A Thermo-Elasto-Viscoplastic Model for Soft Sedimentary Rock

In this paper, a new thermo-elasto-viscoplastic model is proposed, which can characterize thermodynamic behaviours of soft sedimentary rocks. Firstly, as in the Cam-clay model, plastic volumetric strain which consists of two parts, stress-induced part and thermodynamic part, is used as hardening parameter. Both parts of the plastic volumetric strain can be derived from an extended e-ln p relation in which the thermodynamic part is deduced based on a concept of ‘equivalent stress’. Secondly, regarding soft sedimentary rocks as a heavily overconsolidated soil in the same way as the model proposed by Zhang et al. (2005), an extended subloading yield surface (Hashiguchi and Ueno, 1977; Hashiguchi, 1980; Hashiguchi and Chen, 1998) and an extended void ratio difference are proposed based on the concept of the equivalent stress. Furthermore, a time-dependent evolution equation for the extended void ratio difference is formularized, which considers both the influences of temperature and stresses. Finally, it is proved that the proposed model satisfies thermodynamic theorems in the framework of non-equilibrium thermodynamics.     

AN ELASTO-VISCOPLASTIC MODEL FOR SOFT SEDIMENTARY ROCK BASED ON TIJ CONCEPT AND SUBLOADING YIELD SURFACE

In this paper, an elasto-viscoplastic constitutive model with strain softening is developed for soft sedimentary rock using a newly proposed evolution equation for subloading yield surface originally invented by Hashiguchi (1980). In the model, associated flow rule is adopted and tij concept, which can take into consideration the influence of intermediate stress on deformation and strength of geomaterials, is used. In the model, as is the same as Cam-clay model, plastic volumetric strain is used as hardening parameter, which is widely accepted by the researchers who specialize in the constitutive model for geomaterials. The application of the model to the experimental results of soft sedimentary rock indicates that the model not only can describe the time dependency, such as strain rate dependency and creep, but also the strain softening behavior of geologic materials. The material parameters involved in the model have clear physical meanings and can be easily determined with triaxial compression tests and creep tests.     

Test on Soft Sedimentary Rock Under Different Loading Paths and its Interpretation

Tests on soft sedimentary rock under conventional triaxial and plane-strain compression and/or creep have been conducted. The purpose of the tests is to investigate the influence of intermediate principal stress that may affect the strength and dilatancy of the soft sedimentary rock under different loading paths. Meanwhile, theoretical simulations by an elasto-viscoplastic constitutive model were also conducted. Influence of membrane and filter paper was investigated using finite element analysis based on the elasto-viscoplastic model. Furthermore, particular attention was paid to the migration of excessive pore water pressure within a specimen, by continuous monitoring of the inner excessive pore water pressure of specimens and calculation with soil-water coupled finite element-finite difference (FE-FD) method. The shear strength, inherent dilatancy and creep behavior of soft rock were explained experimentally and numerically in detail.     

Improved prediction of shear wave velocity for clastic sedimentary rocks using hybrid model with core data

Accurate measurement of acoustic velocities of sedimentary rocks is essential for prediction of rock elastic constants and well failure analysis during drilling operations. Direct measurement by advanced logging tools such as dipole sonic imager is not always possible. For older wells, such data are not available in most cases. Therefore, it is an alternate way to develop a reliable correlation to estimate the shear wave velocity from existing log and/or core data. The objective of this research is to investigate the nature of dependency of different reservoir parameters on the shear wave velocity (V_s) of clastic sedimentary rocks, and to identify the parameter/variable which shows the highest level of dependency. In the study, data-driven connectionist models are developed using machine learning approach of least square support vector machine (LSSVM). The coupled simulated annealing (CSA) approach is utilized to optimize the tuning and kernel parameters in the model development. The performance of the simulation-based model is evaluated using statistical parameters. It is found that the most dependency predictor variable is the compressional wave velocity, followed by the rock porosity, bulk density and shale volume in turn. A new correlation is developed to estimate V_s, which captures the most influential parameters of sedimentary rocks. The new correlation is verified and compared with existing models using measured data of sandstone, and it exhibits a minimal error and high correlation coefficient (R² = 0.96). The hybridized LSSVM-CSA connectionist model development strategy can be applied for further analysis to predict rock mechanical properties. Additionally, the improved correlation of V_s can be adopted to estimate rock elastic constants and conduct wellbore failure analysis for safe drilling and field development decisions, reducing the exploration costs.     

