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CN116465732A - Method and system for taking value of mechanical parameters of rock mass joint unit - Google Patents

Method and system for taking value of mechanical parameters of rock mass joint unit Download PDF

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CN116465732A
CN116465732A CN202310338475.0A CN202310338475A CN116465732A CN 116465732 A CN116465732 A CN 116465732A CN 202310338475 A CN202310338475 A CN 202310338475A CN 116465732 A CN116465732 A CN 116465732A
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joint unit
rock
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周永强
丁海锋
肖明清
付晓东
薛光桥
盛谦
陈健
徐晨
杨剑
吴佳明
谢壁婷
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Wuhan Institute of Rock and Soil Mechanics of CAS
China Railway Siyuan Survey and Design Group Co Ltd
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China Railway Siyuan Survey and Design Group Co Ltd
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Abstract

本发明属于岩土力学技术领域,并具体公开了一种岩体节理单元力学参数的取值方法及系统。所述方法包括:基于室内岩石基本力学试验,获取完整岩石的宏观力学参数;根据岩体质量分级标准对工程岩体进行岩体等级划分,获取等效岩体力学参数;根据Mohr‑Coulomb准则和关联流动法则,推导节理单元的弹塑性刚度矩阵;根据均匀化理论、极限应变理论,计算节理单元力学参数,并验证节理单元力学参数的合理性。本发明基于等效连续模型的思想,把结构面处理成有一定厚度的软弱夹层,将岩体划分为弹性的岩石单元和弹塑性的节理单元,通过对整个节理岩体单元的分析,综合得到节理单元的力学特性,既能满足工程计算精度,又便于直接应用室内试验测试数据。

The invention belongs to the technical field of rock and soil mechanics, and specifically discloses a method and a system for acquiring mechanical parameters of rock mass joint units. The method includes: obtaining the macroscopic mechanical parameters of the complete rock based on the basic rock mechanics test in the laboratory; classifying the engineering rock mass according to the rock mass quality classification standard to obtain the equivalent rock mass mechanical parameters; deriving the elastoplastic stiffness matrix of the joint unit according to the Mohr-Coulomb criterion and the associated flow law; calculating the mechanical parameters of the joint unit according to the homogenization theory and the ultimate strain theory, and verifying the rationality of the mechanical parameters of the joint unit. Based on the idea of an equivalent continuous model, the present invention treats the structural surface as a weak interlayer with a certain thickness, divides the rock mass into an elastic rock unit and an elastic-plastic joint unit, and obtains the mechanical properties of the joint unit through the analysis of the entire jointed rock unit, which can not only meet the engineering calculation accuracy, but also facilitate the direct application of laboratory test data.

Description

一种岩体节理单元力学参数的取值方法及系统A method and system for obtaining mechanical parameters of rock mass joint units

技术领域technical field

本发明属于岩土力学技术领域,更具体地,涉及一种岩体节理单元力学参数的取值方法及系统。The invention belongs to the technical field of rock and soil mechanics, and more specifically relates to a method and system for acquiring mechanical parameters of rock mass joint units.

背景技术Background technique

岩体作为一种经历漫长成岩历史的地质体,其内部通常分布着大量断裂和节理裂隙。这些微裂隙数量多,尺寸小,对岩体的切割度高,直接影响着岩体的力学性质和变形特征。然而,由于节理裂隙数量极多,逐一模拟是不可行的,因此,如何准确高效地模拟具有众多节理裂隙的岩体结构,成为岩体工程界亟待解决的问题。As a geological body with a long history of diagenesis, rock mass usually has a large number of fractures and joint fissures distributed inside it. These micro-cracks are large in number, small in size, and have a high cutting degree to the rock mass, which directly affects the mechanical properties and deformation characteristics of the rock mass. However, due to the large number of joints and fissures, it is not feasible to simulate one by one. Therefore, how to accurately and efficiently simulate the rock mass structure with many joints and fissures has become an urgent problem to be solved in the field of rock mass engineering.

