Solution For Cylindrical Cavity Expansion Research Articles

Undrained semi-analytical solution for cylindrical cavity expansion in anisotropic soils under biaxial stress conditions

This paper presents an undrained semi-analytical elastoplastic solution for cylindrical cavity expansion in anisotropic soil under the biaxial stress conditions. The advanced simplified SANICLAY model is used to simulate the elastoplastic behavior of soil. The cavity expansion is treated as an initial value problem and solved as a system of eight first-order ordinary differential equations including four stress components and four anisotropic parameters. The results are validated by comparing the new solutions with existing ones. The distributions of stress components and anisotropic parameters around the cavity wall, the expansion process, the stress yield trajectory of a soil element and the shape and size of elastoplastic boundary are further investigated to explore the cavity expansion response of soils under biaxial in situ stresses. The results of extensive parameters analysis demonstrate that the circumferential position of the soil element and the anisotropy of the soils have noticeable impacts on the expansion response under biaxial in situ stresses. Since the present solution not only considers the anisotropy and anisotropy evolution of natural soil, but also eliminates the conventional assumption of uniform radial pressure, the solution is better than other theoretical solutions to explain the pressure test and pile installation effect of shallow saturated soil.

Undrained Solution for Cylindrical Cavity Expansion in Structured Clays Using a Hypoplastic Model

Undrained Solution for Cylindrical Cavity Expansion in Structured Clays Using a Hypoplastic Model

A semi-analytical undrained solution for cylindrical cavity expansion in K 0-consolidated anisotropic soils under plane stress condition

To remove the limitation that the plane stress problem cannot be considered using cylindrical cavity expansion and to explore surface response of cylinder expansion in shallow soil, a semi-analytical undrained solution is developed for cylindrical cavity expansion in anisotropic modified Cam-clay model soils under the plane stress condition. The constitutive relationship is described by the K 0-consolidated anisotropic modified Cam-clay (K 0-AMCC) model, which can properly simulate the mechanical behaviour of the K 0-consolidated natural clays. The problem is equivalent to solving ordinary differential equations to determine the effective stresses, vertical strain, and excess pore water pressure (EPWP). Parametric analyses are conducted to investigate the effective stresses, vertical strain, and EPWPs around the expanded cavity under plane stress condition. The results show a clear influence of over-consolidation ratio on the stresses, vertical strain, EPWP around the cavity, and effective stress paths for a soil particle at the cavity wall. Axial expansion or uplift of soil and negative pore water pressure are observed during cavity expansion under the plane stress condition. There are obvious differences in effective stress components around the cavity under two plane conditions. The effective axial stress around the cavity wall is generally smaller than that under the plane strain condition.

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.

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.

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.

Elastoplastic solutions for cylindrical cavity expansion in unsaturated soils

Elastoplastic solutions are developed in this paper for cylindrical cavity expansion in unsaturated soils, aiming to provide a theoretical model to analyze the pressuremeter test and pile installation in unsaturated soils. The novelty of the solution lies in the subtle coupling of hydraulic behaviour and mechanical behaviour of the soil in the governing equations. An elastoplastic critical state model for unsaturated soils is used to derive the elastoplastic constitutive matrix for both the undrained (constant gravimetric water contents) and drained (constant suction) expansion of a cylindrical cavity in unsaturated soils, which are finally formulated to a system of first-order differential equations. The governing differential equations are solved as an initial value problem with the initial conditions determined by the yield function of the unsaturated soil model and continuous condition. Parametric studies are performed to investigate the expansion responses of the surrounding soil and particular attention is given to the responses at the cavity wall. The results indicate that suction has significant effects on both the mechanical and hydraulic responses of the surrounding soil.

Drained solution for cylindrical cavity expansion in modified Cam clay soil under constant vertical stress

Cavity expansion is a fundamental theoretical problem in geomechanics. For the cylindrical cavity expansion problem, derivations of solutions are usually based on the assumption that the soil is subject to the plane strain condition. However, this is untrue for cavity expansion in pressuremeter tests. This study first derived the equilibrium equation for cylindrical cavity expansion under the constant vertical stress condition. Then, the equilibrium equation was solved for modified Cam clay soils with different overconsolidation ratios (OCRs). The solutions were compared with the responses in the same soils under the plane strain condition. It was found that the ratio of the limiting cavity pressure in the latter to that in the former ranged from 1.31 to 2.76 and increased with an increase in the OCR. Under the constant vertical stress condition, significant heaving occurred in the vicinity of the cavity, and volumetric strain evolved from contraction to dilation as the OCR increased. Significant differences were noted in the stress paths of the two different loading conditions. These results indicate that the assumption of the plane strain condition will lead to overestimation of the limiting cavity pressure and inaccurate prediction of the stress path in the pressuremeter test, especially for heavily overconsolidated soils.

