An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

Ground reaction curves for circular excavations in non-homogeneous,axisymmetric strain-softening rock masses

Fast methods to solve the unloading problem of a cylindrical cavity or tunnel excavated in elasto-perfectly plastic, elasto-brittle or strain-softening materials under a hydrostatic stress feld can be derived based on the self-similarity of the solution. As a consequence, they only apply when the rock mass is homogeneous and so exclude many cases of practical interest. We describe a robust and fast numerical technique that solves the tunnel unloading problem and estimates the ground reaction curve for a cylindrical cavity excavated in a rock mass with properties depending on the radial coordinate, where the solution is no longer self-similar. The solution is based on a continuation-like approach(associated with the unloading and with the incremental formulation of the elasto-plastic behavior), fnite element spatial discretization and a combination of explicit sub-stepping schemes and implicit techniques to integrate the constitutive law, so as to tackle the diffculties associated with both strong strain-softening and elasto-brittle behaviors. The developed algorithm is used for two practical ground reaction curve computation applications. The frst application refers to a tunnel surrounded by an aureole of material damaged by blasting and the second to a tunnel surrounded by a ring-like zone of reinforced(rock-bolted) material.

Instability criterion for the system composed of elastic beam and strain-softening pillar based on gradient-dependent plasticity

A mechanical model is proposed for the system of elastic beam and strain-softening pillar where strain localization is initiated at peak shear stress. To obtain the plastic deformation of the pillar due to the shear slips of multiple shear bands, the pillar is divided into several narrow slices where compressive deformation is treated as uniformity. In the light of the compatibility condition of deformation, the total compressive displacement of the pillar is equal to the displacement of the beam in the middle span. An instability criterion is derived analytically based on the energy principle using a known size of localization band according to gradient dependent plasticity. The main advantage of the present model is that the effects of the constitutive parameters of rock and the geometrical size of structure are reflected in the criterion. The condition that the derivative of distributed load with respect to the deflection of the beam in the middle span is less than zero is not only equivalent to, but also even more concise in form than the instability criterion. To study the influences of constitutive parameters and geometrical size on stability, some examples are presented.

Modified ground response curve(GRC)in strain-softening rock mass based on the generalized Zhang-Zhu strength criterion considering over-excavation

The ground response curve(GRC)depicts the relationship between support reaction force and ground displacement,which improves the understanding of ground-support interaction and provides important references to the tunnel design.However,it is difficult to anticipate the tunneling-induced large deformation with sufficient reliability in soft rock with high geostress since the small strain theory is not applicable.When large deformation occurs,the tunnel needs to be over-excavated.Thus,the GRC should be modified considering the enlarged excavation radius since the actual excavation radius is usually greater than the designed one.To overcome the shortcomings of small strain theory in recognizing ground-support interaction under large deformation circumstances,a new large strain numerical approach for modifying the GRC was proposed considering over-excavation in strain-softening rock masses based on the generalized Zhang-Zhu strength criterion.A case study was conducted based on the Lianchengshan tunnel in China.The modified GRC was employed to investigate the ground-support behavior for different support schemes and to explore the applicability of the stress release measures.Combined with field tests,the proposed approach was validated.By comparing with GRCs proposed by previous work,the present modified GRC was proved to be superior to others.Parametric studies were conducted and it is found that over-excavation,for example,reserving a very large clearance between the surrounding rock and the support,is necessary to reduce ground pressure to a large extent.The yielding supports which can provide high support pressure during the process of deformation are highly recommended when tunneling in high geostress environment.However,if the initial geostress is not very high,it is not necessary to pursue unwarranted overexcavation since the ground pressure applied on the support is mainly the loosening stress when the deformation is large.Ample support stiffness should be provided in the process of deformation to prevent uncontrolled large deformation of surrounding rock.

Analytical solutions for deep tunnels in strain-softening rocks modeled by different elastic strain definitions with the unified strength theory

This paper presents the analytical solutions for the responses of tunnels excavated in rock masses exhibiting strain-softening behavior. Since previous analyses give little consideration to the effect of the intermediate principal stress on the strain-softening rock behavior, the unified strength theory was introduced to analyze the tunnel response. Four cases of different definitions of the elastic strain in the softening and residual regions, used in the existing solutions, were considered. The tunnel displacements,stresses, radii of the softening and residual zones and critical stresses were deduced. The proposed solutions were verified by comparing with numerical simulations, model tests and existing solutions. Furthermore, the solutions of the four cases were compared with each other to investigate the influence of the elastic strain expressions on the tunnel responses. The results showed that the intermediate principal stress coefficient b has a significant effect on the tunnel displacements, stress fields, and plastic radii. Parametric studies were performed to analyze the influences of the softening and residual dilatancy coefficients,softening modulus and residual strength on the tunnel responses. The parametric analysis indicated that the existing models should be carefully evaluated in the analysis of tunnels constructed through average-quality rocks;the proposed solutions outperformed the existing models in solving the mentioned problem.

Design of the yielding support used highly deformable elements for a tunnel excavated in squeezing rock

Yielding support is often used in the squeezing tunnel to prevent damage to the lining induced by large deformation of the surrounding rock.Highly Deformable Elements(HDE)which is often installed along the circumferential direction of the shotcrete lining is a common type of yielding support.To determine the yield parameters of HDE,the support characteristic of the lining using HDE and the ground pressure considering strain-softening of soft rock were analyzed by an analytical method.The analytical solution showed that when considering the strain-softening of squeezing ground,the ground pressure has a non-zero minimum value.The minimum value of ground stress can be used to determine the constant yield stress of the HDE,and the corresponding deformation of the minimum ground pressure can be used to determine the deformation capacity of the HDE.Based on the variation in the design constant yield stress and yield displacement of HDE with the in-situ stress and the mechanical parameters of the soft rock,equations were proposed for determining of the yield parameters of the HDE.

多级开挖边坡强度折减法本构模型分析

运用FLAC3D软件,在Drucker-Prager模型和Strain-Softening模型中引入强度折减概念,实现了Drucker-Prager模型和Strain-Softening模型的强度折减法,并通过简单算例讨论了其在边坡工程数值模拟中的适用性。以湖北省宜昌市白洋长江公路大桥左侧路堑高边坡开挖工程为背景,采用不同本构模型强度折减法对比分析了边坡开挖稳定性。结果表明:边坡开挖中应充分考虑岩土体特性,选用恰当本构模型,才能得到更合理的分析结果。

ON DILATATIONAL PLASTIC CONSTITUTIVE EQUATION OF DUCTILE MATERIALS AND PLASTIC LOADING PATHS AT BIFURCATION

The dilatational plastic constitutive equation presented in this paper is proved to be in aform of generality. Based on this equation, the constitutive behaviour of materials at themoment of bifurcation is demonstrated to follow a loading path with the response as "soft"as possible.