming constant material properties in a very small region, the plastic region is divided into a series of concentric annuli. The solution can be recursively obtained according to the closed-form solution of each annulus, and is suitable to soil with any complex material evolution types. For the cavity with the same cavity expansion a/a0, the required cavity pressure of strain-hardening and/or softening soils is larger and/or smaller than that of elasto-perfectly plastic soils for both spherical and cylindrical cavity expansions. With respect to the same cavity pressure, the displacement and stress around cavity of strain-hardening and/or softening models are larger and/or smaller than those of perfectly plastic model. With respect to the same cavity expansion displacement, the increases in the strength parameters including cohesive strength and friction enlarge the cavity pressure, and slightly decrease the plastic and residual radii.