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.

Charactersitics of Stress-strain Curve of High Strength Steel Fiber Reinforced Concrete under Uniaxial Tension

A whole of 110 specimens divided into 22 groups were tested with varying the volume fraction of steel fibers and the matrix strength of these specimens. The stress-strain behaviors of four types of steel fiber reinforced concrete （SFRC） under uniaxial tension were studied experimentally. When the matrix strength and the fiber content increase, the tensile stress and tensile strain vary differently according to the fiber type. The mechanisms of reinforcing effect for different types of fiber were analyzed and the stress-strain curves of the specimens were plotted. Some experimental factors for stress or strain of SFRC were given. A tensile toughness modulus Re0.5 was introduced to evaluate the toughness characters of SFRC under uniaxial tension. Moreover, the formula of the tensile stress-strain curve of SFRC was regressed. The theoretical curve and the experimental ones fit well, which can be used for references in construction.

ISOCHRONOUS STRESS-STRAIN CURVES OF LOW ALLOY STEEL CROSS-WELD-SPECIMEN AT HIGH TEMPERATURE

In this work, a parametric approach is presented and utilized to determine the creep properties of weldments; then the model of creep strain for cross weld specimen is given. On the basis of the experimental results, attempt has been made to establish equations of the isochronous stress-strain for weld joint that can predict the function of loading and service time in use of the creep data of base metal and weld metal.

Numerical simulation of the stress-strain curve and the stress and strain distributions of the titanium-duplex alloy

The stress-strain curve of an α-β Ti-8Mn alloy was measured and then it was calculated with finite element method （FEM） based on the stress-strain curves of the single α and β phase alloys. By comparing the calculated stress-strain curve with the measured one, it can be seen that they fit each other very well. Thus, the FE model built in this work is effective. According to the above mentioned model, the distributions of stress and strain in the α and β phases were simulated. The results show that the stress gradients exist in both α and β phases, and the distributions of stress are inhomogeneous. The stress inside the phase is generally higher than that near the interface. Meanwhile, the stress in the α phase is lower than that in the β phase, whereas the strain in the α phase is higher than that in the β phase.

The Complete Stress-strain Curve of Recycled Aggregate Concrete under Uniaxial Compression Loading

The mechanical performance of recycled aggregate concrete （RAC） is investigated. An experiment on the complete stress-strain curve under uniaxial compression loading of RAC is carried out. The experimental results indicate that the peak stress, peak strain, secant modulus of the peak point and original point increase with the strength grade of RAC enhanced. On the contrary, the residual stress of RAC decreases with the strength grade enhancing, and the failure of RAC is often broken at the interface between the recycled aggregate and the mortar matrix. Finally, the constitutive model of stress-strain model of RAC has been constituted, and the results from the constitutive model of stress-strain meet the experiment results very well.

Relations of complete creep processes and triaxial stress-strain curves of rock

Based on the results of triaxial compressive creep tests for five kinds of rock under the different stress loading,unloading and cycle-loading-unloading conditions,the creep deformation is not only a function of stress and time,but also it has the corresponding relations to the triaxial stress-strain curves of rock.The deformation properties of soften-strain,harden-strain and ideal plasticity presented by conventional triaxial compressive test curves under the different stress states were utilized,and the creep characteristics,the creep starting stress and the different entire creep process curves of rock were studied systematically according to creep experiment results,and the relations of the triaxial stress-strain curves to the creeping starting stress,the terminating curve,the different creep processes,and the different creep fracture properties were established.The relations presented in this paper were verified partially by the creep experiment results of five types of rock.

MODELLING OF TENSILE STRESS-STRAIN CURVE OF WOVEN FABRICS

A general shape of tensile stress-strain curves of woven fabrics is first recognised by puttingtested and predicted results together.An exponential function with two parameters is then selectedfor the prediction of tensile stress-strain relationship.The predicted results by using the proposedfunction show excellent agreement with experimental data.

