Assessing the range of blasting-induced cracks in the surrounding rock of deeply buried tunnels based on the unified strength theory

Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.

Fundamental Issues Towards Unified Design Theory of Recycled and Natural Aggregate Concrete Components

In the past 20 years,recycled aggregate concrete(RAC),as a type of low-carbon concrete,has become a worldwide focus of research.However,the design methodology for RAC structural components remains a challenge.Consequently,demands for a unified design of natural aggregate concrete(NAC)and RAC components have been presented.Accordingly,this study analyses the necessity of a unified design theory and provides an in-depth demonstration of the strength determination,compressive constitutive relationship,and design method of concrete components.The coefficient of variation of RAC strength is found to be generally higher than that of NAC strength.The compressive and tensile strengths of RAC can be defined and determined using the same method as that used for NAC.The uniaxial compressive constitutive relationship between NAC and RAC has a unified mathematical expression.However,the elastic modulus of RAC decreases,and its brittleness exhibits an increasing trend compared with that of NAC.Finally,to unify the design formulae of RAC and NAC components for bearing capacity,modification factors for RAC components are proposed considering safety and reliability.Additionally,the feasibility of the proposed unified time-dependent design theory is demonstrated in terms of conceptual design and structural measures considering the effects of strength degradation and reinforcement corrosion.It is believed that this study enriches and develops the basic theory of concrete structures.

New Asphalt Pavement Failure Criterion Based on Unified Strength Theory

This study aims to introduce an appropriate analytical method for asphalt pavement based upon unified strength theory （UST）. The traditional maximum shear stress strength theory （MSST） cannot describe the marked difference between tension strength and compressive strength or variable intermediate principal stress, which significantly affects the geotechnical materials. Our studies try to find a new asphalt pavement failure criterion that considers the influence of both tension-compression strength ratio and intermediate principal stress of asphalt mixture. In order to select a suitable theory on pavement material, the UST is introduced and compared with the traditional theory. Results show that the tension-compression strength ratio of asphalt mixture, which is used as a material parameter, dramatically affects the stress and stress distribution law in pavement; the pavement stress level increases dramatically after considering the intermediate principal stresses. Therefore, the UST which considers both tension-compression strength ratio and intermediate principal stress is more in line with the material characteristics of asvhalt pavement.

Fractional derivative statistical damage model of unsaturated expansive soil based on unified hydraulic effect

Unsaturated expansive soil is widely distributed in China and has complex engineering properties.This paper proposes the unified hydraulic effect shear strength theory of unsaturated expansive soil based on the effective stress principle,swelling force principle,and soil–water characteristics.Considering the viscoelasticity and structural damage of unsaturated expansive soil during loading,a fractional hardening–damage model of unsaturated expansive soil was established.The model parameters were established on the basis of the proposed calculation method of shear strength and the triaxial shear experiment on unsaturated expansive soil.The proposed model was verified by the experimental data and a traditional damage model.The proposed model can satisfactorily describe the entire process of the strain-hardening law of unsaturated expansive soil.Finally,by investigating the damage variables of the proposed model,it was found that:(a)when the values of confining pressure and matric suction are close,the coupling of confining pressure and matric suction contributes more to the shear strength;(b)there is a damage threshold for unsaturated expansive soil,and is mainly reflected by strength criterion of infinitesimal body;(c)the strain hardening law of unsaturated expansive soil is mainly reflected by fractional derivative operator.

Unified analytical solution for deep circular tunnel with consideration of seepage pressure,grouting and lining

A new unified analytical solution is presented for predicting the range of plastic zone and stress distributions around a deep circular tunnel in a homogeneous isotropic continuous medium. The rock mass, grouting zone and lining are assumed as elastic-perfectly plastic and governed by the unified strength theory(UST). This new solution has made it possible to consider the interaction between seepage pressure, lining, grouting and rock mass, and the intermediate principal stress effect together. Moreover, parametric analysis is carried out to identify the influence of the related parameters on the plastic zone radius. Under the given conditions, the results show that the plastic zone radius decreases with an increasing cohesion, internal friction angle and hydraulic conductivity of lining and unified failure criterion parameter, respectively; whereas the plastic zone radius increases with the growth of elasticity modulus of lining. Comparison of results from the new solution and the other published one shows well agreement and provides confidence in the new solution proposed.

