Statistical Damage Constitutive Model of Quasi-Brittle Materials

Recent studies have shown that statistical damage mechanics is one effective method to study the failure process of quasi-brittle materials. There are two key problems in setting up the statistical damage constitutive model of quasi-brittle materials, namely, determining the microunit strength and the parameters of statistical distribution that the microunit strength obeys. The four-parameter criterion is a failure criterion consisting of four unknown parameters. When the four parameters equal appropriate values, it may become the Drucker–Prager criterion (for rock), Mohr–Coulomb criterion (for rock), and Hsieh–Ting–Chen criterion (for concrete), so the four-parameter criterion may be used to simulate the elastoplastic behavior of rock and concrete quasi-brittle materials. In the paper, microunit strength is determined with the four-parameter criterion, thus the statistical damage constitutive model suits rock and concrete. The deficiencies of existing methods in determining the distribution parameters are investigated, and a new method for determining the distribution parameters is proposed. First, the theoretical relationships between the parameters and the strain and stress at the peak point of material failure curve are derived; second, the approximate relations between the strain and stress at the peak point of material failure curve and confining pressure are established through the curve fitting method; finally, the relations between the parameters and confining pressure are established. The proposed statistical damage softening constitutive model of quasi-brittle materials has universal meaning, the determination of distribution parameters has strict theoretical basis, and the distribution parameters can be conveniently obtained with general triaxial tests. Numerical examples are also presented to validate the model.     

Three-Dimensional Nonlinear Analyses of a Metro Tunnel in S?o Paulo Porous Clay, Brazil

Tropical residual clays with a highly porous structure react to the stress changes induced by tunneling in such a way that surface settlements can be larger than crown-level settlements along a tunnel axis. This behavior, which is not readily simulated by most numerical analyses, was also observed in the Paraiso tunnel, built for the S?o Paulo Metro, Brazil. This is a shallow tunnel driven through porous clayey soils by the sequential method. Detailed results of field monitoring are presented and discussed. 3D finite-element analyses that allowed a detailed simulation of the construction sequence have been carried out, considering two distinct constitutive models for the soil: a simple elastic-perfectly-plastic Mohr-Coulomb model, and the elastoplastic model developed by Lade. The results of these analyses are compared with the observed behavior as well as with the results from a plane strain finite-element analysis. It is shown that only the 3D finite-element analysis coupled with the more sophisticated soil constitutive model provides a full reproduction of field performance, with particular relevance for the deformations in the soil mass over the tunnel.     

New Approach to Strain Rate Sensitivity of Concrete in Compression

A constitutive law to model the strain-rate-dependent compression behavior of concrete is proposed. It is derived from a mechanical model, where inertia effects influence damage formation. To verify this model an experimental method based on the split Hopkinson bar (SHB) technique is described, one that considers the special properties of concrete specimens. Compressive stress waves with varying peak values and durations were realized using an extended SHB device. Dynamic stress-strain relations—which differ considerably from the corresponding static relations—are derived for the investigated load histories and are modeled with the proposed dynamic constitutive law. While a number of compression load histories are sustained by the specimens, others result in failure. So a dynamic failure criterion is established, connecting failure occurrence, peak stress, and the time to reach the peak stress.     

Agenesis of gall bladder--a diagnostic dilemma

Before laparoscopic cholecystectomy, it is important to clarify the anatomy of the cystic duct. This study assessed three-dimensional CT images (3D images) of the cystic duct obtained non-invasively using helical DIC CT and these images were compared with those obtained with ERCP and DIC. The three-dimensional technique using Helical DIC-CT was applied in 168 patients for laparoscopic cholecystectomy. The cystic duct detected by 3D imaging was evaluated for patency, length and bifurcation. Three-dimensional images showed the cystic duct in 157 of 168 cases (93.5%) and in 81 of 89 cases (91%) in which the cystic duct was not clearly visualized on DIC. Among the 23 cases in which were both 3D images and ERCP undergone, 3D images were equal to those of ERCP in detection of the cystic duct in 20 cases, superior to ERCP in two cases, and inferior to ERCP in one. The technique of 3D images proved useful in demonstrating the patency, length and variations in bifurcation of the cystic duct for surgeons performing laparoscopic cholecystectomy and might be substitute ERCP in preoperative assessment.     

