An approximate nonlinear modified Mohr-Coulomb shear strength criterion with critical state for intact rocks

In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now,leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD,and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comprehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.

Triaxial strength behaviour of rockmass satisfying Modified Mohr-Coulomb and Generalized Hoek-Brown criteria

The triaxial strength of twenty rockmass types was predicted using two non-linear triaxial strength criteria for rockmass i.e. Modified Mohr-Coulomb(MMC) criterion and Generalized Hoek-Brown(GHB)criterion. Four different rockmass classification systems were used for the calculation of MMC criterion parameters while only GSI classification system has been used for calculation of GHB parameters. The representative value of the uniaxial compressive strength and elastic modulus of rockmass have been estimated using probabilistic approach. A hypothetical case of an unsupported tunnel has been analyzed considering both MMC and GHB criteria. The analysis was done using the convergence-confinement method with two different approaches. The first approach predicts the tunnel response using GHB criterion directly. The second approach predicts the tunnel response using equivalent Mohr-Coulomb parameters obtained by linearization of triaxial data points obtained from MMC and GHB criteria. The tunnel response has been estimated in terms of radius of plastic zone, tunnel convergence and tunnel convergence strain. For very poor rockmasses the tunnel response predicted by MMC criterion is less than that predicted by GHB criterion. For poor and fair rockmass, the tunnel response estimated considering both the criteria are comparable except for few cases. Squeezing condition in rockmass has been also evaluated.

Determination of rock resistant coefficient based on Mohr-Coulomb criterion for underwater tunnel

According to the load-structure method, the wall rock with lining can bear the load caused by the surrounding rock, and the rock resistant coefficient (RRC) is a key parameter for evaluating the capacity of this wall rock. Based on the Mohr-Coulomb yield criterion, this paper develops a formula for calculating the RRC, which has been applied to the real engi-neering project, such as Xiamen Xiang’an East Passage Underwater Tunnel Project. The fact shows that this formula is helpful for designers to determine the RRC value.

Elastoplastic homogenization of particulate composites complying with the Mohr–Coulomb criterion and undergoing isotropic loading

This work aims at determining the overall response of a two-phase elastoplastic composite to isotropic loading. The composite under investigation consists of elastic particles embedded in an elastic perfectly plastic matrix governed by the Mohr-Coulomb yield criterion and a non-associated plastic flow rule. The composite sphere assemblage model is adopted, and closed-form estimates are derived for the effective elastoplastic properties of the composite either under tensile or compressive isotropic loading. In the case when elastic particles reduce to voids, the composite in question degenerates into a porous elastoplastic material. The results obtained in the present work are of interest, in particular, for soil mechanics.

DD3单晶的Hill屈服准则应用研究

将Hill屈服准则用于DD3单晶不同温度不同取向的屈服应力预测,结果表明:Hill屈服准则中材料参数的选择对计算结果有很大的影响,且不能同时准确预测单晶三个主要承载方向的屈服强度。根据单晶材料的屈服特点,考虑到单晶材料在任意方向上剪应力及其相互作用对屈服强度的影响,通过在Hill屈服函数中加入一修正项建立了适用于单晶的新屈服函数,能对晶体取向为[001],[011]和[111]的屈服强度进行非常准确的预测,在其它方向上结果也比较满意。

Drucker-Prager准则在拉剪区的修正

针对在岩石塑性力学领域广泛应用的Drucker-Prager准则(简称D-P准则)是一个压剪屈服准则,在拉剪受力状态下不适用的情况,提出在拉剪区修正D-P准则的2种可行性方案。第一种方案是在压剪区,仍采用D-P准则的锥面式,而在拉剪区及其邻近,采用一个球形屈服面代替原来的锥顶附近的锥面。第二种方案是使用一个双曲旋转面近似地代替D-P圆锥面。将这2种方法定义的新的修正的D-P准则简称为D-P-Y准则,它是一个三参数准则,不仅在压剪区符合三轴压缩实验结果,而且在拉剪区也可拟合抗拉强度的资料。同时,它还是一个在全区域处处光滑的正则函数,可以使用经典的正交法则和一致性条件建立本构关系,而不必做任何奇异点的处理,这给应用和编程都带来方便,具有广泛的应用前景。特别地,对于双曲型的D-P-Y准则,当相关参数取0时,可分别退化为D-P准则和Mises准则,因此,在编程中可只编入D-P-Y准则。