Investigation into the stress-strain curves of deformation-induced ferrite transformation in a low carbon steel

A series of tests of deformation-induced ferrite transformation （DIP-T） in a low carbon steel were carried out by the Gleeble-3500 hot simulation machine at a temperature range of Ae3-Ar3. The overall stress-strain curves during DIFT can be divided into three typical types： ＂double-humped＂,＂ single-humped＂ and ＂transitional＂. The peaks exhibited in the curve are involved with deformation-induced transformation which happened in grains or at the grain boundaries. According to the stress-time curve and strain-time curve, strain capacity dramatically postponed the strain-induced transformation, which leads to the start of the transformation right ahead of the finish of deformation and the majority of the ferrite transformation process mainly happened after the deformation. Deformation-induced transformation is a metadynamic transformation process with dynamic nucleation.

Influences of strain softening and seepage on elastic and plastic solutions of circular openings in nonlinear rock masses

Considering the influence of strain softening, the solutions of stress, displacement, plastic softening region radius and plastic residual region radius were derived for circular openings in nonlinear rock masses subjected to seepage. The radial stress distribution curve, ground reaction curve, and relation curve between plastic softening region radius and supporting force in three different conditions were drawn respectively. From the comparisons among these results for different conditions, it is found that when the supporting force is the same, the displacement of tunnel wall considering both seepage and strain softening is 85.71% greater than that only considering seepage. The increase values of radial displacement at 0.95 m and plastic softening region radius at 6.6 m show that the seepage and strain softening have the most unfavorable effects on circular opening stability in strain softening rock masses.

Analysis of pile load-transfer under pile-side softening

A set of analytical equations for the variation of the axial force along depth and the pile-top load-settle-ment curve were established, using tri-linear softening model to pile-side soil and bilinear hardening model to pile-end soil . Influences of the pile-side and pile-end soil behavior on the load-settlement curve were discussed, indica-ting that the lowering reason for the variation step degree of the axial force along depth is the softening of the pile-side soil to result in the side friction lowering when the pile-top load is increased. To verify the reliability of thismethod, the parameters used in calculation are obtained from the test in Zhuzhou area. The obtained results are thencompared with the tested results. Contrast shows that the calculated results and the tested values are very close,which illustrates that the proposed method is reliable.

A work-hardening and softening constitutive model for sand:modified plastic strain energy approach

The paper describes an energy-based constitutive model for sand, which is modified based on the modified plastic strain energy approach, represented by a unique relationship between the modified plastic strain energy and a stress parameter, independent of stress history. The modified plastic strain energy approach was developed based on results from a series of drained plastic strain compression tests along various stress paths on saturated dense Toyoura sand with accurate stress and strain measurements. The proposed model is coupled with an isotropically work-hardening and softening, non-associtated, elasto-plastic material description. The constitutive model concerns the inherent and stress system-induced cross-anisotropic elastic deformation properties of sand. It is capable of simulating the deformation characteristics of stress history and stress path, the effects of pressure level, anisotropic strength and void ratio, and the strain localization.

High temperature stress–strain curves of MnS and their applications in finite element simulation

A novel method for testing stress–strain curves of non-metallic materials was presented.The high temperature stress-strain curves of MnS were preliminarily obtained and corrected to account for the influence of friction.Using the finite element method,the influence of deformation parameters on the deformation evolution of MnS inclusions was investigated based on the experimental reference data.The corresponding physical experiment was designed for comparative analysis.The results indicate that the experimental high-temperature deformation data of MnS are highly reliable.In the process of matrix deformation,the shapes of MnS inclusions change from spherical to ellipsoidal and even to lamellar.There are some differences in the morphological deformation of MnS inclusions located at different positions.With the increase in the initial size of MnS inclusions,the risk of failing the inclusion-flaw inspection increases and the forging quality further deteriorates.

