Analytical And Numerical Analysis Of Large Deformation Cylindarical Cavity Expnasion Under Anisotropic Initial Stress

Classical cavity expansion theory assumes that the initial in-situ stress is isotropic.Therefore,for such projects like horizontal direction drilling(HDD),pipe jacking,and tunnel excavation,in which the in-situ stress is anisotropic,the classical cavity expansion theory cannot be used to explain the disturbance and environmental consequences.A series of research has been conducted on anisotropic stress influence by theoretical and numerical methods in the past,however,most of these solutions were proposed by using the small strain assumption.It is required to conduct the study on large deformation cavity expansion under anisotropic in-situ stress to refine the cavity expansion theory.This paper aims to build up a common analytical model for large deformation cavity expansion in elastoplastic material under biaxial stress and propose the analytical solution for pressure-expansion relationship and ultimate cavity wall pressure.Then,the numerical model could be built by using the large deformation finite element method to further validate the assumptions of the analytical model.After that,the paper will continue to conduct study on the traditional calculation method of HDD maximum mud pressure,and present a new calculation method by introducing the cavity expansion theory with large deformation under anisotropic initial stress.The content of this paper could be summarized as follows:1)The study on stress and deformation distribution of large deformation cylindrical cavity expansion under anisotropic initial stress is conducted by using complex variable theory.The semi-analytical elastic-plastic solutions(1.approximate analytical solution under Tresca criteria;2.approximate analytical solution under Mohr-Coulomb criteria)for pressure-expansion relationship and ultimate cavity wall pressure are proposed.The solution proposed in this paper is an extension of Zhou’s study in 2014.Zhou studied the effect of anisotropic initial stress on cavity expansion mechanism under Tresca yield criteria based on Gibson&Anderson’s study,which adopted the isotropic initial stress assumption.The presented solution could further study the problem under Moher-Coulomb criterion and could degenerate to the solution under Tresca criterion.2)The numerical study on displacement-controlled cylindrical cavity expansion with large deformation under anisotropic in-situ stress in undrained Tresca soil is conducted by using Coupled Eulerian-Lagrangian(CEL)large deformation finite element technique.The numerical results reveal the mechanism of cavity expansion under anisotropic initial stress,and the pattern could be interpreted as follows:The plastic zone can be divided into two parts.One is the elliptical zero-shear stress area surrounding the cavity,the other one is the non-zero-shear stress area located at the protrusion of the plastic zone.It should be noted that the radial stress distribution almost satisfies the radial stress equilibrium equation in the zero-shear stress zone(consistent with the conventional isotropic stress cavity expansion theory).Contrary,this feature changes apparently in non-zero-shear stress area.Furthermore,the proportion of the non-zero-shear stress area in plastic zone gets a notable increase with the decreasing coefficient K and shear strength su.The increasing proportion of non-zero-shear stress area could result in a non-elliptical plastic zone,which is not consistent with the conformal mapping function of the analytical model.3)The effect of soil strength parameters and initial stress condition on ultimate cavity wall pressure under Tresca criteria is discussed by CEL numerical analysis.An empirical solution for the average ultimate cavity wall pressure is presented by parameter analysis.The errors between the empirical solution,presented solution in this paper and Zhou’s approximate solution is analyzed.And the result indicates that the presented solution has a better consistency with empirical prediction.The empirical solution has potential to process the analysis of problems such as Horizontal Directional Drilling(e.g.Tunneling)and pipeline installation.4)The failure mechanism and basic assumptions of traditional method for HDD maximum mud pressure prediction are discussed.After that,a new predicting method of HDD maximum mud pressure is proposed by introducing the pressure-expansion relationship of large deformation cavity expansion under biaxial in-situ stress.Then the predicted maximum mud pressure obtained by different methods is compared with the practical mud pressure record.The result indicates that the presented prediction results,in general,have smaller errors with practical record compared with Delft equation and Xia’s solution.Moreover,the traditional methods have a shortage in analyzing the deformation caused by well-bore excavation,thus the maximum radius of the plastic zone is evaluated by empirical relation.The presented method removes this limitation and the predicted results could be more rational in HDD project with small radius of reamer.