目前,关于等效岩体结构的求解策略主要有两种思路。第一种思路基于对岩土材料中缺陷普遍存在的认识,通过分析不连续结构对材料整体力学行为的影响建立起来的岩体表征单元方法(周创兵,於三大.论岩体表征单元体积REV-岩体力学参数取值的一个基本问题[J].工程地质学报,1999,7(4):332–336.)。该方法通过国标BQ、GSI和RQD指标等岩体质量分级标准划分岩体等级,获取岩体力学参数,并结合数值模拟分析,确定岩体表征单元体积(REV),将岩体表征单元体的力学参数作为工程尺度岩体的力学参数(Kulatilake PH S W.Estimating elastic constants and strength of discontinuous rock[J].Journal of geotechnical engineering,1985,111(7):847-864.何满潮,薛廷河,彭延飞.工程岩体力学参数确定方法的研究[J].岩石力学与工程学报,2001(02):225-229.)。此外,中国专利CN113946958A公开了一种基于离散裂隙网络法求取岩体表征单元REV的方法,该方法能够较合理的反映一般裂隙岩体的宏观力学行为,是目前工程界流行的方法,但受尺寸效应影响,岩体室内试验数据不能作为参数选取的主要依据。第二种思路将岩体视为完整岩石和结构面两相构成,其中,岩石单元和结构面单元均视作各向同性体,但二者组合成的岩体单元则为各项异性体。该方法通过强度等效原则将沿着节理面破坏和岩石破坏两种破坏形式统一起来,得到整体岩体的力学参数。上述强度等效的方法是目前学术研究的前沿,其中,岩石力学参数通过室内力学试验获取,而节理单元的力学参数的取值成为模型是否能准确表征岩体结构力学特性和破坏特征的关键。At present, there are two main approaches to solve the equivalent rock mass structure. The first idea is based on the understanding of the ubiquity of defects in rock and soil materials, and establishes the rock mass representation unit method by analyzing the influence of discontinuous structures on the overall mechanical behavior of materials (Zhou Chuangbing, Yu Sansan. On the rock mass representation unit volume REV-a basic problem of rock mass mechanical parameters [J]. Journal of Engineering Geology, 1999, 7(4): 332-336.). This method divides rock mass grades through the national standard BQ, GSI and RQD indicators and other rock mass quality classification standards, obtains rock mass mechanical parameters, and combines numerical simulation analysis to determine rock mass representation unit volume (REV), and takes the mechanical parameters of rock mass representation unit as mechanical parameters of engineering scale rock mass (Kulatilake PH S W.Estimating elastic constants and strength of discontinuous rock[J].Journal of geotechnical engine ering,1985,111(7):847-864.He Manchao,Xue Tinghe,Peng Yanfei.Research on the Method of Determination of Mechanical Parameters of Engineering Rock Mass[J].Journal of Rock Mechanics and Engineering,2001(02):225-229.). In addition, Chinese patent CN113946958A discloses a method based on the discrete fracture network method to obtain the rock mass representation unit REV. This method can reasonably reflect the macroscopic mechanical behavior of the general fractured rock mass. It is a popular method in the engineering field. However, due to the size effect, the rock mass laboratory test data cannot be used as the main basis for parameter selection. The second way of thinking regards the rock mass as a two-phase composition of complete rock and structural plane. Among them, rock units and structural plane units are regarded as isotropic bodies, but the rock mass units formed by the two are anisotropic bodies. This method unifies the two failure forms of failure along the joint surface and rock failure through the principle of strength equivalence, and obtains the mechanical parameters of the whole rock mass. The strength equivalence method mentioned above is the frontier of academic research at present. Among them, the rock mechanical parameters are obtained through indoor mechanical tests, and the value of the mechanical parameters of the joint unit becomes the key to whether the model can accurately characterize the mechanical properties and failure characteristics of the rock mass structure.

综上所述,当前关于等效岩体结构的求解方法仍具有一定的缺陷,主要体现在:(1)天然岩体中节理分布广泛,所分析介质具有离散不确定性,如果都作为节理单元处理,将会给数值建模和计算带来很大的困难;(2)受尺寸效应影响,岩体的REV值通常很大甚至不存在,实验室试样的测试结果不能直接作为岩体表征单元的力学参数取值依据。To sum up, the current methods for solving the equivalent rock mass structure still have certain defects, which are mainly reflected in: (1) joints are widely distributed in natural rock mass, and the analyzed medium has discrete uncertainties. If they are all treated as joint units, it will bring great difficulties to numerical modeling and calculation; (2) affected by the size effect, the REV value of rock mass is usually very large or even does not exist, and the test results of laboratory samples cannot be directly used as the basis for the mechanical parameters of rock mass characterization units.

基于上述缺陷和不足,本领域亟需提出一种新的岩体节理单元力学参数的取值方法,以克服现有技术中分析介质的离散不确定性以及依据试验结果取值的不准确性。Based on the above defects and deficiencies, there is an urgent need in this field to propose a new method for determining the mechanical parameters of rock mass joint elements, so as to overcome the discrete uncertainty of the analytical medium and the inaccuracy of determining values based on test results in the prior art.

发明内容Contents of the invention

针对现有技术的以上缺陷或改进需求,本发明提供了一种岩体节理单元力学参数的取值方法及系统,其基于等效连续模型的思想,把结构面处理成有一定厚度的软弱夹层,将岩体划分为弹性的岩石单元和弹塑性的节理单元,通过对整个节理岩体单元的分析,综合得到节理单元的力学特性。这种方法综合了室内力学试验和岩石质量分级,既能满足工程计算精度,又便于直接应用室内试验测试数据。In view of the above defects or improvement needs of the prior art, the present invention provides a method and system for obtaining mechanical parameters of rock mass joint units. Based on the idea of equivalent continuous model, the structural surface is treated as a weak interlayer with a certain thickness, and the rock mass is divided into elastic rock units and elastic-plastic joint units. Through the analysis of the entire joint rock mass unit, the mechanical properties of the joint unit are obtained comprehensively. This method combines indoor mechanical tests and rock quality classification, which can not only meet the accuracy of engineering calculations, but also facilitate the direct application of indoor test data.

为实现上述目的,按照本发明的一个方面,提出了一种岩体节理单元力学参数的取值方法,包括以下步骤:In order to achieve the above object, according to one aspect of the present invention, a method for obtaining the mechanical parameters of a rock mass joint unit is proposed, comprising the following steps:

S1基于室内岩石基本力学试验,获取完整岩石的宏观力学参数;S1 is based on indoor basic rock mechanics tests to obtain macroscopic mechanical parameters of intact rocks;

S2根据岩体质量分级标准对工程岩体进行岩体等级划分,获取等效岩体力学参数;S2 Classify the engineering rock mass according to the rock mass quality classification standard, and obtain equivalent rock mass mechanical parameters;

S3根据Mohr-Coulomb准则和关联流动法则,推导节理单元的弹塑性刚度矩阵;S3 derives the elastic-plastic stiffness matrix of the joint element according to the Mohr-Coulomb criterion and the associated flow rule;

S4根据均匀化理论,代入完整岩石力学参数、等效岩体力学参数以及节理单元的弹塑性刚度矩阵计算节理单元强度参数,同时,基于极限应变理论以及等效岩体力学参数计算等效岩体极限应变;S4 According to the homogenization theory, the complete rock mechanical parameters, the equivalent rock mass mechanical parameters and the elastic-plastic stiffness matrix of the joint unit are substituted to calculate the strength parameters of the joint unit, and at the same time, the equivalent rock mass ultimate strain is calculated based on the ultimate strain theory and the equivalent rock mass mechanical parameters;

S5根据所述等效岩体极限应变、节理单元强度参数计算机理单元断裂能,并以此确定节理单元力学参数。S5 calculates the fracture energy of the physical unit according to the equivalent rock mass ultimate strain and the strength parameters of the joint unit, and determines the mechanical parameters of the joint unit based on this.