考虑原状土初始应力状态的修正SMP屈服准则

原状土与重塑土力学性质方面的差异性,来源于两者初始应力状态的不同及由此引起的结构性差异。重塑土的屈服曲面以等倾线为基线,原状土由于在形成过程中处于三向不等压状态,故其屈服曲面应以K0固结线(初始应力线)为基线。基于松冈-中井的空间滑动面屈服准则,在考虑初始K0固结状态的基础上给出了适用于原状土的修正SMP屈服准则。修正SMP屈服面由常规SMP屈服面绕位于σ2Oσ3平面上的直线σ2=-σ3旋转得到,旋转的角度等于等倾线与K0固结线之间的夹角。与在子午面和π平面上研究重塑土的屈服行为类似,研究原状土的屈服应该在通过K0固结线的子午面和通过σ1+K0σ2+K0σ3=c的χ平面上进行。针对砂雨法试样的真三轴实验结果计算表明,与常规SMP屈服准则相比,基于K0固结线的修正SMP屈服准则更适合描述自然沉积土的强度和屈服特征。

岩石弹塑性损伤本构模型建立及在隧道工程中的应用

在实际隧道施工过程中,隧道开挖引起地下岩体应力重分布使得围岩的微裂纹扩展损伤,并伴随有塑性流动变形。在地下水环境中对于孔隙和微裂隙围岩介质受到应力作用时,在内部将产生高孔隙水压力影响岩石的力学性质,也改变了围岩的破坏模式。为了研究损伤引起的刚度退化和塑性导致的流动两种破坏机制的耦合作用,从弹塑性力学和损伤理论的角度出发,同时引入修正有效应力原理来考虑孔隙水压力的作用,建立基于Drucker-Prager屈服准则的弹塑性损伤本构模型;针对该本构模型推导了孔隙水压力作用下弹塑性损伤本构模型的数值积分算法-隐式返回映射算法,分别对预测应力返回到屈服面的光滑圆锥面或尖点奇异处两种可能的情况给出了详细的描述,隐式返回映射算法具有稳定性和准确性的特点;大多数弹塑性损伤模型中涉及参数多且不易确定的问题,采用反分析方法获得损伤参数,解决了损伤参数不易确定的难题;采用面向对象的编程方法,使用C++语言编制了弹塑性损伤本构求解程序,并对所建立的弹塑性损伤模型和所编程序进行了试验和数值两个方面的验证;最后将其在吉林抚松隧道工程中进行应用,模拟了塑性区和损伤区的发展变化。研究结果表明:所建立的弹塑性损伤本构模型能够较好地描述岩石的力学性能、塑性和损伤变化趋势,所编程序能够进行实际工程问题的模拟,对现场施工给予一定的指导。

镍基单晶板非晶轴方向复合型裂纹尖端塑性区

裂纹尖端塑性区对研究裂纹开裂扩展具有重要意义。通过对Hill屈服准则进行修正,给出一考虑拉剪应力耦合的修正Hill屈服准则。应用修正Hill屈服准则对镍基单晶合金板中、非晶轴方向Ⅰ/Ⅱ复合型裂纹尖端的塑性区进行了分析。在平面应力和平面应变状态下,得到Ⅰ/Ⅱ复合型裂纹尖端塑性区的解析解。讨论了拉剪应力耦合、应力比及裂纹面与材料晶轴间夹角对裂尖塑性区的影响。结果表明,考虑拉剪应力耦合时的裂纹尖端塑性区比不考虑拉剪耦合时的小,拉剪应力耦合对平面应力状态下的裂尖塑性区影响比对平面应变状态下的影响大。无论是平面应力状态还是平面应变状态,Ⅰ/Ⅱ复合型裂纹应力比对裂纹尖端塑性区形状均不产生明显影响,但对塑性区范围的影响较大。裂纹面与材料晶轴间的夹角对裂尖塑性区的形状影响较大。

Strength behaviour of sandstone subjected to polyaxial state of stress

The paper presents an experimental investigation on the strength behaviour of natural rock subjected to polyaxial state of stress. The polyaxial tests were conducted on cubical specimens of sandstone obtained from the Shivpuri district in Madhya Pradesh state of India, The specimens having nominal dimensions of100 mm x 100 mm x 100 mm were tested using a polyaxial testing machine. Twenty-five combinations of intermediate and minor principal stresses were applied and the specimens were loaded till failure occurs. It was observed that the intermediate principal stress has a substantial effect on the strength of the Shivpuri sandstone. A database of rock strength under various combinations of σ_2 and σ_3 was obtained for the Shivpuri sandstone. The database was used to study the predictability of five most commonly used strength criterion. Root mean square error(RMSE), average absolute relative error percentage(AAREP) and coefficient of accordance(COA) were used as indices for the measure of goodness of fit. It was observed that the least error in the prediction was shown by modified Mohr Coulomb criterion followed by modified Weibols and Cook criterion. A probability analysis of the error in prediction was also done.