Unified semi-analytical solution for elastic-plastic stress of deep circular hydraulic tunnel with support yielding

A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plastic and governed by the unified strength theory (UST).Different major principal stresses in different engineering situations and different support yielding conditions are both considered.The unified solution obtained in this work is a series of results,rather than one specific solution,hence it is suitable for a wide range of rock masses.In addition,parametric study is conducted to investigate the effect of intermediate principal stress.The result shows the major principal stress should be rationally chosen according to different engineering conditions.Finally,the applicability of the unified solution is discussed according to the critical pressures.

Unified elastoplastic finite difference and its application

Two elastoplastic constitutive models based on the unified strength the- ory （UST） are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua （FLAC/FLAC3D）, which includes an associated/non- associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different （SD） materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening be- havior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD mate- rial structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.

非对称破坏模式下临坡地基的Meyerhof承载力新解

利用统一强度理论的平面应变强度方程,综合考虑中间主应力、基础至坡肩的水平距离、边坡高度和基底粗糙情况等因素,提出临坡地基坡面非对称破坏模式和坡底非对称破坏模式,继而建立条形基础下临坡地基新的Meyerhof承载力解答,给出具体应用步骤并开展理论退化分析与对比验证。研究表明:考虑坡后土体强度贡献所提出的非对称破坏模式更符合临坡地基的实际破坏形态;所得临坡地基Meyerhof承载力解答与文献模型试验和数值模拟均吻合良好;中间主应力可明显提高临坡地基的承载力;临坡地基承载力随边坡高度增加先减小后恒定。研究结果合理反映了土体强度的中间主应力效应、破坏模式的非对称性以及基础旁侧土体强度等工程实际情况,对临坡地基优化设计具有一定的理论指导意义。

基于统一强度理论的扰损围岩巷道脆塑性解答

钻爆法施工常造成岩质巷道扰损区围岩性能劣化。针对扰损围岩、扰损外围岩的弹塑性状态下不同的扰损围岩巷道力学模型,采用统一强度理论、弹-脆-塑性模型和非关联流动法则,建立扰损围岩巷道有关应力、位移和塑性区半径的脆塑性解答,探讨巷道力学模型的转换路径及判定方法,并将结果进行对比、验证,获得各因素的影响规律。研究表明:提出的巷道脆塑性解答合理反映了中间主应力、围岩扰损范围和峰后强度、剪胀特性的综合影响,通过参数组合变换可退化为多种解答并得到正确性验证,具有重要的理论意义和应用前景;巷道力学模型判定与中间主应力、围岩扰损范围密切相关,显著影响巷道应力-位移分布和围岩特征曲线;支护压力和巷道稳定变形随着围岩峰后强度下降、剪胀特性参数增加而明显增大。

卸载状态下非均质圆形寒区隧道围岩弹塑性统一解

以统一强度理论作为卸载状态下寒区隧道冻结围岩屈服准则,综合考虑围岩非均质特性和中间主应力效应对冻结围岩强度影响,建立寒区隧道应力位移弹塑性力学模型,联合各区域边界条件,计算获得冻结围岩均质与非均质状态下,弹性解、塑性统一解以及塑性区半径的隐式方程,分别对其应力位移场讨论分析。研究表明:考虑冻结围岩的非均质特性,塑性区环向应力峰值增大40%,塑性区范围相对减少40.4%,内壁位移减少9.3%,弹性极限承载力提高41%,塑性极限承载力提高14%,影响显著。中间主应力效应能充分发挥非均质冻结围岩承载潜能,计算得到的承载力明显增大,塑性半径明显减小。所得结果可为寒区隧道开挖支护设计以及数值模拟,提供理论指导。

An elasto-plastic constitutive model for soft rock considering mobilization of strength

A new elasto-plastic constitutive model is presented in the framework of plasticity theory. The strength characteristics of a diatomaceous soft rock is investigated. The friction angle and cohesion of soft rock are mobilized as a function of plastic strain. A hyperbolic hardening function for the mobilized friction and a mixed parabolic and exponential equation for the mobilized cohesion are proposed. In view of the unified strength theory and the mobilizations of strength components, a yield function is given. A plastic potential function is determined by using the non-associated plastic flow rule. An elasto-plastic constitutive model is developed and verified. The results indicate that the proposed model can predict the behavior of soft rock accurately. The advantages of the proposed constitutive model are analyzed. The evidences support that the proposed constitutive model is a mixed hardening/softening model. A hump hardening/softening function for mobilized friction is extended to a more generalized condition.