作为进一步优选的,步骤S1中,所述室内岩石基本力学试验包括岩石单轴压缩和岩石巴西劈裂试验,根据岩石单轴压缩试验获取完整岩石的弹性模量Er和泊松比vr;根据岩石巴西劈裂试验获取完整岩石的抗拉强度ft rAs further preferred, in step S1, the indoor rock basic mechanics test includes rock uniaxial compression and rock Brazilian splitting test, according to the rock uniaxial compression test to obtain the elastic modulus E r and Poisson's ratio v r of the complete rock; according to the rock Brazilian splitting test to obtain the tensile strength f t r of the complete rock.

作为进一步优选的,步骤S2中,所述等效岩体力学参数包括弹性模量Em、泊松比vm、粘聚力cm、内摩擦角和抗拉强度ft mAs a further preference, in step S2, the equivalent rock mass mechanical parameters include elastic modulus E m , Poisson's ratio v m , cohesion c m , internal friction angle and tensile strength f t m .

作为进一步优选的,步骤S3包括以下步骤:As further preferred, step S3 includes the following steps:

S31构建屈服函数f和第一材料参数m(κ)与第二材料参数σc(κ)表达式,选择Mohr-Coulomb准则作为节理单元的屈服准则,构建屈服函数:S31 Construct the yield function f and the expression of the first material parameter m(κ) and the second material parameter σ c (κ), select the Mohr-Coulomb criterion as the yield criterion of the joint element, and construct the yield function:

f(σ13,κ)=m(κ)σ13c(κ)=0f(σ 13 ,κ)=m(κ)σ 13c (κ)=0

式中,σ1和σ3分别是材料的最大主应力和最小主应力,内变量κ表征材料的硬化程度;In the formula, σ 1 and σ 3 are the maximum principal stress and minimum principal stress of the material, respectively, and the internal variable κ represents the degree of hardening of the material;

S32构建节理单元的弹塑性刚度矩阵,其中,塑性变形采用与屈服面相关联的流动法则,所述节理单元的弹塑性刚度矩阵[Kep]的计算模型如下:S32 constructing the elastic-plastic stiffness matrix of the joint element, wherein the plastic deformation adopts the flow law associated with the yield surface, and the calculation model of the elastic-plastic stiffness matrix [K ep ] of the joint element is as follows:

式中,[Ke]为节理单元的弹性刚度矩阵,R为硬化模量,σ为节理单元应力的矢量表示。where [K e ] is the elastic stiffness matrix of the joint element, R is the hardening modulus, and σ is the vector representation of the stress of the joint element.

作为进一步优选的,步骤S4包括以下步骤:As further preferably, step S4 includes the following steps:

S41求解节理单元刚度:根据连续介质的刚度等效原则,求解节理单元的法向刚度KN和切向刚度KSS41 Calculation of joint element stiffness: according to the principle of equivalent stiffness of continuous media, the normal stiffness K N and tangential stiffness K S of the joint element are calculated;

S42求解节理单元抗拉强度和抗剪强度:根据均匀化理论要求,节理单元和等效岩体单元的屈服点保持一致,构建节理单元的抗拉强度ft、初始粘聚力c0和初始内摩擦力的计算公式。S42 Calculate the tensile strength and shear strength of the joint unit: According to the homogenization theory, the yield point of the joint unit and the equivalent rock mass unit should be consistent, and the tensile strength f t , initial cohesion c 0 and initial internal friction of the joint unit should be constructed calculation formula.

作为进一步优选的,所述节理单元的法向刚度KN和切向刚度KS的计算公式如下:As a further preference, the calculation formulas of the normal stiffness K N and the tangential stiffness K S of the joint element are as follows:

式中,h为等效岩体单元的厚度,Er和vr分别为完整岩石的弹性模量和泊松比,Em和vm分别为工程岩体的弹性模量和泊松比;In the formula, h is the thickness of the equivalent rock mass unit, E r and v r are the elastic modulus and Poisson's ratio of the intact rock, respectively, E m and v m are the elastic modulus and Poisson's ratio of the engineered rock mass, respectively;

作为进一步优选的,所述节理单元的抗拉强度ft、初始粘聚力c0和初始内摩擦力的计算公式分别为:As a further preference, the tensile strength f t , initial cohesion c 0 and initial internal friction of the joint unit The calculation formulas are respectively:

ft=ft m f t =f t m

式中,ft m、cm和/>分别为等效岩体单元的抗拉强度、粘聚力和内摩擦角,/>为等效岩体在初始屈服点的剪应变。In the formula, f t m , c m and /> are the tensile strength, cohesion and internal friction angle of the equivalent rock mass unit, respectively, /> is the shear strain of the equivalent rock mass at the initial yield point.