Characterization of Models for Time-Dependent Behavior of Soils

Different classes of constitutive models have been developed to capture the time-dependent viscous phenomena (creep, stress relaxation, and rate effects) observed in soils. Models based on empirical, rheological, and general stress-strain-time concepts have been studied. The first part is a review of the empirical relations, which apply only to problems of specific boundary conditions and frequently involve natural time alone. The second part deals with different rheological models used for describing the viscous effects in the field of solid mechanics. The rheological models are typically developed for metals and steel but are, to some extent, used to characterize time effects in geomaterials. The third part is a review of constitutive laws that describe not only viscous effects but also the inviscid (rate-independent) behavior of soils, in principle, under any possible loading condition. Special attention is paid to elastoviscoplastic models that combine inviscid elastic and time-dependent plastic behavior. Various general elastoviscoplastic models can roughly be divided into two categories: Models based on the concept of overstress and models based on nonstationary flow surface theory. Although general in structure, both have shortcomings when used for modeling of soils.     

Unified Catastrophic Model for Collapsible Loess

A unified model considering the microstructure instability and a set of complete constitutive relations, which describes the volumetric collapse and shearing collapse simultaneously, is developed for collapsible loess in the framework of the catastrophe theory. The validity of the model is verified by comparing the results calculated using the model with the data of triaxial compression tests performed on Lanzhou loess. The following characteristics of collapsing deformation are explained and reproduced successfully using the model: (1) the existence of two turning points on each deformation curve, (2) the shear curves under various stress ratios intersect one another, (3) the ratio of the shear strain to the volumetric strain is a function of the stress ratio, and (4) the initial collapse condition is approximately a circle.     

Axisymmetric Wrinkling of Cylinders with Finite Strain

A simple analytical solution for the bifurcation buckling of a cylinder under axial loading is provided including finite-strain effects. Thus, the small strain theory result of Batterman is generalized. In addition to the thin shell theory solution (excluding shear deformations), a solution including shear deformation effects is also given. All solutions can be evaluated for either the flow or deformation theory of plasticity. The finite-strain constitutive theory used is one in which small strain type relationships apply between the Jauman rate of the Kirchhoff stress tensor and the deformation rate tensor. The analytical results are compared to finite-element analyses to test the validity of the assumptions made. The solutions are explicit. Starting with a point on the stress-strain curve, one calculates explicitly the diameter-to-thickness ratio D∕t for a cylinder that will buckle at that level of stress and strain (repeating this as necessary to generate a plot of wrinkling strains as a function of D∕t). Unless the tangent modulus at bifurcation is large compared to the stress, the results clearly indicate that finite strains have an important stabilizing effect, leading to higher bifurcation strains.     

Three-Dimensional Hoek-Brown Strength Criterion for Rocks

A great number of rock strength criteria have been proposed over the past decades. Of these different strength criteria, the Hoek-Brown strength criterion has been used most widely, because: (1) it has been developed specifically for rock materials and rock masses; (2) its input parameters can be determined from routine unconfined compression tests, mineralogical examination, and discontinuity characterization; and (3) it has been applied for over 20?years by practitioners in rock engineering, and has been applied successfully to a wide range of intact and fractured rock types. The Hoek-Brown strength criterion, however, does not take account of the influence of the intermediate principal stress, although much evidence has been accumulating to indicate that the intermediate principal stress does influence the rock strength in many instances. In this paper, a three-dimensional (3D) version of the Hoek-Brown strength criterion has been proposed. The original Hoek-Brown strength criterion is just a two-dimensional (2D) version of the proposed 3D strength criterion. The 3D strength criterion not only inherits the advantages of the original Hoek-Brown strength criterion, but can take account of the influence of the intermediate principal stress. Polyaxial or true triaxial compression test data of intact rocks and jointed rock masses has been collected from the published literature and used to validate the proposed 3D Hoek-Brown strength criterion. Predictions of the proposed 3D Hoek-Brown strength criterion are in good agreement with the test data for a range of different rock types. The proposed 3D Hoek-Brown strength criterion is also compared with a simplified 3D Hoek-Brown strength criterion proposed by Pan and Hudson. The Pan-Hudson criterion cannot be considered a true 3D version of the Hoek-Brown criterion, because it does not reduce to the form of the original Hoek-Brown criterion at either triaxial or biaxial state. The Pan-Hudson criterion underpredicts the strength at the triaxial state, but overpredicts the strength at the biaxial state.     