An Elasto-viscoplastic Constitutive Model with Strain-softening for Soft Sedimentary Rocks

In general, soft sedimentary rocks exhibit strain-softening and time-dependent behavior. In the present paper, an elasto-viscoplastic constitutive model for soft rocks is proposed, that can universally describe time-dependent behavior such as creep, stress relaxation and strain rate sensitivity by extending Adachi and Oka's elasto-viscoplastic model for frozen sand. It is found that the proposed model can be applied to the time-dependent behavior of a soft tuffaceous rock called Tomuro Stone under the strain rate constant triaxial compression, drained triaxial creep and undrained triaxial stress relaxation.     

Modification of thermo-elasto-viscoplastic model for soft rock and its application to THM analysis of heating tests

In deep geological disposal for high level radioactive waste, one of the most important factors is to study the thermo-hydraulic-mechanical (THM) behavior of the natural barrier, usually a host rock, during the heat process and hydraulic environment change. In this paper, a thermo-elasto-viscoplastic model proposed by Zhang and Zhang (2009) is firstly modified by adopting the t_ij concept (Nakai and Mihara, 1984) so that the influence of intermediate stress can be properly considered. The performance of the modified model is confirmed with drained triaxial compression tests and creep tests on soft sedimentary rock and manmade soft rock under different temperatures. Based on the modified model, a program called ‘SOFT’, using the finite element method (FEM) and the finite difference method (FDM) in the soil–water–heat coupling problem, has been developed to simulate the aforementioned THM behavior of geological materials. In order to verify the applicability of the program, an isotropic element heating test for soft rock under drained condition with different initial overconsolidation ratio (OCR), is firstly simulated by the proposed THM FE-FD program. In the test, the thermal volumetric change was found to be dependent on OCR. The simulated results show that the THM phenomenon observed in the laboratory test can be explained by the proposed numerical method. Meanwhile, a real-scale field heating test reported by Gens et al. (2007) is also simulated by the same THM FE-FD program. The material parameters of the rock involved in the constitutive model are determined based on the element tests for the rock in the laboratory. It is shown that the simulated results agreed well with the test results such as the time change of the temperature, the excess pore water pressure (EPWP) and the heat-induced strain.     

沉积软岩的三轴蠕变实验研究及分析评价

在常年恒温、恒湿的实验室中，在不同围压以及不同应力比条件下，对3种沉积软岩系统地进行了长期三轴蠕变压缩实验研究。对所获得的大量实验结果进行研讨后，运用粘弹性流变模型求得非破坏时各种软岩的蠕变系数，同时，用柔量可变模型模拟破坏时的蠕变行为。系统地把握了多种软岩在不同条件下的强度、变形特性，探讨了各种软岩的变形、变形速率、时间依存性等影响因素，为预测软弱岩体的长期力学稳定性提供了重要依据。     

含弱面砂岩非线性黏弹塑性流变模型研究

 利用CSS–3940YJ型岩石剪切流变试验机,对向家坝水电站左岸坝基挤压带含弱面砂岩进行剪切流变试验。试验结果表明：该岩石属于典型的软岩,在恒定剪应力水平下具有显著的亚稳定蠕变特性。在应力达到一定水平时,岩石经过衰减和亚稳定蠕变之后发生加速蠕变破坏。根据含弱面砂岩剪切蠕变特性,对非线性流变元件进行改进,定义其在应力阈值前后分别等同于牛顿黏壶和非线性黏塑性体。将改进的元件与广义Kelvin模型串联,组合成四元件流变模型。该模型可以充分反映岩石亚稳定蠕变和加速蠕变特征,并具有结构简单、参数少的优点。推导四元件流变模型的本构方程,从理论上对岩石非线性蠕变特性进行分析。采用所建立的模型对岩石进行剪切流变力学参数辨识,并研究应力水平超过阈值后的参数辨识方法。通过模型计算结果与试验结果的比较,对提出的非线性黏弹塑性流变模型进行验证,显示所建模型的正确性与合理性。     

考虑围压效应的修正软岩热弹黏塑性本构模型

 大量的软岩三轴剪切试验表明,不同的围压下,软岩力学特性变化非常大。随着围压的增加,软岩的应变软化和剪胀性变弱;当围压足够大时,甚至表现为应变硬化和剪缩。已有软岩热弹黏塑性本构模型针对不同的围压大小,需要设定不一样的参数,使其应用到数值分析上带来一定困难。为了能用统一参数来描述软岩受围压影响的力学性质,对已有的软岩热黏弹塑性本构模型进行修正。修正模型中所有参数都具有明确的物理意义且都可通过常规三轴试验确定。通过实验数据与计算结果对比,验证了修正本构模型的正确性。     

A constitutive model for rock interfaces and joints

A constitutive model based on limit concept is proposed to predict the behavior of rock interfaces and joints. For the limit case of an interface with thickness approaching zero, an ellipse yield function is adopted and associated flow rule is recommended. This yield function is not of proportional type, and its motion in stress space is governed by its center position and the hardening rule of yield function. The shear anisotropy is described by a shape function that incorporates the elastic shear stiffness, yield function and hardening rule. An equivalent relative displacement is obtained based on normalized plastic work and limit concept. This equivalent relative displacement yields a hardening rule from which the dilatancy is directly associated with the asperity of the interface. The validity of the proposed constitutive model is verified using data obtained from several existing experimental studies on natural and artificial rock joints.     