作为进一步优选的,步骤S4中,所述计算等效岩体极限应变包括:根据极限应变理论,采用数值极限分析方法求解和/> As a further preference, in step S4, the calculation of the equivalent rock mass ultimate strain includes: according to the ultimate strain theory, using the numerical limit analysis method to solve and />

式中,为等效岩体单元在单向受压条件下的侧向应变,cm为等效岩体单元的粘聚力,/>为等效岩体单元的内摩擦角,Em和vm分别为等效岩体的弹性模量和泊松比。In the formula, is the lateral strain of the equivalent rock mass unit under unidirectional compression, cm is the cohesion of the equivalent rock mass unit, /> is the internal friction angle of the equivalent rock mass unit, and E m and v m are the elastic modulus and Poisson's ratio of the equivalent rock mass, respectively.

作为进一步优选的,步骤S5中,根据节理单元应力-应变曲线计算节理单元的I型断裂能GI和II型断裂能GIIAs a further preference, in step S5, the type I fracture energy G I and type II fracture energy G II of the joint unit are calculated according to the stress-strain curve of the joint unit:

式中,fs和fs'分别为节理单元的初始抗剪强度和残余抗剪强度;Δε和Δγ分别为节理单元从初始屈服点至破坏点的法向累积应变和切向累积应变。In the formula, f s and f s ' are the initial shear strength and residual shear strength of the joint element, respectively; Δε and Δγ are the normal cumulative strain and tangential cumulative strain of the joint element from the initial yield point to the failure point, respectively.

作为进一步优选的,还包括:基于有限-离散元耦合软件/程序,对单轴压缩和巴西劈裂试验进行数值模拟,验证所述节理单元力学参数取值的适用性和合理性。As a further preference, it also includes: based on the finite-discrete element coupling software/program, numerical simulation of uniaxial compression and Brazilian splitting tests is performed to verify the applicability and rationality of the mechanical parameters of the joint unit.

按照本发明的另一个方面,还提供了一种岩体节理单元力学参数的取值系统,用于实现上述的方法。According to another aspect of the present invention, a system for obtaining values of mechanical parameters of rock mass joint units is also provided for realizing the above-mentioned method.

总体而言,通过本发明所构思的以上技术方案与现有技术相比,主要具备以下的技术优点:Generally speaking, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:

1.本发明基于等效连续模型的思想,把工程岩体中的结构面处理成具有一定厚度的软弱夹层,将等效岩体单元划分为弹性的岩石单元和弹塑性的节理单元,使得各项异性的等效岩体单元可分为两个互相作用的各项同性单元。所建立的等效岩体模型既考虑了节理对岩体力学性能的影响,又在宏观上可视为连续体,从而克服传统方法在模拟一般节理裂隙岩体时建模困难和计算效率低下的问题。1. The present invention is based on the idea of the equivalent continuous model, processes the structural plane in the engineering rock mass into a weak interlayer with a certain thickness, and divides the equivalent rock mass unit into an elastic rock unit and an elastic-plastic joint unit, so that the anisotropic equivalent rock mass unit can be divided into two interacting isotropic units. The established equivalent rock mass model not only considers the influence of joints on the mechanical properties of rock mass, but also can be regarded as a continuum macroscopically, so as to overcome the problems of modeling difficulties and low calculation efficiency of traditional methods in simulating general jointed and fractured rock mass.

2.本发明考虑节理对岩体力学性能的影响,采用Mohr-Coulomb准则和相关联的流动法则来描述节理单元的弹塑性变形,并基于均匀化理论和极限应变理论,通过对整个节理岩体单元综合分析,推导了节理单元力学参数的计算公式。推导过程综合考虑了室内力学试验和岩体质量分级,从而克服传统方法直接采用室内力学试验结果的不准确性,能更精准地反映节理岩体的宏观力学行为。2. The present invention considers the influence of joints on the rock mass mechanical properties, adopts the Mohr-Coulomb criterion and the associated flow law to describe the elastoplastic deformation of the joint unit, and based on the homogenization theory and the limit strain theory, through the comprehensive analysis of the whole joint rock mass unit, deduces the calculation formula of the joint unit mechanical parameters. The derivation process comprehensively considered the indoor mechanical test and rock mass quality classification, so as to overcome the inaccuracy of the traditional method of directly using the indoor mechanical test results, and can more accurately reflect the macroscopic mechanical behavior of the jointed rock mass.

3.本发明推导的节理单元力学参数取值公式中的计算参数物理意义明确,均可通过岩石力学试验结果和岩体质量分级标准获得,取值结果可通过有限-离散元耦合软件/程序验证,方法简单便捷、实用性强、易于推广,是一种既能满足工程计算精度,又便于直接应用室内试验测试数据的节理岩体等效参数分析方法。3. The calculation parameters in the joint element mechanical parameter value formula derived by the present invention have clear physical meanings, and can be obtained through rock mechanics test results and rock mass quality classification standards. The value results can be verified by finite-discrete element coupling software/programs. The method is simple and convenient, has strong practicability, and is easy to popularize. It is a joint rock mass equivalent parameter analysis method that can not only meet engineering calculation accuracy, but also facilitate direct application of laboratory test test data.