Investigation on the Suitability of Two-Dimensional Depth-Averaged Models for Bend-Flow Simulation

A numerical experiment is carried out to study the suitability of two-dimensional (2D) depth-averaged modeling for bend-flow simulation, in which the geometry of the studied channel is rectangular. Two commonly used 2D depth-averaged models for bend-flow simulation are considered in this study of which the bend-flow model includes the dispersion stress terms by incorporating the assumption of secondary-current velocity profile, and the conventional model neglects the dispersion stress terms. The maximum relative discrepancy of the longitudinal velocity, obtained from the comparison of these two models, is used as a criterion to judge their applicability for bend-flow simulation. The analysis of simulation results indicated that the maximum relative difference in longitudinal velocity is mainly related to the relative strength of the secondary current and the relative length of the channel. Empirical relations between the maximum relative difference in the longitudinal velocity, the relative strength of the secondary current, and the relative length of the channel for both the channel-bend region and the straight region following the bend have been established. The proposed relations provide a guideline for model users to determine the proper approach to simulate the bend-flow problem by either using the conventional model or the bend-flow model. Experimental data have been adopted herein to demonstrate the applicability and to verify the accuracy of the proposed relations.     

Analysis and Implementation of Resilient Modulus Models for Granular Solids

Constitutive equations based upon stress dependent moduli, like K-θ and Uzan-Witczak, are widely used to characterize the resilient response of granular materials for the analysis and design of pavement systems. These constitutive models are motivated by the observation that the granular layers used in pavement structures shake down to (nonlinear) elastic response under construction loads and will, therefore, respond elastically under service loads typically felt by these systems. Due to their simplicity, their great success in organizing the response data from cyclic triaxial tests, and their success relative to competing material models in predicting the behavior observed in the field, these resilient modulus constitutive models have been implemented in many computer programs used by researchers and design engineers. This paper provides an analysis of the nonlinear solution algorithms that have been used in implementing these models in a conventional nonlinear 3D finite-element framework. The analysis shows that these conventional algorithms are destined to fail at higher load levels. The paper offers two competitive methods for global analysis with these models. A comparative study of eight possible implementations of the algorithms described in the paper is made through two simulation examples.     

Application of Lade's Criterion to Cam-Clay Model

Lade's criterion is one of the best criteria for describing the shear yield and failure behavior of soils in 3D stresses, and the original Cam-clay model is the most popular and fundamental elastoplastic model for normally consolidated clays. In this paper, a transformed stress tensor is proposed for combining Lade's criterion and the Cam-clay model. The transformed stress is deduced from what makes the curved surface of Lade's criterion become a cone with the axis being the space diagonal, i.e., Lade's criterion becomes the extended Mises type criterion in the transformed principal stress space. The Cam-clay model revised by Lade's criterion is capable of describing the mechanical behavior of soils in general stresses. It is presented that the revised model can simulate well the drained and undrained behavior of soils, not only under triaxial compression conditions, but also under plane strain, true triaxial, and hollow cylinder conditions. The elastoplastic models for soils, in which only the first and second stress invariants are used, can be extended simply to the model, including the third stress invariant by adopting Lade's criterion.     