A load-transfer function for the side resistance of drilled shafts in soft rock

The shear stress and shear displacement relationship for the rock socket sidewalls is required for the calculation of the drilled shaft butt settlement under the service loads. This paper first introduces a comprehensive database of in situ axial load tests on drilled shafts, anchors and plugs that are embedded in different soft rock formations. The database includes measurements of (i) the initial shear stiffness, (ii) the peak shear stress and (iii) the post-peak reduction in shear stresses for the socket sidewalls. In addition to the load test results, information on soft rock mass mechanical properties and rock socket geometry is also included. It is found that (i) the initial shear stiffness is directly related to the deformation modulus of the soft rock mass and inversely proportional to the rock socket diameter and length, (ii) the mobilized peak shear stress is related to the drained friction angle of the rock mass and normal stress on the socket sidewalls at failure. The rock mass friction angle is related to the rock type and the geological strength index, and the normal stress at failure is directly related to deformation modulus of rock mass and inversely to the product of rock socket length and diameter, and (iii) the post-peak brittleness is related to the soft rock type and the post-peak shear displacement. An empirical framework for the prediction of the load-transfer function for side resistance of sockets in soft sedimentary and fine-grained rock is developed using the load test database introduced herein. The proposed framework accounts for the socket geometrical characteristics, and the rock mass engineering properties. The pre-peak range in the load-transfer function is modeled using a hyperbolic function, and the post-peak range is modeled using a brittleness index to account for the reduction in shear stresses with post-peak displacement.     

堆积软岩的黏弹塑性本构模型及其数值计算应用

 堆积软岩的主要力学特性有应变软化、流变、受中间主应力影响等,为了尽可能完整地描述这些力学特性,提出一个全新的黏弹塑性本构模型。该模型基于下负荷面和tij概念,以超固结状态与正常固结状态之间的孔隙比差r为状态变量,并在该状态参量的演化律中引入非齐次函数,使模型能综合描述软岩的应变软化、流变和受中间主应力影响的力学特性。新模型仅比剑桥模型多了4个参数,而且4个参数都具有明确物理意义,可通过常规三轴试验确定。以降雨引起的软岩边坡的渐进性破坏为工程背景,用水土耦合有限元来探讨2种不同地下水位变化对边坡破坏的影响,从坡体的剪应变分布、位移矢量、破坏的传播等方面分析边坡的破坏机制。     

Experimental investigation and constitutive modeling of the shear creep behavior of an overconsolidated soft clay

This paper presents the results of shear creep experimental investigations carried out on Huzhou overconsolidated soft clay and subsequently proposes a constitutive model that is able to reproduce the shear creep characteristics under complex stress conditions. First, shear creep characteristics are obtained based on the analysis of results from drained triaxial shear creep tests conducted on clay samples. Then, the Yin-Graham equivalent time is extended into shear stress states; thus, the concept of shear equivalent time is formulated. Using the shear creep characteristics observed from experiments and the shear equivalent time concept, a shear stress-strain-strain rate creep model reflecting a complex loading history and loading path is proposed. Finally, the model is solved numerically with the fourth-order Runge-Kutta method, and the predictions are compared with the measured values. The results show that (1) the shear creep coefficient of Huzhou overconsolidated soft clay varies with the overconsolidation ratio levels, and there is a good correspondence between them, which is similar to the relationship of the volumetric creep coefficient and overconsolidation ratio; (2) the predicted curves of the new model are in good agreement with measured curves, which demonstrates that the model can well simulate the shear creep characteristics of soft clay under complex stress conditions.