附图说明Description of drawings

图1是本发明实施例涉及的一种岩体节理单元力学参数的取值方法的流程图;Fig. 1 is a flow chart of a method for obtaining values of mechanical parameters of a rock mass joint unit related to an embodiment of the present invention;

图2中的(a)为室内单轴压缩试验示意图,图2中的(b)为室内巴西劈裂试验示意图;(a) in Fig. 2 is a schematic diagram of an indoor uniaxial compression test, and (b) in Fig. 2 is a schematic diagram of an indoor Brazilian splitting test;

图3中的(a)为本发明方法涉及的节理单元粘聚力参数随κ的变化趋势图,图3中的(b)为本发明方法涉及的节理单元内摩擦角参数随κ的变化趋势图;(a) in Fig. 3 is the variation trend diagram of the cohesion parameter of the joint unit involved in the method of the present invention with κ, and (b) in Fig. 3 is the variation trend diagram of the joint unit internal friction angle parameter involved in the method of the present invention with κ;

图4中的(a)为节理单元法向应力-应变曲线图,图4中的(b)为节理单元切向应力-应变曲线图;(a) in Fig. 4 is the normal stress-strain curve of the joint unit, and (b) in Fig. 4 is the tangential stress-strain curve of the joint unit;

图5中的(a)为本发明涉及的FDEM-单轴压缩数值仿真模型图,图5中的(b)为本发明涉及的FDEM-巴西劈裂数值仿真模型图;(a) in Fig. 5 is the FDEM-uniaxial compression numerical simulation model figure involved in the present invention, and (b) in Fig. 5 is the FDEM-Brazil splitting numerical simulation model figure involved in the present invention;

图6中的(a)为本发明涉及的单轴压缩数值仿真的有限-离散元应力-应变曲线图,图6中的(b)为本发明涉及的巴西劈裂数值仿真的有限元应力-应变曲线。(a) in Fig. 6 is the finite-discrete element stress-strain curve of numerical simulation of uniaxial compression involved in the present invention, and (b) in Fig. 6 is the finite element stress-strain curve of numerical simulation of Brazilian splitting involved in the present invention.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本发明进行进一步详细说明。应当理解,此处所描述的具体实施例仅用以解释本发明,并不用于限定本发明。此外,下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not constitute a conflict with each other.

如图1所示,本发明实施例提供的一种岩体节理单元力学参数的取值方法,包含以下步骤:As shown in Figure 1, a method for obtaining the mechanical parameters of a rock mass joint unit provided by an embodiment of the present invention includes the following steps:

步骤1、基于室内岩石基本力学试验,获取完整岩石的宏观力学参数。即基于室内岩石基本力学试验,获取完整岩石的宏观力学参数。具体的,在所述步骤1中,岩石力学试验包括单轴压缩和巴西劈裂试验,如图2所示。根据岩石单轴压缩试验获取完整岩石的弹性模量Er和泊松比vr;根据岩石巴西劈裂试验获取完整岩石的抗拉强度ft r。本发明中,单轴压缩和巴西劈裂试验均属于现有技术,常规的单轴压缩和巴西劈裂试验即可满足获取本发明岩石参数的要求。其具体结构和方法,本发明中不再赘述。Step 1. Obtain the macro-mechanical parameters of the complete rock based on the basic indoor rock mechanics test. That is, the macroscopic mechanical parameters of the complete rock are obtained based on the basic mechanical tests of the rock in the laboratory. Specifically, in the step 1, the rock mechanics test includes uniaxial compression and Brazilian splitting test, as shown in FIG. 2 . The elastic modulus E r and Poisson's ratio v r of the intact rock are obtained from the rock uniaxial compression test; the tensile strength f t r of the intact rock is obtained from the Brazilian splitting test of the rock. In the present invention, both uniaxial compression and Brazilian splitting tests belong to the prior art, and conventional uniaxial compression and Brazilian splitting tests can meet the requirements for obtaining rock parameters of the present invention. Its specific structure and method will not be repeated in the present invention.

步骤2、基于岩体质量分级标准划分岩体等级,获取工程岩体的宏观力学参数。即:根据岩体质量分级标准对工程岩体进行岩体等级划分,获取等效岩体力学参数。具体的,岩体质量等级划分标准包括国标BQ、GSI和RQD指标等。根据岩体质量分级标准,对工程中岩体进行等级划分,获取工程岩体的弹性模量Em、泊松比vm、粘聚力cm、内摩擦角和抗拉强度ft mStep 2. Classify the rock mass based on the rock mass quality classification standard, and obtain the macroscopic mechanical parameters of the engineering rock mass. That is: according to the rock mass quality classification standard, the engineering rock mass is graded to obtain the equivalent rock mass mechanical parameters. Specifically, the rock mass quality classification standards include the national standard BQ, GSI and RQD indicators. According to the rock mass quality classification standard, classify the rock mass in the project, and obtain the elastic modulus E m , Poisson's ratio v m , cohesion c m , and internal friction angle of the engineering rock mass and tensile strength f t m .

步骤3、基于Mohr-Coulomb准则和关联流动法则,推导节理单元的弹塑性刚度矩阵。具体的,可按如下步骤求解节理单元的弹塑性刚度矩阵:Step 3. Based on the Mohr-Coulomb criterion and the associated flow rule, the elastic-plastic stiffness matrix of the joint element is derived. Specifically, the elastic-plastic stiffness matrix of the joint element can be solved according to the following steps:

步骤3.1、构建屈服函数f和第一材料参数m(κ)与第二材料参数σc(κ)表达式:选择Mohr-Coulomb准则作为节理单元的屈服准则,则屈服函数f(σ13,κ)可以表示为:Step 3.1. Construct the expressions of the yield function f and the first material parameter m(κ) and the second material parameter σ c (κ): choose the Mohr-Coulomb criterion as the yield criterion of the joint element, then the yield function f(σ 13 ,κ) can be expressed as:

f(σ13,κ)=m(κ)σ13c(κ)=0 (1)f(σ 13 ,κ)=m(κ)σ 13c (κ)=0 (1)