Time Integration in Discontinuous Deformation Analysis

Discontinuous deformation analysis (DDA) is a discrete element method that was developed for computing large deformation in fractured rock masses. In this paper we present details of the DDA time integration scheme, where the acceleration is taken constant over the time step, equal to the acceleration at the end of the time step (“right Riemann”). The integration scheme has several advantages: (1) Self-starting, (2) accelerations never need to be computed which reduces implementation complexity, (3) unconditionally stable, and (4) dissipative, contains algorithmic damping which may be important considering the penalty formulation of DDA. However, the right Riemann scheme is implicit, requiring expensive factorization or iteration to solve the resulting system of equations, and is accompanied by a bifurcation in the spectrum when the time step is large with respect to the period. This bifurcation has important ramifications for controlling spurious resonance in DDA simulations due to linear scaling in system stiffness compared to cubic scaling of the system mass as the characteristic length of the domain increases.     

Micromechanical Analysis for Interparticle and Assembly Instability of Sand

Instability of granular material may lead to catastrophic events such as the gross collapse of earth structures, and thus it is an important topic in geotechnical engineering. In this paper, we adopt the micromechanics approach for constitutive modeling, in which the soil is considered an assembly of particles, and the stress-strain relationship for the assembly is determined by integrating the behavior of the interparticle contacts in all orientations. Although analyses regarding material instability have been extensively studied for a soil element at the constitutive level, it has not been considered at the interparticle contact level. Through an eigenvalue analysis, two modes of instability are identified at the local contact level: the singularity of tangential stiffness matrix and the loss of positiveness of second-order work. The constitutive model is applied to simulate drained and undrained triaxial tests on Toyoura sand of various densities under various confining pressures. The predictions are compared with experimentally measured instability at the assembly level. The modes of stability at the interparticle contact level and their relations to the overall instability of the assembly are also analyzed.     

面向三维城市地理信息系统的体相交分析方法的实现与应用

提出一种应用于三维城市地理信息系统的空间分析方法:体相交分析.该方法先后输入两个体数据集,经过分析计算,输出一个关系集合,集合中的每一条关系代表第一个输入数据集中的一个体对象与第二个输入数据集中的一个或多个体对象之间存在的相交关系.基于003D数据模型,实现了一种稳定、快速的体相交分析算法,并将其应用到一个三维城市地理信息系统项目(TG-U-3D)之中.在该项目中,体相交分析用于辅助检测城市地下空间规划过程中的用地冲突,以及查询某一城市设施所位于或者穿越的地层.     

Associated and Non‐Associated Aspects of the Constitutive Laws for Coupled Elastic/Plastic Materials

Previous analyses are amplified to demonstrate that when the constitutive equations for geo‐materials, in which the elastic moduli depend on the plastic strain, are derived from basic thermo‐mechanical principles, the resulting rate forms of the equations have a symmetric stiffness matrix (tensor). This result is at odds with existing analyses, which have concluded that these matrices should be non‐symmetric. The consequences of these results for stability, bifurcation, and shear band formation are discussed.     

3D Numerical Simulation of Deposition Patterns due to Sand Disposal in Flowing Water

A 3D numerical model has been developed to study the deposition patterns for sediment dumping in ambient water with cross-flow. The model formulation is based on the governing equations for the conservation of mass, momentum, and density excess, assuming the discrete particles can be represented by a continuous field of density difference with a specified settling velocity. To model the turbulence generated by the particles, a buoyancy extended k-ε model is employed. Numerically, the governing equations are split into three parts in the finite-difference solution: advection, dispersion, and pressure propagation. The advection part is solved by a characteristics-based scheme, the dispersion part is solved by the central difference method, and the pressure propagation part is solved implicitly by using the Gauss-Seidel iteration method. The computed results show that two different deposition patterns exist. One is oblong, and the other is horseshoe-shaped, depending on the ratio of the initial negative buoyancy flux of the sand discharge and the horizontal momentum flux of the flow. The computed results are in satisfactory agreement with experiments. The existence of the two different deposition patterns is explained by using the concept of bifurcation of buoyant plumes.     

