A statistical damage constitutive model based on unified strength theory for embankment rocks

Abstract

Fluctuant marine and reservoir water levels are the main failure-inducing factors for embankment slopes. The soft embankment rocks, e.g., red-bed mudstone, eroded by the reservoir water level in the Three Gorges Reservoir area greatly influence the stability of the embankment slopes. In this study, unified strength theory was innovatively applied for damage evaluation and combined with the Weibull distribution to obtain the strength statistics of micro units. Additionally, one damage constitutive model and one damage evolution model considering the initial damage, strain softening and damage weakening were proposed. Then, a series of tests, e.g., modified cyclic wetting and drying test, triaxial compression test and modified numerical simulation test for reservoir embankment red-bed mudstone, were conducted to verify the feasibility of the proposed models. In addition, grey system theory was originally used to evaluate the effects of the Weibull distribution parameters (m and w) and the confining stress on the peak stress. Finally, the proposed model was tentatively applied to the modification of the limit failure height model of the bedded rock slopes. The verification implies that the proposed model results are consistent with the testing results, especially in the simulation of compaction, elastic deformation and strain softening and in the prediction of peak strength. The results from grey system theory analysis indicate that the micro unit strength parameter (w) has the most obvious effect on the strength. Moreover, the modified method based on the damage evolution model for calculating the limit failure height of the bedded rock slopes is conservative.     

Sensitive bounding surface constitutive model for structured clay

The main purpose of the paper is to present a relatively simple, yet realistic, constitutive model for simulations of structured sensitive clays. The proposed constitutive model can simulate 1‐D and isotropic consolidation, and drained and undrained shear response of sensitive structured clay. The proposed sensitive bounding surface model is based on concepts from the modified Cam clay model 8 and bounding surface plasticity 27 , with the addition of a simple degradation law. The key material parameters are M, λ, κ, and ν from the modified Cam clay framework, h from the bounding surface framework to model a smoothed elasto‐plastic transition, and ω_v, ω_q, and S_sr to model softening associated with destructuration. The model has separate parameters to model destructuration caused by volumetric strain and deviatoric strain. The model is capable of modeling unusual behavior of strain softening during 1‐D compression (i.e., a reduction of effective stress as void ratio decreases). A good match between test results and the model simulation is demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling the behavior of sandstone based on generalized plasticity concept

With the concept of generalized plasticity, a constitutive model for describing the deformation behavior of sandstone is proposed in this paper. This proposed model is characterized by the following features: (i) nonlinear elasticity under hydrostatic and shear loading; (ii) associated flow rule for pre‐peak simulation; (iii) substantial plastic deformation during shear loading; and (iv) significant shear dilation and distortion prior to the failure state. This model requires 10 material parameters, including three for elasticity and seven for plasticity. All of the parameters can be determined, in a straightforward manner, by the suggested procedures. The proposed model has been validated by comparing the triaxial test results of the Mushan sandstone under different hydrostatic stress, different stress paths, and cyclic loading condition. It is also versatile in simulating the deformation behaviors of two other sandstones. Upon slight modification of the model, the post‐peak behavior of sandstone can be reasonably predicted using proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

A fully coupled elastic–plastic hydromechanical model for compacted soils accounting for clay activity

A constitutive model, accounting for multiphase and multiscale coupling, is proposed for the water retention domain and the stress–strain response of compacted clayey soils. The model is based on a conceptual interpretation of the microfabric evolution of compacted soils along generalised hydromechanical paths, detected by means of mercury intrusion porosimeter tests. Multiphase coupling is provided by the mutual interaction between the mechanical and the hydraulic states. Multiscale coupling is introduced by a measure of the size of the aggregates, which influences both the retention and the stress–strain response, in the phenomenological constitutive equations. Model capabilities are verified by comparison with relevant experimental data from laboratory tests on compacted Boom clay and other selected experimental data on different compacted clayey soils. Copyright © 2012 John Wiley & Sons, Ltd.     

From solid to granular gases: the steady state for granular materials

This paper aims at extending the well‐known critical state concept, associated with quasi‐static conditions, by accounting for the role played by the strain rate when focusing on the steady, simple shear flow of a dry assembly of identical, inelastic, soft spheres. An additional state variable for the system, the granular temperature, is accounted for. The granular temperature is related to the particle velocity fluctuations and measures the agitation of the system. This state variable, as is in the context of kinetic theories of granular gases, is assumed to govern the response of the material at large strain rates and low concentrations. The stresses of the system are associated with enduring, frictional contacts among particles involved in force chains and nearly instantaneous collisions. When the first mechanism prevails, the material behaves like a solid, and constitutive models of soil mechanics hold, whereas when inelastic collisions dominate, the material flows like a granular gas, and kinetic theories apply. Considering a pressure‐imposed flow, at large values of the normal stress and small values of the shear rate, the theory predicts a nonmonotonic shear rate dependence of the stress ratio at the steady state, which is likely to govern the evolution of landslides. Copyright © 2013 John Wiley & Sons, Ltd.     