Finite Element Modeling of Stress Strain Curve and Micro Stress and Micro Strain Distributions of Titanium Alloys— A Review

Most of the alloys like titanium, steel, brass, copper, etc., are used in engineering applications like automobile, aero- space, marine etc., consist of two or more phases. If a material consists of two or more phases or components it is very difficult to predict the properties like mechanical and other properties based on simple laws such as rule of mixtures. Titanium alloys are capable of producing different microstructures when it subjected to heat treatments, so much of money and time are squandering to study the effect of microstructure on mechanical properties of titanium alloys. This squandering can be reduced with the help of modeling and optimization techniques. There are many modeling tech- niques like Finite element method, Mat lab, Mathematical modeling etc. are available. But Finite element method is widely used for prediction because of capable of producing distributions of stresses and strains at any different loads. From the literature it is observed that there is a good agreement between the calculated and measured stress strain curves. This review paper describes the effect of volume fraction and grain size of alpha phase on the stress strain curve of the titanium alloys. It also can predict the effect of strength ratio on stress strain curve by using FEM. This informa- tion will be of great use in designing and selecting the titanium alloys for various engineering applications.

On the calibration of a shear stress criterion for rock joints to represent the full stress-strain profile

Conventional numerical solutions developed to describe the geomechanical behavior of rock interfaces subjected to differential load emphasize peak and residual shear strengths.The detailed analysis of preand post-peak shear stress-displacement behavior is central to various time-dependent and dynamic rock mechanic problems such as rockbursts and structural instabilities in highly stressed conditions.The complete stress-displacement surface(CSDS)model was developed to describe analytically the pre-and post-peak behavior of rock interfaces under differential loads.Original formulations of the CSDS model required extensive curve-fitting iterations which limited its practical applicability and transparent integration into engineering tools.The present work proposes modifications to the CSDS model aimed at developing a comprehensive and modern calibration protocol to describe the complete shear stressdisplacement behavior of rock interfaces under differential loads.The proposed update to the CSDS model incorporates the concept of mobilized shear strength to enhance the post-peak formulations.Barton’s concepts of joint roughness coefficient(JRC)and joint compressive strength(JCS)are incorporated to facilitate empirical estimations for peak shear stress and normal closure relations.Triaxial/uniaxial compression test and direct shear test results are used to validate the updated model and exemplify the proposed calibration method.The results illustrate that the revised model successfully predicts the post-peak and complete axial stressestrain and shear stressedisplacement curves for rock joints.

Stress-strain Model of Corroded Concrete under Uniaxial Compressive Loading

The prism specimens of corroded concrete were subjected to uniaxial compressive load to develop the stress-strain model. Compared to the un-corroded concrete, the mechanical prop- erties of corroded concrete, such as peak strength, Young＇s modulus, and residual deformation, et al are degraded. The concrete, which were subjected to the aggressive media in the environment, were resulted in randomly distributed pre-loading flaws and defects. The propagation of these corrosion flaws during the procedure of loading was the main reason of degradation of corroded concrete properties. By the application of the statistic theory of continuum damage, the compressive stress-strain curve of corroded concrete was simulated. The initial damage factor was introduced to represent the corrosive effects of different media. The present damage constitutive model agreed well with the test results.

Stress-strain analysis of loess triaxial shear test by PFC^(3D)

In order to compensate for limitations of microscopic study on loess triaxial tests, taking the loess in Longxi area as an example, the authors established the loess triaxial test model by using PFC3D software and simulating tfiaxial shear test under the different confining pressures in 0 kPa, 50 kPa and 300 kPa. Compared with laboratory triaxial shear test, the numerical simulation test has a guiding role in loess mechanical strength analysis.