考虑损伤效应的二向不等压深埋圆形隧道弹塑性统一解

为了研究二向不等压地应力环境下深埋圆形隧道损伤后的力学响应问题,通过考虑深部围岩的损伤效应,基于统一强度理论建立二向不等压深埋圆形隧道弹塑性解,依托华丽高速东马场隧道验证解的准确性和适用性;研究损伤效应和中间主应力对围岩应力分布和变形的影响,并探讨不同侧压力系数、剪胀系数和支护反力下深埋圆形隧道围岩的损伤程度。研究结果表明:二向不等压深埋圆形隧道开挖后,围岩峰后的损伤效应会加剧隧道的挤压变形,考虑损伤效应的变形计算结果与现场实测结果更接近;中间主应力能提高围岩的承载能力,抑制隧道的挤压变形,不考虑中间主应力会高估隧道的变形潜势;侧压力系数决定围岩损伤区的形状和大小,施工时应根据围岩不同位置的损伤程度对关键变形部位进行注浆加固;剪胀系数越大,围岩的损伤程度越大,损伤区的范围越大;支护反力能抑制围岩的损伤效应,在实际工程中需及时施作支护约束围岩变形,以改善围岩的受力情况。

采用FRP、钢管、混凝土的组合柱轴压承载力统一计算公式

随着FRP与传统材料的组合应用,国内外学者提出了适用不同工程背景的FRP、钢管、混凝土新型组合柱形式。考虑到其约束效果可以采用统一的侧向约束系数来评价,针对大多数基于FRP、钢管、混凝土的组合柱提出较为简便的统一计算公式。为建立适用范围广的组合柱轴压承载力统一计算公式,回顾了已有的FRP、钢管、混凝土组合柱形式,并按其约束形式分为四类截面。根据双剪统一强度理论,引入钢管屈服强度折减系数、方钢管的不均匀约束系数来考虑极限状态时钢管轴向应力低于其屈服强度的特点,分别推导出四类截面的组合柱轴压承载力计算公式。该公式考虑了组合柱的套箍指标、钢管屈服强度折减系数和组合柱截面尺寸影响,形式简单,适用范围广。通过与试验数据对比,提出的统一计算公式的理论计算值与试验值较为吻合。

基于统一强度理论的自紧身管残余应力分析

基于统一强度理论,考虑材料拉压异性和鲍辛格效应的影响,采用双线性强化材料模型对身管进行自紧分析,推导了身管加载应力、卸载应力、残余应力及工作应力的解析解,得到了弹塑性交界面半径、反向屈服半径的计算公式,提出了最佳自紧度和自紧压力的计算方法,通过与实验数据进行对比,验证了本文理论解的正确性,分析了材料拉压强度比、中间应力系数等参数对身管残余应力、弹塑性交界面半径、反向屈服半径和最佳自紧压力的影响。结果表明,反向屈服半径、弹塑性交界面半径、弹塑性交界面处残余应力与材料拉压强度比成正比,与中间应力系数成反比;最佳自紧压力与材料拉压强度比成反比,与中间应力系数成正比。

考虑围岩膨胀特性的深埋圆形隧道弹塑性统一解

针对隧道及地下工程中围岩吸水膨胀导致应力与位移场变化难以量化的问题,基于弹塑性与湿度应力场理论,采用统一强度理论与非关联流动法则,推导考虑中间主应力效应与围岩吸水膨胀特性的深埋圆形隧道弹塑性统一解.首先,结合考虑湿度变化的平衡方程与本构方程,获得围岩弹性状态下的应力与位移解;然后,提出围岩弹塑性状态的判定方法,并基于统一强度理论推导围岩塑性状态下的解析解;最后,通过算例对比分析验证本文所推统一解的准确性,并进一步探究中间主应力、湿度膨胀系数以及含水率变化对围岩应力场与塑性区半径的影响规律,研究结果表明:本文与已有文献所求塑性区半径偏差仅为0.136%,验证了本文所推统一解的合理性;在所提供支护抗力相同的前提下,考虑围岩膨胀特性计算所得塑性区半径扩大,弹-塑性界面的环向应力增加,考虑围岩膨胀特性所得塑性区半径与环向应力是不考虑膨胀特性的1.06倍;当统一强度理论参数从0.0增加到1.0时,弹-塑性界面的环向应力增幅为6.6%,塑性区半径降幅为13.9%,隧道洞壁位移降幅为16.0%;当湿度膨胀系数分别取值0.00与0.10时,由于湿度膨胀系数影响引起的弹-塑性界面环向应力与塑性区半径增量分别达17.98%与27.4%;当最大含水率从0.00增加到0.06时,弹-塑性界面的环向应力增幅为16.9%,塑性区半径增幅为23.1%,隧道洞壁位移增幅为100%.研究成果可为膨胀岩隧道结构设计提供理论依据.

