Analysis of cylindrical cavity expansion in a strain weakening material

doi:10.1016/0266-352X(85)90021-7

Computers and Geotechnics

Volume 1, Issue 3, 1985, Pages 161-180

https://doi.org/10.1016/0266-352X(85)90021-7 Get rights and content

Abstract

A numerical technique is suggested that allows a prediction of the behaviour of a single phase, strain softening material during the expansion of a long cylindrical cavity. The method provides the entire pressure-expansion relationship, including the identification of the limit pressure at large deformations.

The numerical solutions, obtained using the finite element technique and allowing for finite deformations, show very good agreement with closed form answers that are available for a restricted class of material models. Results are also presented for the more general, dilatant (or collapsing), strain softening materials for which closed form solutions do not exist. The importance of the rate of dilation and rate of softening in determining the behaviour during cavity expansion is illustrated.

References (13)

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Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity
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Cemented sand under static loading
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There are more references available in the full text version of this article.

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This paper presents a semi-analytical solution for calculating soil stresses and pore pressures in the vicinity of an expanding cylindrical cavity. The main features of the solution are: i) realistic modelling of time-dependent soil behaviour, by means of an elastic-viscoplastic constitutive model, and ii) accurate prediction of soil strength under the stress path followed during plane-strain undrained cavity expansion, by using the transformed stress method to formulate the solution in the three-dimensional stress space and adopting an appropriate failure criterion. Predictions of the presented solution are benchmarked against a published solution, and are comprehensively analysed to identify the effect of the failure criterion and of the cavity expansion rate on the soil stresses and pore pressures developing in the vicinity of the cavity, and the associated stress paths.
Elastoplastic solution of drained expansion of a cylindrical cavity in structured soils considering structure degradation
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Citation Excerpt :
Thus, they are unable to capture the remarkable feature concerning soil strain hardening/softening (Vesic, 1972; Carter et al., 1979; Chu et al., 1992; Adachi and Oka, 1995). Additionally, some approximations and (or) simplifications, mainly including the non-associated flow rule and large deformation theory (Carter and Yeung, 1985; Yu and Houlsby, 1990; Yu and Houlsby, 1991; Yang and Zou, 2011), are made for the description of the soil deformation behaviour after yielding. Subsequently, cylindrical cavity expansion has gradually been employed for more complex geotechnical engineering problems by adopting critical state constitutive models (e.g., the Cam-clay (CC) model, the modified Cam-clay (MCC) model, and the anisotropic modified Cam-clay (AMCC) model) (Au et al., 2006; Wang et al., 2010; Mcmahon et al., 2013; Li et al., 2019; Chen et al., 2020; Li et al., 2021; Yang et al., 2021).
An elastoplastic solution of drained cylindrical cavity expansion is presented based on a well-known critical state model for soils exhibiting a natural structure. The model referred to as the structured Cam-clay (SCC) model is capable of describing the properties of the soil structure and its subsequent stress-induced degradation. The asymmetric stiffness matrix of the elastoplastic constitutive equation for structured soils is derived due to the assumption of the non-associated plastic flow rule. The solution procedure is formulated by transforming the boundary value problem of cylindrical cavity expansion into the problem of solving four ordinary differential equations with three stress components and the specific volume as the basic unknown variables. The theoretical solution is numerically calculated and validated against the existing solution and finite element simulation results. Furthermore, the significance of the soil structure and its stress-induced degradation in the expansion response, and the interaction between the soil structure and overconsolidation are emphasized by extensive parametric analyses. The results demonstrate that the soil structure has a substantial influence on the cavity expansion response, and its degradation is closely related to overconsolidation. Particularly, among the solutions considered, the solution considering the soil structure provides higher effective stress values near the cavity surface due to the additional strength conveyed by the natural structure.
Three dimensional discrete element simulation of cylindrical cavity expansion from zero initial radius in sand
2020, Computers and Geotechnics
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However, as more complex and realistic soil models were developed, analytical solutions could be considered as overly simplified, and numerical techniques may be the most effective way to obtain accurate solutions [7,8]. Hence, numerical solutions were developed to consider more realistic and sophisticated soil constitutive models in cohesive and cohesionless soils under fully drained or undrained conditions [8–12]. Along with progress made in the development of fundamental solutions for cavity expansion in geomaterials, the cavity expansion theories have been widely adopted to analyse real-life geotechnical problems such as the installation of driven piles, interpreting pressuremeter and cone penetration tests and so forth.
This study seeks to assess the influence of choice of initial cavity radius on the soil response during cavity expansion in sandy soil adopting three-dimensional discrete element simulations and obtaining the size of the influence zone when the expansion starts from zero initial radius. Sandy soil is modelled adopting rolling resistance contact model to capture the effects of particle interlocking, and the microscopic parameters are calibrated utilising linear model deformability method for both loose and dense sands against experimental results. Four cylindrical cavity expansions that commenced from different initial radii are simulated in dense and loose sand specimens. The large-scale three-dimensional model is proposed with more than 500,000 particles, enabling precise volumetric dilation and contraction predictions using strain rate tensors. During the cavity expansion process, cavity pressure is constantly recorded by appropriate subroutines, while the stress-strain and void ratio variations are continuously monitored using an array of prediction spheres situated close to the internal cavities.