Mg元素含量对Al-2Si-0.8Fe合金抗退火软化和导电性能的影响

采用光学显微镜、扫描电镜、布氏硬度计、电子万能材料试验机和涡流导电仪等研究了Mg元素含量对Al-2Si-0.8Fe合金的微观组织、力学性能及导电性能的影响。结果表明:随着Mg元素含量的增加,铸态Al-2Si-0.8Fe合金的硬度和抗拉强度不断提高,而对其导电性能的影响相对较小;当Mg含量增至1.5%时,铸态合金的硬度和抗拉强度达到最大值,分别为77.1 HBW和190 MPa,较Al-2Si-0.8Fe合金的硬度(42.3 HBW)和抗拉强度(123.5 MPa)分别提升了82.3%和53.8%,而导电性能的下降幅度控制在2.9%以内。低温退火处理后,合金的导电率有所提升;当Mg含量超过1%时,退火态合金的硬度显著降低,出现退火软化现象;而在Mg含量低于1%时,退火态合金的抗拉强度和硬度并未明显下降,分别达到201.7 MPa和78 HBW,显示出良好的抗退火软化特性。添加少量的Mg后,合金的组织主要由初生α-Al、共晶Mg_(2)Si相以及长针状β-Al_(5)FeSi相构成,而随着Mg含量的增加,会发生β-Al_(5)FeSi→π-Al_8Mg_(3)FeSi_(6)反应,导致合金中Mg_(2)Si强化相数量减少,无法弥补铸态合金固溶强化对硬度的提升效果,从而产生退火软化现象。

基于被动区土弹簧刚度降低过程的基坑围护结构计算增量法及软化p-y曲线

基坑围护结构的计算常采用基于杆系有限元的增量法,被动区土弹簧刚度在基坑开挖作用下发生动态降低导致土抗力软化,目前缺少在非线性地基模型基础上对该问题的研究。通过引入两个刚度变化系数来综合量化被动区土弹簧参数随基坑开挖的动态变化过程,建立了基于该过程的基坑围护结构计算增量法。针对非线性地基模型,提出了细化增量法进行数值计算。采用线弹性、理想弹塑性以及双曲线3种基本土弹簧模型计算得到被动区软化p-y曲线,对比显示,基于双曲线基本模型得到的等效水平抗力系数变化曲线更符合实际规律。工程实例计算显示,基于基本土弹簧为双曲线的计算结果与不同开挖阶段墙的位移监测数据对应更好。参数分析显示,与被动区土体极限抗力pu相关的刚度变化系数对计算结果影响较大,采用此方法应着重关注被动区pu的计算方法及开挖卸荷对pu的影响。

考虑软化效应的滨海软土区基桩受力与变形特性分析

为探讨水平荷载作用下滨海软土区基桩受力与变形性能,首先根据滨海软土区基桩受荷特点建立相应的简化受力模型;其次,考虑滨海软土的软化效应,对现有的p‑y曲线模型进行修正;据此导出滨海软土区基桩挠曲微分方程,并通过传递矩阵法对其内力及位移进行求解,获得考虑软化效应的滨海软土区基桩非线性计算方法;最后,结合相关工程案例,分析软化参数、桩径和桩体弹性模量对基桩水平承载性能的影响。研究结果表明:采用传递矩阵法对软土区水平受荷桩进行受力分析精度较高,计算效率也高,可为相关工程提供参考;软化参数每增加0.3,地面处桩身水平位移分别减小24.12%和43.04%;桩径每增加0.7 m,地面处桩身水平位移分别减小62.63%和79.65%,桩体位移及内力的影响深度随桩径增大而增大;桩体弹性模量由25.5 GPa增加到36.0 GPa时,桩身变形量分别减小了6.25%和23.06%。

冻结钙质黏土力学特性及修正邓肯-张模型的研究

淮南地区分布着广泛的钙质黏土地层,是冻结法施工的重难点,建立合适的力学模型是解决冻结壁设计的关键。以淮南地区钙质黏土为研究对象,进行不同含水率和温度下的单轴抗压试验,得到其应力-应变曲线。基于试验结果,建立描述钙质黏土的修正邓肯-张模型,将修正的邓肯-张模型进行简化、确定参数,并对曲线进行验证,结果表明:在较低含水率下冻结钙质黏土的应力-应变曲线呈现应变软化的趋势,其强度随着温度降低、含水率增大而增大;通过对比修正邓肯-张模型的计算值和试验值,表明所建立的模型能够很好地描述冻结钙质黏土应力-应变曲线的规律。模型的参数较少,易确定,可以为工程实际提供一定的理论依据。