其中,σ1和σ3分别是材料的最大主应力和最小主应力;内变量κ表征材料的硬化程度,它决定了硬化/软化材料的屈服面将如何变化,其取值通常与塑性应变有关;第一材料参数m(κ)是表征压缩强度与表征拉伸强度之比;第二材料参数σc(κ)表征无侧限的压缩强度。第一材料参数m(κ)和第二材料参数σc(κ)以及内变量κ的表达式为:Among them, σ 1 and σ 3 are the maximum principal stress and minimum principal stress of the material, respectively; the internal variable κ represents the hardening degree of the material, which determines how the yield surface of the hardened/softened material will change, and its value is usually related to the plastic strain; the first material parameter m(κ) is the ratio of the characteristic compressive strength to the characteristic tensile strength; the second material parameter σ c (κ) represents the unconfined compressive strength. The expressions of the first material parameter m(κ), the second material parameter σ c (κ) and the internal variable κ are:

其中,c(κ)和分别是节理岩体的粘聚力和内摩擦角,在弹塑性阶段为内变量κ的线型函数,即随着内变量κ增大而降低,但降低的程度不同,如图3所示。c0和/>分别是节理单元的初始粘聚力和初始内摩擦角,/>和κr分别是单元完全破坏时的内摩擦角和内变量;和dεp分别是等效塑性应变和塑性应变增量。Among them, c(κ) and are the cohesion and internal friction angle of the jointed rock mass, respectively, and are linear functions of the internal variable κ in the elastic-plastic stage, that is, they decrease with the increase of the internal variable κ, but the degree of decrease is different, as shown in Figure 3. c 0 and /> are the initial cohesion and initial internal friction angle of the joint unit, respectively, /> and κ r are the internal friction angle and internal variable when the element is completely destroyed, respectively; and dε p are the equivalent plastic strain and plastic strain increment, respectively.

步骤3.2、构建节理单元的刚度矩阵K:塑性变形采用与屈服面相关联的流动法则,则节理单元的弹塑性刚度矩阵[Kep]的表达式为:Step 3.2, constructing the stiffness matrix K of the joint element: the plastic deformation adopts the flow law associated with the yield surface, then the expression of the elastoplastic stiffness matrix [K ep ] of the joint element is:

其中,[Ke]为节理单元的弹性刚度矩阵,KN和KS是节理单元的法向刚度和切向刚度系数;R为硬化模量,在屈服点时,R为0;σ为节理单元应力的矢量表示。Among them, [K e ] is the elastic stiffness matrix of the joint element, K N and K S are the normal stiffness and tangential stiffness coefficients of the joint element; R is the hardening modulus, and at the yield point, R is 0; σ is the vector representation of the stress of the joint element.

步骤4、基于均匀化理论和极限应变理论,计算节理单元力学参数。其中,本发明中,均匀化理论是运用均匀化准则以及应力平衡和运动约束条件,将具备两种不同力学性能的单元组合成一种新的单元。根据均匀化理论,节理和岩石之间的相对位移发生在节理单元内部,两交界面保持完全粘结。均匀化理论要求,节理单元和等效岩体单元的屈服点保持一致,即在节理单元达到屈服应变时,该时刻节理单元和岩体单元的应力状态均满足屈服函数。极限应变理论是将单向受力下的极限应变作为单向受力下的岩土类材料的破坏的判据。极限应变理论认为,当材料刚达到屈服时为初始屈服,具有弹性极限应变,随着塑性的发展,材料发生破坏,此时应变达到极限应变。本发明的等效岩体单元和节理单元采用弹塑性本构,因此,利用极限应变理论来计算岩体单元和节理单元的极限应变是可行的。Step 4. Calculate the mechanical parameters of the joint element based on the homogenization theory and the ultimate strain theory. Among them, in the present invention, the homogenization theory is to combine the units with two different mechanical properties into a new unit by using the homogenization criterion, stress balance and motion constraint conditions. According to the homogenization theory, the relative displacement between the joint and the rock occurs inside the joint unit, and the two interfaces remain completely bonded. The homogenization theory requires that the yield point of the joint unit and the equivalent rock mass unit be consistent, that is, when the joint unit reaches the yield strain, the stress state of the joint unit and the rock mass unit at this moment both satisfy the yield function. The ultimate strain theory takes the ultimate strain under unidirectional stress as the criterion for the failure of rock and soil materials under unidirectional stress. The ultimate strain theory believes that when the material just reaches yield, it is the initial yield and has an elastic limit strain. With the development of plasticity, the material is destroyed, and the strain reaches the ultimate strain at this time. The equivalent rock mass unit and the joint unit of the present invention adopt elastic-plastic constitutive structure, therefore, it is feasible to calculate the ultimate strain of the rock mass unit and the joint unit by using the ultimate strain theory.

在所述步骤4中,岩石单元采用弹性本构,岩体单元采用理想弹塑性本构,可按如下步骤计算节理单元的力学参数:In the step 4, the rock element adopts the elastic constitutive structure, and the rock mass element adopts the ideal elastic-plastic constitutive structure, and the mechanical parameters of the joint element can be calculated according to the following steps:

步骤4.1、求解节理单元刚度:根据连续介质的刚度等效原则,节理单元的法向刚度KN和切向刚度KS计算公式如下:Step 4.1. Solve the stiffness of the joint element: According to the equivalent principle of stiffness of the continuum, the calculation formulas of the normal stiffness K N and the tangential stiffness K S of the joint element are as follows:

式中:In the formula:

其中,h为等效岩体单元的厚度;Er和vr分别为完整岩石的弹性模量和泊松比,取值根据室内单轴压缩试验应力应变曲线的初始直线段;Em和vm分别为等效岩体的弹性模量和泊松比,取值依据岩体质量分级标准。Among them, h is the thickness of the equivalent rock mass unit; E r and v r are the elastic modulus and Poisson's ratio of the intact rock, respectively, and their values are based on the initial straight line section of the stress-strain curve of the indoor uniaxial compression test; E m and v m are the elastic modulus and Poisson's ratio of the equivalent rock mass, respectively, and their values are based on the rock mass quality classification standard.