考虑温度和损伤的圆形巷道围岩弹塑性分析

为研究圆形巷道围岩在温度应力和损伤作用的下塑性区半径及应力分布规律,基于统一强度理论,推导了围岩在温度应力和损伤耦合作用下的应力场、位移场和塑性区范围的计算公式。结合具体算例,分析了损伤、温度应力等因素对巷道围岩应力和塑性区范围的影响,计算结果表明:损伤和温度应力等因素均对巷道围岩应力和塑性区半径产生较大影响,其中损伤-温度应力共同作用时所造成的塑性区半径最大,相较于仅有围岩应力作用时的塑性区范围增加了8.1%。因此探究巷道在温度应力和损伤作用下围岩塑性区半径及应力分布规律是必要的,可以为巷道工程的优化支护设计和稳定性分析提供理论依据。

Strength criterion of composite solid propellants under dynamic loading

Based on the dynamic loading(1-100 s^(-1)) experiments under different temperatures(223-298 K) and stress states, uniaxial and biaxial strength criterion of a Hydroxyl-terminated polybutadiene(HTPB)based composite solid propellant were further investigated. These experiments were conducted through the use of a new uniaxial INSTRON testing machine, different new designed gripping apparatus and samples with different configurations. According to the test results, dynamic uniaxial tensile strength criterion of the propellant was directly constructed with the master curve of the uniaxial maximum tensile stress. Whereas, a new method was proposed to determine the dynamic uniaxial compressive strength of the propellant in this study. Then uniaxial compressive strength criterion of the propellant was constructed based on the related master curve. Moreover, it found that the uniaxial tensilecompressive strength ratio of the propellant is more sensitive to loading temperature under the test conditions. The value of this parameter is about 0.4 at room temperature, and it reduces to 0.2-0.3 at low temperatures. Finally, the theoretical biaxial strength criterion of HTPB propellant under dynamic loading was constructed with the unified strength theory, the uniaxial strength and the typical biaxial tensile strength. In addition, the theoretical limit lines of the principal stress plane for the propellant under dynamic loading at different temperatures were further plotted, and the scope of the limit line increases with decreasing temperature.

Unified solutions for stresses and displacements around circular tunnels using the Unified Strength Theory

The unified solutions are presented for stresses and displacements around a circular tunnel subjected to a hydrostatic stress field.The rock mass is assumed to be elastic-brittle-plastic and governed by the Unified Strength Theory.The displacements are obtained accounting for three different definitions for elastic strains and different Young's modulus in the plastic zone.The unified solutions obtained in this paper are especially versatile in reflecting the intermediate principal stress effect to different extents for different materials.The conventional solutions,based on the Mohr-Coulomb failure criterion and the Generalized Twin Shear Stress yield criterion,are special cases of the present unified solutions.The new unified solutions can compare with those computed by the latest generalized Hoek-Brown failure criterion.The results obtained demonstrate the importance of the intermediate principal stress influence for the stresses and displacements analysis.The effects of different definitions for elastic strains and different Young's modulus in the plastic zone on the displacements are significant.

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.

钢管混凝土边框剪力墙受剪承载力计算方法对比研究

为研究不同力学模型在钢管混凝土边框剪力墙受剪承载力计算中的适用性,总结了国内外学者推导的经验公式和理论模型,建立了基于软化拉压杆模型、统一强度理论和国内外相关规范的承载力计算方法,对比分析了理论力学模型和多国规范在预测此类组合墙受剪承载力上的表现,探讨了轴压比、高宽比、宽厚比和材料性能等对计算结果误差的影响;最后结合已有试验数据,验证了各模型的计算精度和适用性。结果表明:由于未考虑构件各部分所分担的剪力,多数规范模型理论计算结果普遍低于试验值,而统一强度理论与软化拉压杆模型计算结果相对准确;软化拉压杆模型计算方法能充分考虑墙体各部分对承载力的贡献,计算偏差基本控制在20%以内;在各项参数变动的前提下,软化拉压杆模型更能准确预测钢管混凝土边框剪力墙的受剪承载力,计算值与试验值吻合良好,能合理反映钢管混凝土边框剪力墙的受剪机理,为其承载力计算方法的优化设计提供理论依据。