The results confirm that the initial cavity radius chosen has conspicuous effects on the cavity pressure, the stress path, the volumetric strain and the deviatoric stress, especially at the initial stage of expansion; however, these effects become less pronounced and are ultimately minor as the cavity reaches full expansion. The results confirmed that given the same expansion volume, the pressure required to create a cavity is significantly larger than expanding an existing cavity in the same soil medium, whereas the pressure needed to maintain an already expanded cavity is not sensitive to the choice of initial cavity radius. The results obtained were further validated adopting the variations of stress path, deviatoric stress and volumetric strain in the vicinity of the cavity wall. The findings from this study may provide practicing engineers with confidence in determining the appropriate size of the pilot hole in driven pile installation and horizontal directional drilling for trenchless piping in sandy soil. In addition, the lateral soil displacement induced by cavity expansion is also examined in this study. It is concluded that the radial displacement due to cavity expansion in loose sand can reach 25 $a_{f}$ ( $a_{f}$ representing the final cavity radius), while a larger influence zone must be considered by practicing engineers when dealing with dense sand.
Influence of particle contact models on soil response of poorly graded sand during cavity expansion in discrete element simulation
2018, Journal of Rock Mechanics and Geotechnical Engineering
Citation Excerpt :
However, obtaining closed-form solutions may become difficult when more realistic constitutive models are incorporated, and therefore numerical approaches can offer a better solution (Carter et al., 1979a). Hence, there are numerous analyses available adopting numerical techniques and simulations based on continuum method for cavity expansion (Carter et al., 1979b; Carter and Yeung, 1985; Mo et al., 2014; Li et al., 2017). However, the discrete element studies may provide researchers with a microscopic level of insight to study the complex cavity expansion related problems.
The discrete element method (DEM) has been extensively adopted to investigate many complex geotechnical related problems due to its capability to incorporate the discontinuous nature of granular materials. In particular, when simulating large deformations or distortion of soil (e.g. cavity expansion), DEM can be very effective as other numerical solutions may experience convergence problems. Cavity expansion theory has widespread applications in geotechnical engineering, particularly to the problems concerning in situ testing, pile installation and so forth. In addition, the behaviour of geomaterials in a macro-level is utterly determined by microscopic properties, highlighting the importance of contact models. Despite the fact that there are numerous contact models proposed to mimic the realistic behaviour of granular materials, there are lack of studies on the effects of these contact models on the soil response. Hence, in this study, a series of three-dimensional numerical simulations with different contact constitutive models was conducted to simulate the response of sandy soils during cylindrical cavity expansion. In this numerical investigation, three contact models, i.e. linear contact model, rolling resistance contact model, and Hertz contact model, are considered. It should be noted that the former two models are linear based models, providing linearly elastic and frictional plasticity behaviours, whereas the latter one consists of nonlinear formulation based on an approximation of the theory of Mindlin and Deresiewicz. To examine the effects of these contact models, several cylindrical cavities were created and expanded gradually from an initial radius of 0.055 m to a final radius of 0.1 m. The numerical predictions confirm that the calibrated contact models produced similar results regarding the variations of cavity pressure, radial stress, deviatoric stress, volumetric strain, as well as the soil radial displacement. However, the linear contact model may result in inaccurate predictions when highly angular soil particles are involved. In addition, considering the excessive soil displacement induced by the pile installation (i.e. cavity expansion), a minimum distance of 11a (a is the cavity radius) is recommend for practicing engineers to avoid the potential damages to the existing piles and adjacent structures.
Resin injection in clays with high plasticity
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Citation Excerpt :
The reported test results in sandy soils showed the positive effect of the resin injection [11,12], but further investigations are still necessary for clays, particularly for clays with high plasticity. Furthermore, the analysis of a cylindrical or spherical cavity has been applied to practical problems such as the interpretation of pressuremeter tests, the bearing capacity of deep foundations, and the installation of the driven piles [13–26]. In this context, this paper presents some in situ experimental results in a clay soil with high plasticity at different depths before and after injection.
Regarding the injection process of polyurethane resins in clays with high plasticity, this paper presents the experimental results of the pressuremeter and cone penetration tests before and after injection. A very important increase in pressure limit or in soil resistance can be observed for all the studied depths close to the injection points. An analytical analysis for cylindrical pore cavity expansion in cohesive frictional soils obeying the Mohr–Coulomb criterion was then used to reproduce the pressuremeter tests before and after injection. The model parameters were calibrated by maintaining constant the elasticity parameters as well as the friction angel before and after injection. A significant increase in cohesion was observed because of soil densification after resin expansion. The estimated undrained cohesions, derived from the parameters of the Mohr–Coulomb criterion, were also compared with the cone penetration tests. Globally, the model predictions show the efficiency of resin injection in clay soils with high plasticity.
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Analysis of cylindrical cavity expansion in a strain weakening material

Abstract

Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity

Int. J. Numer. Anal. Methods Geomech.

The quasi-static expansion of a spherical cavity in metals and ideal soils

Quarterly Journal of Mechanics and Applied Mathematics

Cemented sand under static loading

Geotech Engg Divn, ASCE

Theories of plasticity and the failure of soil masses

Rapid expansion of a cylindrical cavity in a rate-type soil

Int. J. Numer. Anal. Methods Geomech.

In-situ measurement of soil properties with the pressurementer

Civil Eng. and Public Works Review