Elimination of Hot Tears in Steel Castings by Means of Solidification Pattern Optimization

A methodology of how to exploit the Niyama criterion for the elimination of various defects such as centerline porosity, macrosegregation, and hot tearing in steel castings is presented. The tendency of forming centerline porosity is governed by the temperature distribution close to the end of the solidification interval, specifically by thermal gradients and cooling rates. The physics behind macrosegregation and hot tears indicate that these two defects also are dependent heavily on thermal gradients and pressure drop in the mushy zone. The objective of this work is to show that by optimizing the solidification pattern, i.e., establishing directional and progressive solidification with the help of the Niyama criterion, macrosegregation and hot tearing issues can be both minimized or eliminated entirely. An original casting layout was simulated using a transient three-dimensional (3-D) thermal fluid model incorporated in a commercial simulation software package to determine potential flaws and inadequacies. Based on the initial casting process assessment, multiobjective optimization of the solidification pattern of the considered steel part followed. That is, the multiobjective optimization problem of choosing the proper riser and chill designs has been investigated using genetic algorithms while simultaneously considering their impact on centerline porosity, the macrosegregation pattern, and primarily on hot tear formation.     

New Approach to Determine Three-Dimensional Contacts in Blocks System: Penetration Edges Method

Detection of contacts between three-dimensional (3D) blocks is a key problem in three-dimensional distinct element analysis. In this paper, the limitations of the c–p method are discussed. The writers have also put forward the “penetration edges method” for the detection of contacts in 3D blocks system. The contact relations between two 3D blocks are classified into seven types and 3D contact detection is determined by the contact type. The principle of this new approach is simple to implement and can overcome the limitation of the c–p method as discovered in this study. Limited case studies have indicated that the present algorithm is as efficient as the c–p method but is free from the limitation of this method.     

Pressure-Dependent Elasticity and Energy Conservation in Elastoplastic Models for Soils

This paper presents a study on the consequences of combining energy conservative or non-conservative elasticity within a plasticity framework. Toward this end, a versatile energy potential function is first presented and examined. It is shown to cover a wide range of existing empirical relations for pressure-dependent stiffness of soils. Utilization of these functions within hyperplastic constitutive framework allows for the resulting models to satisfy the Law of Energy Conservation for both elastic and plastic components of soil behavior. Apart from the theoretical rigor, a very important result of this approach is that it automatically implies stress-induced cross-anisotropy of the elastic component of soil behavior and dilatancy term occurs due to shear modulus dependency on pressure. Proper modeling of these phenomena, normally neglected by conventional hypoelastic-plastic models, has been shown to have a significant effect on the accuracy of the model predictions of undrained behavior of overconsolidated clays both in laboratory tests and in tunnel excavation problem.     

一个基于孔洞演化机制的韧性断裂预测模型

在韧性断裂中微观孔洞演化机制的基础上,提出了一个基于孔洞演化机制的非耦合型韧性断裂预测模型.模型充分考虑了两种典型的孔洞演化机制:孔洞的长大机制和孔洞的拉长扭转机制.该模型引入了三个具有不同物理意义的材料参数:材料对不同孔洞演化机制的敏感度、应力状态敏感度系数和材料的损伤阈值,并使用等效塑性应变增量表征其对韧性损伤累积过程的驱动作用.为了使模型可以更好地反映三维应力状态对材料韧性断裂性能的影响,将该模型从主应力空间转换到由应力三轴度、罗德参数和临界断裂应变构成的三维空间,得到了由模型确定的三维韧性断裂曲面,并研究了相关参数对三维韧性断裂曲面及平面应力二维韧性断裂曲线的影响.利用5083-O铝合金、TRIP690钢和Docol 600DL双相钢三个典型的轻质高强板材的韧性断裂数据验证了该模型对不同材料和不同应力状态的适用性和准确性.