     

K0超固结土的统一硬化模型

将所建立的超固结土模型推广为能够反映超固结土的初始应力各向异性的弹塑性模型。它是通过将潜在强度Mf、特征应力比M和状态应力比ηk引入到模型的统一硬化参数中,使模型具有预测超固结土的初始应力各向异性、剪缩、剪胀、硬化、软化和应力路径依赖性等基本特性的功能。采用SMP强度准则并结合变换应力方法对模型实现了三维化。通过与试验结果比较表明,提出的模型能够较好地描述初始应力各向异性超固结土的应力应变特性。     

Strain Energy-Based Elasto-Viscoplastic Constitutive Modelling of Sand for Numerical Simulation

It is shown that the use of visco-plastic shear or volumetric strain as the stress history-independent hardening parameter in an elasto-viscoplastic model for sand may result in inaccurate numerical simulations of geotechnical boundary value problems. A new elasto-viscoplastic constitutive model for sand is proposed, formulated based on a stress path-independent irreversible (or visco-plastic) strain energy-based hardening function. The function was derived based on results from drained plane strain compression (PSC) tests on saturated dense Toyoura sand along a wide variety of stress path. The model is coupled with an existing isotropically work-hardening and -softening, non-associated, elasto-plastic model for sand. The constitutive model takes into account the effects of loading rate due to viscous properties on the stress-strain behaviour as well as those of pressure level, inherent anisotropy and void ratio and work softening associated with strain localization into a shear band. It is shown that the proposed model can much better simulate the effects of stress history on the deformation characteristics of sand than many previous models. The FEM code incorporating the model is validated by simulating physical PSC tests and bearing capacity model tests of a strip footing on sand performed by previous studies.     

沉积岩的一种时间效应模型

提出沉积岩的一种时间效应模型。沉积岩的固有各向异性用一个标量各向异性参数描述,引入一个损伤因子来考虑时间效应,材料的单轴抗压强度是时间、微结构张量和应力的函数。建立了一个描述各向异性沉积岩变形过程的全塑性模型。用提出的模型对一些试验进行了模拟,结果表明该模型能有效地描述沉积岩的固有各向异性及其时间效应。     

Application of Micromechanics Model to Study Anisotropy of Soils at Small Strains

A micromechanics model is used to analyse the stiffness anisotropy of soils at small strains. Five material constants for a cross-anisotropic elastic material are related to micromechanics variables such as fabric anisotropy, contact stiffness, particle radius, and the number of contacts in a given volume of particulate assembly. The analytical results from the model are compared with the published experimental data on small-strain stiffness anisotropy in order to estimate typical soil fabric conditions of sands and clays. The relationship between the small-strain shear modulus obtained from triaxial tests and shear tests is examined using the micromechanics model. The analysis shows that, when a soil is stiffer in the horizontal direction, the shear modulus evaluated from the conventional triaxial drained tests underestimates G_vh and G_hh. The opposite is true when a soil is stiffer in the vertical direction. When a soil is sheared in undrained condition, the measured shear modulus is closer to G_vh than G_hh, especially when the soil is stiffer in the horizontal direction. The effect of soil anisotropy on the stiffness measured from different stress paths in triaxial condition is investigated.     

剪胀和破坏耦合的节理岩体本构模型的研究

 摘要：根据节理岩体切向加载作用下的变形机制,把微凸体在磨损破坏过程中引起的剪胀软化现象和伴随的强化现象分开考虑,提出一种新的本构模型。试验结果表明,在法向和切向载荷共同作用下,由于微凸体的爬坡和啃断作用,节理岩体均会发生一定程度的剪胀和磨损,累积到一定程度就产生软化现象,在此引入一个初始剪应力概念体现上述特征。另一方面,由于破碎颗粒的碾压和迁移作用,使得抗剪力学行为由微凸体粗糙度控制逐渐转变为由结构面上形成的紧密夹层的力学行为所控制,抗剪强度提高,在此通过弹塑性随动强化模型来体现这一变形行为。当随动强化模型与初始剪应力相结合时,即为节理岩体切向加载作用下的剪应力–切向位移本构关系。通过对各种已有试验曲线的对比分析,验证该模型的正确性。     

K0固结结构性软黏土的本构模型

本文在修正剑桥模型的基础上综合考虑了软黏土的各向异性、结构性及其演变和屈服面硬化规则中塑性剪切应变的影响,将传统模型发展为适用于K0固结结构性软黏土的本构模型。本文模型借鉴Collins等人提出的符合热力学耗散原理的本构模型,同时在描述土体结构性演变的过程中参考了Asaoka等人的次加载/超加载屈服面本构模型,并采用了具有明确物理意义的内变量。与传统的修正剑桥模型相比,增加了3个分别表征软黏土各向异性和结构性的参数(θn,R和R*)以及两个演化参数(m和a),而参数R和R*的初始值则可由结构性土的屈服应力比YSR和灵敏度St获得。本文选取了典型的浙江温州软黏土和Bothkennar软黏土,对比了三轴压缩的计算和试验结果,体现了本模型在结构性软黏土计算上相对于传统本构模型优越性。