步骤4.2、求解节理单元抗拉强度和抗剪强度:根据均匀化理论要求,节理单元和等效岩体单元的屈服点保持一致,则节理单元的抗拉强度ft、初始粘聚力c0和初始内摩擦力的计算公式为:Step 4.2, Solve the tensile strength and shear strength of the joint unit: according to the homogenization theory, the yield point of the joint unit and the equivalent rock mass unit are consistent, then the tensile strength f t , initial cohesion c 0 and initial internal friction of the joint unit The calculation formula is:

ft=ft m (16)f t = f t m (16)

式中:In the formula:

其中,ft m、cm分别为等效岩体单元的抗拉强度、粘聚力和内摩擦角,取值根据岩体质量分级标准;/>为等效岩体在初始屈服点的剪应变,具体取值详见步骤4.3。Among them, f t m , c m and are the tensile strength, cohesion and internal friction angle of the equivalent rock mass unit respectively, and the values are taken according to the rock mass quality classification standard;/> is the shear strain of the equivalent rock mass at the initial yield point, see step 4.3 for the specific value.

步骤4.3、求解节理单元的断裂能:图4为节理单元应力-应变曲线,曲线屈服后阶段所围面积为单元的断裂能,则节理单元的I型断裂能GI和II型断裂能GII的计算公式为:Step 4.3, solving the fracture energy of the joint unit: Fig. 4 is the stress-strain curve of the joint unit, and the area enclosed by the stage after the curve yields is the fracture energy of the unit, then the calculation formulas of the type I fracture energy G I and the type II fracture energy G II of the joint unit are:

其中,fs和fs'分别为节理单元的初始抗剪强度和残余抗剪强度;Δε和Δγ分别为节理单元从初始屈服点至破坏点的法向累积应变和切向累积应变。Δε和Δγ的计算公式如下:Among them, f s and f s ' are the initial shear strength and residual shear strength of the joint element, respectively; Δε and Δγ are the normal cumulative strain and tangential cumulative strain of the joint element from the initial yield point to the failure point, respectively. The calculation formulas of Δε and Δγ are as follows:

其中,t为节理单元的厚度;和/>为等效岩体单元拉伸破坏时初始屈服点和完全破坏点处的拉应变;/>和/>为等效岩体单元剪切破坏时初始屈服点和完全破坏点处的剪应变。根据极限应变理论,/>和/>可采用数值极限分析方法求解,它们的关系式如下:Among them, t is the thickness of the joint element; and /> is the tensile strain at the initial yield point and the complete failure point of the equivalent rock mass unit; /> and /> is the shear strain at the initial yield point and the complete failure point when the equivalent rock mass unit is sheared. According to the ultimate strain theory, /> and /> It can be solved by numerical limit analysis method, and their relational expressions are as follows:

其中,为等效岩体单元在单向受压条件下的侧向应变。in, is the lateral strain of the equivalent rock mass unit under unidirectional compression.

步骤5、基于有限-离散元耦合软件,对单轴压缩和巴西劈裂试验进行数值模拟,验证本发明节理单元力学参数取值方法的适用性和合理性。在所述步骤5中,通过有限-离散元软件,将上述步骤1的完整岩石力学参数作为实体单元的输入参数,将上述步骤3~4计算所得的节理的力学参数作为节理单元的输入参数,进行单轴压缩和巴西劈裂的数值模拟。数值模型如图5中的(a)(b)所示,模型应力-应变曲线结果如图6中的(a)和(b)。通过对比有限-离散元模拟结果和工程岩体质量分级结果,验证本发明提出的一种岩体节理单元力学参数取值方法的适用性和合理性。Step 5. Based on the finite element-discrete element coupling software, perform numerical simulation on the uniaxial compression and Brazilian splitting tests, and verify the applicability and rationality of the method for obtaining the mechanical parameters of the joint element of the present invention. In the step 5, using the finite-discrete element software, the complete rock mechanical parameters in the above step 1 are used as the input parameters of the solid element, and the mechanical parameters of the joints calculated in the above steps 3 to 4 are used as the input parameters of the joint element, and numerical simulations of uniaxial compression and Brazilian splitting are performed. The numerical model is shown in (a) (b) in Fig. 5, and the stress-strain curve results of the model are shown in (a) and (b) in Fig. 6. By comparing the finite-discrete element simulation results with the quality classification results of engineering rock mass, the applicability and rationality of a method for obtaining mechanical parameters of rock mass joint units proposed by the present invention are verified.

本领域的技术人员容易理解,以上所述仅为本发明的较佳实施例而已,并不用以限制本发明,凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等,均应包含在本发明的保护范围之内。It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims (10)