Drained analyses of cylindrical cavity expansion in sand incorporating a bounding-surface model with state-dependent dilatancy

• Governing differential equations of the cylindrical cavity expansion problem are solved as an initial value problem . • Rigorous definitions of the invariant stresses permit the examination of the effect of k 0 value. • Model parameters that are of paramount importance for the cylindrical cavity expansion analyses are presented. This paper presents a semi-analytical drained solution for cylindrical cavity expansion in sand. By introducing an auxiliary variable, defined as the ratio of the original position to the current position of a material particle, the governing differential equations of the cylindrical cavity expansion problem can be transformed into a group of first-order ordinary differential equations. These equations are solved as an initial value problem by incorporating a bounding-surface model with state-dependent dilatancy. This approach does not require the division of the material around the cavity into an elastic zone and a plastic zone. The state-dependent dilatancy model employed in this study allows the investigation of the effects of the initial relative density and mean normal stress of the sand, whereas the rigorous definitions of the invariant stresses permit the examination of the effect of the initial ratio of the horizontal stress to the vertical stress. Moreover, the model parameters that are of paramount importance for the cylindrical cavity expansion analyses are determined via comprehensive parametric studies.

Drained Elastoplastic Solution for Cylindrical Cavity Expansion in K0-Consolidated Anisotropic Soil

This paper presents a semianalytical solution for drained expansion of a cylindrical cavity in K0-consolidated clay. The solution is derived based on the K0-based anisotropic modified Cam-clay model (K0-AMCC), which can properly consider the initial stress anisotropy and the initial stress-induced anisotropy of natural soils. Parametric studies are carried out to investigate the effects of different overconsolidation ratios on the growth of plastic zone and cavity pressure, the distributions of the stress components and the specific volume around the cavity, and the effective stress path. The results are compared with the published solution based on the modified Cam-clay model to study the effects of the initial stress anisotropy and the initial stress-induced anisotropy on the cylindrical cavity expansion. The present solution provides a more realistic interpretation for practical geotechnical engineering problems such as pressuremeter tests and cone penetration tests.

A semi-analytical solution for cylindrical cavity expansion in elastic–perfectly plastic soil under biaxial in situ stress field

This paper presents an elastic–plastic semi-analytical solution for cylindrical cavity expansion in undrained soil (incompressible material) under the biaxial in situ stress condition. The soil around a cylindrical cavity is assumed to behave as elastic–plastic perfectly plastic material, as characterised by Tresca yield strength with the associated flow rule. Based on Galin's solution, the stress and the elastic–plastic boundary around the cylindrical cavity can be determined using the conformal mapping technique and complex variable theory. Then, by considering incompressible and small strain–displacement conditions, the problem of kinematics is reduced to solving a system of the second-order ordinary differential equations, which results in the general solution for the radial and circumferential displacements in the plastic zone around the cylindrical cavity. Subsequently, the constant coefficients of the general solution can be determined by the displacement continuity condition at the elastic–plastic...

A semi-analytical solution for cylindrical cavity expansion in elastic–perfectly plastic soil under biaxial in situ stress field

This paper presents an elastic–plastic semi-analytical solution for cylindrical cavity expansion in undrained soil (incompressible material) under the biaxial in situ stress condition. The soil around a cylindrical cavity is assumed to behave as elastic–plastic perfectly plastic material, as characterised by Tresca yield strength with the associated flow rule. Based on Galin's solution, the stress and the elastic–plastic boundary around the cylindrical cavity can be determined using the conformal mapping technique and complex variable theory. Then, by considering incompressible and small strain–displacement conditions, the problem of kinematics is reduced to solving a system of the second-order ordinary differential equations, which results in the general solution for the radial and circumferential displacements in the plastic zone around the cylindrical cavity. Subsequently, the constant coefficients of the general solution can be determined by the displacement continuity condition at the elastic–plastic boundary using the least-squares method. The new elastic–plastic analytical solution presented in this paper extends Galin's solution, particularly by giving a closed-form equation for the kinematics around the cylindrical cavity, which could reflect the ‘non-circular effect’ of the cylindrical cavity during the expansion in a biaxial in situ stress field. The new solution completes the theoretical framework for addressing the fundamental problem of cylindrical cavity expansion, and also provides a useful theoretical tool for potential application in geotechnical engineering problems such as in situ testing (pressuremeter tests in a biaxial in situ stress field).