A visco‐elasto‐plastic model for granular materials under simple shear conditions

The numerical simulation of rapid landslides is quite complex mainly because constitutive models capable of simulating the mechanical behaviour of granular materials in the pre‐collapse and post‐collapse regimes are still missing. The goal of this paper is to introduce a constitutive model capable of capturing the response of dry granular flows from quasi‐static to dynamic conditions, in particular when the material experiences a sort of solid‐to‐fluid phase transition. An ideal assembly of identical spheres under simple shear conditions is considered. In the constitutive model, void ratio and granular temperature have been chosen as state variables, and both shear and normal stresses are computed as the sum of two contributions: the quasi‐static one and the collisional one. The former is determined by using a perfect elasto‐plastic model including the critical state concept, while the latter is derived from the kinetic theory of granular gases. The evolution of the granular temperature, fundamentally governing the material phase transition, is obtained by imposing the kinetic fluctuating energy balance. The constitutive relationship has been integrated, under both constant pressure and constant volume conditions, and the influence of shear strain rate, initial void ratio and normal pressure on the mechanical response has been investigated. Copyright © 2015 John Wiley & Sons, Ltd.     

A bounding surface plasticity model for unsaturated soil at small strains

Most existing hydromechanical models for unsaturated soils are not able to fully capture the nonlinearity of stress–strain curves at small strains (less than 1%). They cannot therefore, for example, accurately predict ground movements and the performance of many earth structures under working conditions. To tackle this problem, a state‐dependent bounding surface plasticity model has been newly developed. Particularly, the degradation of shear modulus with strain at small strains ranging from 0.001% to 1% is focused. The proposed model is formulated in terms of mean average skeleton stress, deviator stress, suction, specific volume and degree of saturation. Void ratio‐dependent hydraulic hysteresis is coupled with the stress–strain behaviour. Different from other elastoplastic models for unsaturated soils, plastic strains are allowed inside bounding surfaces. In this paper, details of model formulations and calibration procedures of model parameters are presented. To evaluate the capability of the new model, it is applied to simulate a series of triaxial compression tests on compacted unsaturated silt at various suctions. Effects of suction, drying and wetting as well as net stress on unsaturated soil behaviour are well captured. The model shows good predictions of the degradation of shear modulus with strain over a wide range of strains from 0.001% to 1%. Copyright © 2015 John Wiley & Sons, Ltd.     

A constitutive model for unsaturated soil–structure interfaces

A constitutive model for simulation of the behavior of unsaturated interfaces is presented here. The model is an extension of an existing critical state compatible interface model for dry and saturated interfaces that was already proposed by one of the authors [Lashkari, A. 2013. Int. J. Numer. Anal. Meth. Geomech. 37 (8): 904–931]. For a proper simulation of the behavior of partially saturated interfaces, the extended model is formulated in terms of two pairs of work conjugate stress–strain‐like variables. The modified model simulations are compared with the existing data of dry, unsaturated, and saturated interfaces. For each interface type, it is shown that the proposed model can capture the essential elements of the behavior using a unique set of parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

结构性海洋黏土损伤模型的二次开发及应用

原状土的结构性作为21世纪土力学的核心问题,一直以来受到学者们的广泛关注。软黏土的结构性损伤这一力学行为会对海洋结构物基础造成不可忽略的影响。以海底原状土的结构性特征为研究对象,推导了考虑黏土结构性的SANICLAY模型的数值实现格式。通过子增量步显式算法和有限元的二次开发,实现了结构性多屈服面本构模型在有限元方法中的应用。通过与不同应力路径下的三轴试验结果对比,验证了开发的子程序可准确模拟海洋黏土所具有的结构性。基于不同应力路径试验的数值模拟结果,研究了不同固结和剪切条件下土体塑性势面和屈服面的演化规律,揭示了土体固结可降低结构性损伤程度以及剪切过程中土体产生结构性损伤的机制。将二次开发的子程序应用到具体的边值问题中,开展了可考虑土体结构性影响的海上风电筒型基础静承载力研究,揭示了土体结构性对筒型基础的地基破坏模式、峰值承载力和残余承载力的影响;引入残余衰减比来表征土体结构性破坏后筒型基础的残余承载力,并建立了残余衰减比与结构损伤因子之间的关系。     

非规则砂岩节理剪切变形本构关系试验研究

岩石节理剪切变形对岩体工程的安全性和稳定性具有重要影响。为研究常法向应力下岩石节理剪切变形本构关系,采用RDS-200型岩石直剪仪对非规则砂岩节理进行了不同法向应力下的直剪试验。根据岩石节理剪切应力?位移全程曲线形状特征,将其依次划分为峰前压密阶段、线性阶段、屈服阶段和峰后软化阶段;根据剪切应力在峰后软化阶段降低幅度和速率大小,将岩石节理剪切应力?位移曲线划分为3种类型：峰后平台型、峰后缓降型和峰后跌落型。基于岩石节理剪切应力?位移曲线各阶段剪切变形特征,采用分段函数建立了岩石节理剪切变形本构模型。与其他模型相比,新提出的岩石节理剪切变形本构模型对试验数据拟合精度更高,更好地描述了岩石节理剪切应力?位移全程曲线。另外,在通过岩石节理直剪试验由经验公式确定模型参数之后,所提出本构模型可在不同法向应力下实现对不同粗糙度岩石节理剪切应力?位移曲线的预测。研究结果对岩石节理剪切变形的数值模拟和工程估计具有一定的实用价值。