Constitutive models in stability analysis of rock slope

Equivalent Mohr-Coulomb yield criterion was established,and the relationship between different constitutive models was studied.The application of equivalent Mohr-Coulomb yield criterion in Ansys was achieved by means of transforming material parameters.The stability research aiming at the most common rock slope without conspicuous slide surface was accomplished,the methods of measurably assessing the stability of rock slope without conspicuous slide surface were explored,and the disadvantages of method of minimum slide-resisted reserve as dangerous slide path were pointed out.The results show that through the calculation and analysis of cases,the conception that measurable assessment of the stability of rock slope without conspicuous slide surface can be achieved under condition that equivalent Mohr-Coulomb yield criterion is validated.Its safety parameter formula is explicit in theory and credible in results.The results obtained are approximate to those obtained by using finite element intensity reducing method.

Non-linear Analysis of Bridge“Guglie”in Venice:Sensitivity to Designed and Realized Shape

In this paper,numerical non-linear analyses of the “Guglie” bridge,located in the historical city of Venice(Italy),are proposed.The focus is twofold:on the sensitivity of the realized shape of the bridge by reference to originally designed shape;and on sensitivity to mechanical parameters of constituent materials.The history of this bridge is very interesting,and the bridge actually built is different from the Marchesini’s project(1580).In fact,in the original design drawing,the shape of the arch is a perfect circle arch,while the shape of the actually built arch is not perfectly circular.Hence,in the aim to evaluate sensitivity of bridge behaviour to designed and realized shape,non-linear analyses are carried on by means of FEMs(Finite Element Models)under in-plane state hypothesis.Furthermore,parametric tests are also performed for evaluating the influence of masonry mechanical parameters on non-linear bridge behaviour.

基于修正Mohr-Coulomb屈服准则的冻结砂土损伤本构模型

为了探讨冻土的强度和变形特性以及反映低围压下的应变软化和高围压下的应变硬化现象,建立不同围压影响下的冻结砂土损伤本构模型,其能合理解释冻土内部微裂隙向宏观破碎带转化过程。通过引入修正Mohr-Coulomb屈服准则来描述冻土微元强度破坏准则,利用冻土内部微缺陷分布的离散性和随机性特点,假设微元强度服从Weibull随机分布,并根据统计学和连续损伤力学理论建立能反映冻土破损全过程的损伤本构模型。通过低温三轴试验数据确定模型参数值,讨论Weibull分布参数n和F_0的物理意义,并修正分布参数随围压的变化规律;讨论并分析冻结砂土的黏聚力c、内摩擦角φ和损伤变量D随围压变化的演化规律。最后将模型预测结果与试验值进行对比,表明该模型能够较好地模拟冻结砂土应力–应变全过程曲线,并能反映随围压的增大曲线由应变软化逐渐向应变硬化过渡的现象;同时模拟了体积变形曲线,并能反映随围压的增大体变曲线由剪胀向剪缩转变特性。

修正双屈服面模型三维化在水泥砾质土中的应用

采用变换应力方法将空间滑动面破坏准则应用于修正双屈服面模型,使该模型合理三维化。在不增加新参数的情况下可描述水泥砾质土的力学特性,利用水泥砾质土三轴试验结果对三维化后的修正双屈服面模型进行初步验证。结果表明,在低水泥掺入比(wc≤5%)的条件下,三维化后的修正双屈服面模型能够较好地反映水泥砾质土应力~应变关系的软化现象,且充分体现了体变~应变关系在低围压下的剪胀性和高围压下的剪缩性;但当水泥掺入比wc为8%且围压为200 k Pa时,水泥砾质土的脆性显著增强,其剪胀性也十分显著,水泥砾质土达到峰值强度后呈现脆性破坏,导致该模型计算值与试验值误差较大。该研究成果可为水泥砾质土应用于高土石坝心墙料力学特性研究提供一定的技术支撑。

基于FLAC^(3D)梁单元修正的隧道/巷道拱架支护模拟方法(英文)

目的:基于常用的数值模拟软件FLAC^(3D)进行二次开发,弥补现有数值模拟方法的缺陷,提出一种准确有效的隧道/巷道拱架支护数值模拟方法。创新点:1.引入抗弯和抗压能力的相关性,改进梁单元压弯极限判据;2.通过FISH语言编程,实现梁单元修正和拱架精确模拟。方法:1.通过对FLAC^(3D)中梁单元支撑理论的分析,明确其存在的缺陷,并利用算例进行证实(图4~6);2.基于传统强度理论,对梁单元现有压弯极限判据进行改进(图7和8);3.通过FISH语言编程,实现梁单元修正模型嵌入(图9);4.通过算例分析,对新模拟方法的效果进行验证(图10和13)。结论:1.改进了梁单元压弯极限判据,通过FISH语言编程实现了梁单元的修正及拱架屈服失效的模拟。2.构件压弯试验和巷道拱架支护实例分析表明:修正模型体现了在压弯组合荷载作用下梁单元屈服时弯矩和轴力的相关性;实现程序是有效的且灵敏度较高;提出的新模拟方法使计算偏差得到有效压制,拱架模型呈现出的力学行为及围岩支护作用更加接近实际,计算精度和设计可靠度更高。