复杂裂隙岩体等效力学参数及工程应用研究
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摘要
岩体力学参数研究之所以复杂且多年来一直被众多学者关注,在于岩体内部发育了大量不同规模的结构面。一般说来,大多数造岩矿物都可以认为是线性弹性体,但是岩石是多矿物的多晶体,有些晶体发育并不完全。此外,岩石构造中总有这样或那样的缺陷,如晶粒排列不细密,有细微裂隙、孔隙、软弱面等等,这样就使得岩石在荷载作用下的变形特性与造岩矿物有所不同。至于岩体,由于存在各种节理、裂隙、断层等天然结构面,则其变形特性就更加复杂。由于这些结构面的存在,使得岩体宏观力学参数表现出不均匀性、各向异性和尺寸效应等特征。岩体等效力学参数与岩体中发育的结构面的粗糙度、大小、隙宽、产状和分布密度等有关。因而,在研究岩体等效参数之前,首先得分析岩体中结构面的分布规律及其特征。
在岩体工程中,根据结构面发育规模,可将其分为五级,各级结构面对岩体力学性质及稳定性所起的作用不同,本文的研究对象是具有随机分布特征的Ⅳ、Ⅴ级结构面,其中Ⅳ级结构面的发育情况,直接反映了岩体的完整性,控制着岩体的强度,它的发育程度、特性和组合状态等都影响到岩体的工程地质特性和受力后岩体变形、破坏的方式。这类结构面的分布极为复杂,但从统计意义上来说,反映岩体结构面分布特征的几何参数服从一定的概率分布规律。目前工程上通常在野外精测线统计的基础上,运用概率统计学的原理,采用Monte-Carlo模拟技术,借助计算机等处理手段,模拟与实测结构面在统计特征上相同的结构面网络,进而可确定一系列具有普遍意义的岩体力学参数,包括岩体变形参数和强度参数。
岩体的变形主要是岩块、不连续面及充填物三者变形的总和,而后两者的变形起着控制作用。常采用弹性模量、变形模量及泊松比等指标表征岩体的变形特性,实际工程中可通过室内试验与现场试验来研究岩体的变形特性,该方法测得的变形参数仅能反映岩样或测试点周围有限范围内岩体的力学特性,不能代表所测岩体的宏观变形参数。由于试验方法存在局限性,国内外专家学者们提出按经验来估算岩体变形参数。主要估算方法有岩体质量计算法(RMR法、Q法、GSI法和RMi法等)和声波测试法等。近年来,随着分形几何、遗传算法、模糊数学和神经网络等非线性学科的发展,使其在岩体参数估算中得到越来越广泛的应用,位移反分析作为另一种力学参数确定方法也不宜忽视。
人们对岩体强度理论的研究,最早始于18世纪Rankine提出的最大正应力理论。在一百多年的发展过程中,岩体强度理论一直是众多专家、学者研究的重点,并已提出许多有应用价值的强度准则。在岩体强度理论还不完善的今天,经验强度准则占据了重要的位置,尤其是Hoek-Brown强度准则。而相关强度参数的确定则成为国内外研究的前缘课题。在漫长的地质历史条件下,岩石受各种各样的构造作用产生了形态各异、大小不等的多种结构面,当外荷进一步作用时,这些岩石力学性质在一定程度上受这些结构面控制,或者说,岩体的破坏实质上是结构面的相互作用与扩展的过程,因而从岩体破坏机理出发研究岩体强度具有重要的理论和工程意义。工程岩体的破坏通常是由大量非贯通节理和岩桥共同破坏组成的,与贯通节理岩体相比,非贯通节理岩体的受力及破坏特征有很大的变化,表现为原生节理和自节理端部扩展的岩桥断面所组成的复合破坏面。而岩桥的变形、贯通破坏模式和强度特性在很大程度上受非贯通节理面的规模、密度和空间分布特征的控制。
如何根据所测岩石和裂隙的力学参数、岩体节理裂隙分布情况及初始应力条件,评价岩体的力学参数是值得研究的问题。从宏观来看,岩体由岩石和不同结构面组成,相互结合后的岩体的综合强度及变形参数很难确定。然而岩体力学参数是岩土工程稳定性评价和设计最直接、最重要的依据,直接决定计算分析成果,关系到能否充分利用岩体自身承载能力、节省岩体加固和支护的工程量及工程费用,因而准确确定岩体力学参数是岩土工程设计的关键。确定岩体力学参数最常用的是等效连续介质法。等效连续介质法是将岩体近似看作连续介质,依照一定的等效原则进行处理而获取岩体的宏观力学参数,它从本质上来说是一种近似处理的方法。
本文运用岩体力学、弹性力学和断裂力学相结合,数理统计分析和数值分析方法相结合,拱坝与周围地质体相结合的系统研究方法,编制了裂隙岩体三维结构面网络模拟程序,提出了结构面体积频率的计算方法;以应变等效原理为前提,推导了复杂裂隙岩体等效变形参数的计算方法,同时基于断裂力学理论、Griffith强度理论和Mohr-Coulomb强度理论,提出裂隙尖端可能扩展方向的确定方法,进而探析岩桥的破坏机理,分析复杂裂隙岩体等效抗剪强度参数的确定方法。最后以贵州省鱼简河水库拱坝坝肩裂隙岩体为研究对象,分析了坝址区岩体节理发育特征,对岩体的宏观变形参数和综合抗剪强度参数进行了估算,并利用有限元软件ANSYS分析了拱坝的变形和应力场特征。论文完成的主要工作包括以下几个方面:
1、介绍了Kulatilake测窗法和测线法平均迹长的估算方法,提供了结构面几何参数几种常见的概率密度函数随机数生成方法。鱼简河水库坝址区岩体发育的结构面几何参数统计结果分析表明,结构面间距服从负指数分布,倾向服从对数正态或正态分布,倾角服从对数正态、正态或指数分布,迹长服从负指数或对数正态分布,隙宽服从负指数、正态或对数正态分布。接着利用Mircosoft EXCEL 2007提供产生均匀随机数的函数RAND(),编写了常见概率密度函数随机数生成程序,最后根据AtuoCAD软件的Visual LISP语言编制了岩体三维结构面网络模拟可视化程序,并应用于鱼简河水库坝址区岩体。
2、基于结构面网络模拟程序,提出岩体结构面体积频率的计算方法。确定任意组结构面体积频率的基本思路为:给该组结构面体积频率赋一初值,根据该值利用岩体三维结构面网络模拟程序,生成一个岩体结构面网络样本,计算该样本在测线走向上的线频率;然后改变该组结构面体积频率大小,按照上述过程再计算该组结构面在测线走向上的线频率,根据一系列体积频率和与之对应的线频率,建立两者之间的函数关系,然后将该组结构面测线走向上的实测线频率带入该函数,即可确定其体积频率。岩体结构面总的体积频率为各组结构面体积频率的代数和。体积频率的分析结果表明:①结构面线频率λ与体积频率λ_v呈现良好的线性关系,可用形如λ_v=aλ(其中a为常数)的函数表示;②当迹长服从负指数分布时,常数a约为2.5～4.0,而当迹长服从对数正态分布时,常数a约为1.0。
3、提出裂隙岩体等效变形参数的估算方法。将岩体变形视为完整岩块变形和结构面变形两部分变形之和,分别研究完整岩块和结构面变形的计算方法,然后利用“应变等效原理”对所有结构面逐一进行等效,最后得到岩体的等效变形参数。复杂裂隙岩体等效变形参数的计算公式为(4-51)和(4-52)。以贵州省鱼简河水库拱坝工程为例,计算了拱坝坝肩共7个岩组的等效变形参数,并分析了它们的力学尺度效应和不同尺度下的波动性,得到两个结论:①岩体尺寸越大,变形参数波动性越小,即岩体变形参数随尺寸增大逐渐趋于稳定,而且最终不同尺寸下的岩体变形参数稳定性为一固定值;②结构面与岩石变形参数差别越大,岩体变形参数折减程度越大,随着结构面变形参数增大,岩体变形参数对结构面变形参数的敏感度降低,达到某一值后,甚至可以不考虑结构面变形参数的影响。
4、裂纹扩展机理的探讨。通过对前人试验和观点的总结,结合断裂力学理论,推导了单裂隙岩体周围应力场函数的表达式,依据Griffith强度理论确定了裂隙尖端张裂纹的可能扩展方向,即张裂角θ_t,确定张裂角的公式为(5-29)。由该公式可知,若函数G＜0,则等式β(θ_1)=0成立时,θ_t=θ_1,此时张裂纹扩展方向与最大主应力方向一致,若函数G＞0,则等式f(θ_1)=0成立时,θ_t=θ_1,此时张裂纹扩展方向与最大主应力存在一个夹角,夹角大小为β;依据Mohr-Coulomb强度理论确定了裂隙尖端剪裂纹的可能扩展方向,即剪裂角θ_c,剪切裂纹方向与最大主应力方向的夹角为π/4+φ/2(φ为岩石的内摩擦角)。任何情况下,张裂角和剪裂角都满足关系式(5-30)。将此结论推广到非贯通双节理中,归纳了非贯通双节理岩桥的三种破坏模式,即拉破坏、剪切破坏和复合拉剪破坏。
5、提出了含单组随机节理岩体的抗剪强度参数估算方法。假设二维岩体结构面网络模型内发育有一组等倾角的节理,该节理的间距和迹长服从某概率密度函数随机分布规律,岩体破坏时破坏面涉及到的节理的中心点都落在破坏面始末点的连线上。相邻节理之间的岩桥破坏机理可根据上述结论进行判断,同时可计算相应的张裂纹和剪裂纹的倾角和长度。根据Lajtai岩桥破坏理论,可确定各段节理面和岩桥的抗剪力和剪切力,从而可计算破坏路径上总抗剪力和剪切力,两者相等时即为岩体破坏的临界条件,根据上述假设和原理编制了岩体抗剪强度计算程序。根据一系列临界应力条件,按照Mohr-Coulomb强度理论,可确定考虑该组节理岩体的宏观抗剪强度参数。分别预测每一组结构面单独存在时岩体的抗剪强度,取最小抗剪强度作为岩体的综合强度。最后以贵州省鱼简河水库拱坝工程为例,对坝址区岩体抗剪强度进行了预测。
6、以贵州省鱼简河水库拱坝工程为例,建立了该拱坝工程的三维地质模型,利用有限元方法,分析了该拱坝坝体的应力场和变形场的分布特征,由于地层T_(2s)~(3-2)岩体有多层软弱夹层,其变形参数难以准确确定,故分析了该层岩体变形模量在不同工况下对坝体的变形的影响分析。结果表明,坝体在x方向的位移较小,且受变形参数和外部荷载的影响甚微,可以忽略不计,坝体在Y方向的位移受静水压力的影响较大,其次为地层T_(2s)~(3-2)变形参数的影响。
本文的主要创新性成果有:
1、提出了岩体结构面体积频率的一种计算方法。该方法能与岩体结构面网络模拟有机结合。