Basic Mechanical Parameter Relations of Soft Clay in Pearl River Delta

Basic parameters relations among CPT parameters, un-drained strength and other mechanical parameters of soft clay are presented based on an elastic-plastic solution for cylindrical cavity expansion for soil investigation in energy engineering. The relation between CPT parameters and shear strength from vane test is also presented based on the result. Thus, the CPT parameters can be determined directly by elastic parameters and shear strength or vane shear parameters and vice versa. That makes it possible to save the high test costs and provide theoretical formulas to avoid some tests which are limited due to the site and/or other condition. Results are compared between the relations and in situ data at a large-scale project in the Pearl River Delta. The results showed consistency between the relation and in situ data.

Exact drained solution for cylindrical cavity expansion in modified Cam Clay soil

This work presents a novel, exact solution for the drained expansion of a cylindrical cavity in modified Cam Clay soil. Following the rigorous definitions for the mean and deviator stresses and therefore an exact constitutive relationship, the problem is formulated as a set of first-order simultaneous differential equations in the plastic zone with the aid of an auxiliary variable. The solution procedure proposed has the advantage over the conventional similarity method in that it is directly applicable to the cavity expansion problem of finite initial radius. Also the solution derived is sufficiently general to be applied to a more realistic situation of non-isotropic in situ stress condition and to the cavity contraction problem. Extensive parametric studies have been carried out to illustrate the effect of the overconsolidation ratio on the cavity expansion and stress distributions around the cavity, as well as on the stress path and specific volume change due to expansion. The present solution can and is used here as a benchmark for numerical solutions of cavity expansion in modified Cam Clay soil using Abaqus, the finite-element analysis commercial program.

Exact undrained elasto-plastic solution for cylindrical cavity expansion in modified Cam Clay soil

This paper presents an exact semi-analytical analysis for cylindrical cavity expansion in modified Cam Clay critical state soil under the undrained condition. By assuming small-strain deformation in the elastic region and large-strain deformation in the plastic region, the formulation of the problem is reduced to solving a system of first-order ordinary differential equations for the radial, tangential and vertical effective stresses in the plastic zone. The pore pressure distribution can subsequently be determined from the radial equilibrium equation in terms of the total stresses. The semi-analytical solution derived in this paper follows the rigorous definitions for the two effective stress invariants instead of approximate ones, as usually assumed in the existing literature, and applies to the more general case where the out-of-plane (vertical) in situ stress may be different from the in-plane (horizontal) one. The results show clearly that the stress history (overconsolidation ratio) has a significant influence on the stress and pore pressure distributions around the cavity. The present solution provides an exact and realistic theoretical framework for predicting the soil behaviour around the cylindrical cavity, with applications to the interpretation of pressuremeter tests and to pile installation problems. It also serves as a valuable benchmark for verifying various cavity expansion numerical methods involving the critical state plasticity model.

Unified Analytical Solution for Cylindrical Cavity Expansion of Saturated Soil Based on Large Deformation and Non-Drainage

Soil around the cylindrical pore is divided into elastic and plastic regions. In the elastic region, the small deformation theory is applied while in the plastic region, the large deformation theory and unified strength criterion are applied. According to the stress equilibrium equation and the boundary condition of continuous stress and deformation, the theoretical solution to plastic region radius, limit expansion pore pressure excess pore pressure and excess pore water pressure of the cylindrical cavity expansion can be derived when considering large deformation and non-drainage problems. Compared to the theoretical results of Cao L.F., the theoretical calculation results are closer to the field test results which show that the theory has a certain value in engineering application. Through calculations and analysis, it is also derived that expansion pore pressure increase is non-linear with the increase of b value, while the excess pore water pressure is just the opposite.