The cyclic response in saturated sand is gaining increasing interest owing to the soil-structure interaction in seismic regions. The evolution of the pore water pressure in liquefiable soil can significantly reduce soil strength and impact the structural dynamic response. This paper proposes a semi-analytical solution for a cylindrical cavity subjected to cyclic loading in saturated sands, incorporating an anisotropic, non-associated SANISAND model. The problem is formulated as a set of first-order partial differential equations (PDEs) by combining geometric equations, equilibrium equations, stress-strain relationships and boundary conditions. Due to the non-self-similar nature of this problem, these PDEs are solved by the hybrid Eulerian-Lagrangian approach to determine the cyclic response of the cavity. Then finite-element simulations with a user-defined subroutine are performed to validate the proposed solution. Finally, parametric studies are presented with the focus on soil parameters and cyclic loading history. It is found that the cyclic responses of the cavity in saturated sands are sensitive to the initial void ratio, and the at-rest coefficient of earth pressure primarily affects the monotonic response but marginally affects the cyclic response. Cylindrical cavities are more likely to liquefy when the sands are compacted in a loose state and under lower displacement amplitudes. The proposed solution has potential use for future research on the cyclic response of the soil-structure interaction in geotechnical engineering.

The particle breakage effect in sand exerts a significant influence on the design of underground space structure. However, the existing theories seldom consider the breakage effect and often lack accurate descriptions of void ratio changes, leading to substantial errors in the numerical calculations compared to the actual scenario. This study employs the simple critical state sand model (SIMSAND) to account for the particle breakage effect and transforms the drained cylindrical cavity expansion problem into a set of first-order ordinary differential equations described by the Lagrangian method. The analytical solution of the cylindrical cavity expansion problem is calculated using Matlab programming codes. Firstly, Fontainebleau sand is investigated to analyse the influence of initial stress, void ratio and specific volume around the cavity. The combined effects of initial stress and particle breakage on the soil around the cavities result in dilatancy characteristics and a reduction in void ratio. The stress path analysis reveals that the soil around the cavities only reaches a critical state under high initial stresses. Secondly, a plane strain numerical model is established for twice expansion to verify the calculation outcomes from the cylindrical cavity expansion theory. Finally, an axisymmetric cone penetration test (CPT) model is developed to analyse the theoretical and numerical solutions for expansion stress and sleeve friction. The research results indicate that the CPT in sand need to consider the particle breakage effect, especially under high stress conditions. Without considering particle breakage, the sleeve friction is overestimated. These research findings can offer guidance for geotechnical engineering applications, such as CPT, pressuremeter tests and predictions of bearing capacity for pile foundations in sand. Based on the cavity expansion theory and numerical simulations, particle breakage effect of sand is studied. The findings reveal that neglecting the particle breakage effect leads to a marked increase in the calculation results.image

This paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr-Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary K-0 values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with K-0=1. It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K-0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle theta in between 5 pi/3 and 11 pi/6 or on the specific line of theta = 11 pi/6. The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr-Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive-frictional soils.

Drilling with prestressed concrete (DPC) pipe pile is a nonsqueezing pile sinking technology, employing drilling, simultaneous pile sinking, a pipe pile protection wall, and pile side grouting. The unloading induced by drilling, the pipe pile supporting effect, and the dissipation of the negative excess pore-water pressure after pile sinking, all of which have significant effects on the recovery of soil pressure on the pile side, are the main concerns of this study, which aim to establish a method to reasonably evaluate the timing selection of pile side grouting. The theoretical solutions for characterizing the unloading and dissipation of the negative excess pore-water pressure are presented based on the cylindrical cavity contraction model and the separated variable method. By inverse-analyzing the measured initial pore pressure change data from borehole unloading, initial soil pressures on the pile side of each soil layer are determined using the presented theoretical solutions. Then, the presented theoretical solutions were verified through a comparative analysis with the corresponding measured results. Moreover, by introducing time-dependent coefficients alpha(t1) and alpha(t2) to characterize the pore pressure dissipation and rheology effects, the effects of the negative excess pore-water pressure dissipation on the pile-side soil pressure recovery are discussed in detail.