1. The method for evaluating the mechanical parameters of the rock mass joint unit is characterized by comprising the following steps of:
s1, acquiring macroscopic mechanical parameters of the complete rock based on an indoor rock basic mechanical test;
s2, classifying the rock mass of the engineering rock mass according to the rock mass quality classification standard to obtain equivalent rock mass mechanical parameters;
s3, deducing an elastic-plastic rigidity matrix of the joint unit according to Mohr-Coulomb criterion and associated flow rule;
s4, substituting the mechanical parameters of the complete rock, the mechanical parameters of the equivalent rock and the elastic-plastic rigidity matrix of the joint unit to calculate the strength parameters of the joint unit according to the homogenization theory, and simultaneously, calculating the limit strain of the equivalent rock based on the limit strain theory and the mechanical parameters of the equivalent rock;
s5, calculating the fracture energy of the joint unit according to the ultimate strain of the equivalent rock mass and the strength parameter of the joint unit, and determining the mechanical parameter of the joint unit according to the fracture energy.
2. The method for evaluating mechanical parameters of a rock mass joint unit according to claim 1, wherein in step S1, the indoor rock basic mechanical test comprises a rock uniaxial compression test and a rock brazil split test, and the elastic modulus Er and poisson ratio v of the whole rock are obtained according to the rock uniaxial compression test r The method comprises the steps of carrying out a first treatment on the surface of the Obtaining the tensile strength f of the complete rock according to the Brazilian rock splitting test t r
3. The method for evaluating mechanical parameters of a rock mass joint unit according to claim 1, wherein in step S2, the equivalent rock mass mechanical parameters include an elastic modulus E m Poisson ratio v m Cohesive force c m Angle of internal frictionAnd tensile strength f t m
4. The method for evaluating mechanical parameters of a rock mass joint unit according to claim 1, wherein the step S3 comprises the steps of:
s31 building a yield function f and a first material parameter m (kappa) and a second material parameter sigma c (kappa) expression, selecting Mohr-Coulomb criterion as yield criterion of the joint unit, constructing yield function:
f(σ 13 ,κ)=m(κ)σ 13c (κ)=0
in sigma 1 Sum sigma 3 The maximum principal stress and the minimum principal stress of the material are respectively, and the internal variable kappa represents the hardening degree of the material;
s32, constructing an elastoplastic stiffness matrix of the joint unit, wherein the elastoplastic stiffness matrix [ K ] of the joint unit is constructed by adopting a flow rule associated with a yielding surface through plastic deformation ep ]The calculation model of (2) is as follows:
in [ K ] e ]The elastic stiffness matrix of the joint unit is represented by R, R and sigma, wherein R is the hardening modulus, and sigma is the vector representation of the stress of the joint unit.
5. The method for evaluating mechanical parameters of a rock mass joint unit according to claim 1, wherein step S4 comprises the steps of:
s41, solving joint unit rigidity: solving the normal rigidity K of the joint unit according to the rigidity equivalent principle of the continuous medium N And tangential stiffness K S
S42, solving the tensile strength and the shear strength of the joint unit: according to the homogenization theory requirement, the yield points of the joint unit and the equivalent rock mass unit are kept consistent, and the tensile strength f of the joint unit is constructed t Initial cohesion c 0 And initial internal friction forceIs a calculation formula of (2).
6. The method for evaluating mechanical parameters of a rock mass joint unit according to claim 5, wherein the normal stiffness K of the joint unit N And tangential stiffness K S The calculation formula of (2) is as follows:
in the method, in the process of the invention,h is the thickness of the equivalent rock mass unit, E r And v r Elastic modulus and poisson ratio of the complete rock, E m And v m The elastic modulus and the poisson ratio of the equivalent rock mass are respectively;
tensile strength f of the joint unit t Initial cohesion c 0 And initial internal friction forceThe calculation formulas of (a) are respectively as follows:
f t =f t m
in the method, in the process of the invention,f t m 、c m and->Tensile strength, cohesion and internal friction angle of equivalent rock mass units, respectively +.>Is the shear strain of the equivalent rock mass at the initial yield point.
7. The method according to claim 1, wherein the mechanical parameter of the rock mass joint unit is a valueThe method is characterized in that in step S4, the calculating the equivalent rock mass limit strain comprises: according to the limit strain theory, solving by adopting a numerical limit analysis methodAnd->
In the method, in the process of the invention,c is the lateral strain of the equivalent rock mass unit under the unidirectional compression condition m As the cohesion of the equivalent rock mass unit,is the internal friction angle of the equivalent rock mass unit E m And v m The elastic modulus and poisson ratio of the equivalent rock mass are respectively.
8. The method for evaluating mechanical parameters of a rock mass joint unit according to claim 1, wherein in step S5, the type I breaking energy G of the joint unit is calculated from the stress-strain curve of the joint unit I And type II break energy G II
Wherein f s And f' s The initial shear strength and the residual shear strength of the joint unit are respectively; delta epsilon and delta gamma are the normal and tangential cumulative strains of the joint unit from the initial yield point to the failure point, respectively.
9. The method for evaluating mechanical parameters of a rock mass joint unit according to any one of claims 1 to 8, further comprising: based on finite-discrete element coupling software, carrying out numerical simulation on uniaxial compression and Brazilian split tests, and verifying the applicability and rationality of the mechanical parameter values of the joint units.
10. A system for the valuing of mechanical parameters of a rock mass joint unit, characterized by implementing the method of any one of claims 1-9.
CN202310338475.0A 2023-03-31 2023-03-31 Method and system for taking value of mechanical parameters of rock mass joint unit Pending CN116465732A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117409870A (en) * 2023-10-18 2024-01-16 中国矿业大学 Mesomechanics prediction method for lateral limit compression deformation of soil-rock mixture
CN118857961A (en) * 2024-08-05 2024-10-29 中南大学 A method for determining equivalent mechanical parameters of jointed and fissured rock mass

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117409870A (en) * 2023-10-18 2024-01-16 中国矿业大学 Mesomechanics prediction method for lateral limit compression deformation of soil-rock mixture
CN117409870B (en) * 2023-10-18 2024-05-24 中国矿业大学 A mesomechanical prediction method for the confined compression deformation of soil-rock mixture
CN118857961A (en) * 2024-08-05 2024-10-29 中南大学 A method for determining equivalent mechanical parameters of jointed and fissured rock mass

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