Stress and deformation analysis of a cavity in an infinite/finite medium is a fundamental applied mechanics problem of interest in multiple physics and engineering disciplines. This paper develops a complete semianalytical solution for the cylindrical cavity expansion in nonassociated Mohr-Coulomb materials, by using the graphical approach and Lagrangian formulation of the cavity boundary value problem (through tracing the responses of a single material point at the cavity wall). The novelty of the new solution framework lies not only in the relaxation of the stringent intermediacy assumption for the vertical stress as usually adopted in the previous analyses, but also in the comprehensive consideration of nonhydrostatic initial stress conditions via arbitrary values of K0 (the coefficient of earth pressure at rest defined as the ratio between the horizontal and vertical initial stresses). The essence of the so-called graphical method, i.e., the unique geometrical analysis and tracking of the deviatoric stress trajectory, is fulfilled by leveraging the deformation requirement that during cavity expansion the progressive development of the radial and tangential strains must maintain to be compressive and tensile, respectively. With the incorporation of the radial equilibrium condition, the problem is formulated to solve a single first-order differential equation for the internal cavity pressure with respect to a pivotal auxiliary variable, for all the distinct scenarios of K0 being covered. Some selected results are presented for the calculated cavity pressure-expansion curve and limit cavity pressure through an example analysis. The definitive semianalytical solution proposed will be not only substantially advancing the current state of knowledge on the fundamental cavity expansion theory, but also able to serve as a unique benchmark for truly verifying the correctness and capability of the classical cornered Mohr-Coulomb constitutive model built in commercial finite element programs.

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.

This study analyzes the stability of surrounding rock for a circular opening based on the energy and cavity expansion theory, and regards the surrounding rock failure of circular opening as an unstable state driven by energy. Firstly, based on the large-strain cylindrical cavity contraction and energy dissipation method, the deformation caused by the excavation of surrounding rock is regarded as the cylindrical cavity contraction process. By introducing the energy dissipation mechanism, the energy dissipation solution of cylindrical cavity contraction is obtained. The energy dissipation process of surrounding rock is characterized by the strain energy changes in the elastic and elasto-plastic regions of this cavity contraction analysis. Secondly, the deformation control effect of support and surrounding rock parameters on the energy dissipation of surrounding rock is studied based on the energy dissipation solution of surrounding rock under support conditions. Finally, the effectiveness and reliability of the analytical approach was demonstrated by comparing the support design results with those in the literature. The research results indicate that the three-dimensional mechanical properties and dilatancy angle of rock and soil mass have a significant impact on the energy support design of surrounding rock. This study provides a general analysis method for the stability analysis of surrounding rock of deep buried tunnels and roadway.

An elastoplastic analysis scheme for the cylindrical cavity expansion in offshore islands unsaturated soils considering anisotropy is established. The hydraulic properties and anisotropy caused by stress of unsaturated soils are coupled in an elastoplastic constitutive matrix for unsaturated soil to obtain the governing equations for the cylindrical cavity expansion problem, with an analytical solution that utilizes the original hydro-mechanical state of the soil as the initial conditions. Through a comparative analysis with other analytical solutions, the effectiveness of the new solution is verified. Moreover, the swelling response of the cylindrical cavity expansion in unsaturated soils is examined by systematically analyzing different parameters of the surrounding soil. The findings reveal that the development and rate of anisotropy in normal consolidated soil and over-consolidated soil exert a significant impact on the soil's mechanical characteristics. Nevertheless, the alteration in the model constant h has little effect on the soil's mechanical characteristics. The analytical solution introduces anisotropy and broadens the expansion theory of unsaturated soils to yield a more comprehensive theoretical framework for the comprehensive analysis of offshore islands' unsaturated soils.

Soils are known to be inherently anisotropic, resulting in complex responses to loading. This paper aims to develop an elastoplastic solution for the undrained expansion of a cylindrical cavity in sands adopting a non-associated and anisotropic model, SANISAND. The rigorous derivation of the stress-strain state of the soil element is provided following a standardized solving procedure. The dilatancy and crushing of the soil are invoked in the three-dimensional cavity expansion solution by adopting the critical state soil mechanics and limiting compression curve, respectively. By combining this with a governing equation that considers the undrained condition, the stress-strain state of the surrounding soil around the cavity can be determined. A subroutine is then implemented into the ABAQUS FEM simulation to verify the solution. The solutions are also validated against those based on an isotropic model, and anisotropic sand is used to investigate the effects of the initial effective mean stress, at-rest coefficient of earth pressure, and overconsolidation ratio on the stress distribution, stress path, and boundary surfaces.