2、提出了复杂裂隙岩体等效变形参数和含单组随机节理岩体的抗剪强度参数的确定方法。为工程应用提供了可靠的依据。
3、提出了裂隙尖端张裂纹和剪裂纹可能扩展方向的确定方法。依据Griffith强度理论提出了裂隙尖端张裂纹的可能扩展方向,依据M0hr-Coulomb强度理论确定了裂隙尖端剪裂纹的可能扩展方向。
It is because of a lot of different scale discontinuities that many scholars have always been concerned on mechanics parameters of complexity rock mass over the years.Generally most of rock-forming minerals can be considered to be linear elastic body,but rock is a multi-mineral polycrystalline,some crystal doesn't grow entirely.In addition,structure of rock have shortcomings in one way or another,such as not-detailed grain,subtle cracks,porosity,weak surface,etc.and those make the deformation characteristics of rock different from that of minerals in the loading.To rock mass,its deformation characteristics are more complex because there are many natural discontinuities,such as joints,fissures,faults etc.Because of these discontinuities the macro-mechanical parameters of rock mass show asymmetrical,anisotropic and size effect characteristics.Rock equivalent of rock mechanics parameters are concerned with the roughness, size and gap width,the occurrence and distribution density of discontinuities.So rock discontinuities should be analysis firstly.
In geotechnical engineering,discontinuities can be divided into five classes by their growth scale.Each class discontinuities play the different role in mechanical properties and stability rock mass,and the object of this paper is theⅣandⅤ-class structure plane,which obey random distribution.The growth degree ofⅣ-class structure plane reflect directly the integrity of the rock mass and control the rock mass strength,its growth extent,characteristics and composition affect the engineering geological characteristics,deformation and failure mannal of rock mass.The distribution of such discontinuities is extremely complicated,however their geometric parameters is subject to certain probability distribution in statistical.Nowadays fracture network simulation technique is the common method that applies statistical probability theory,a Monte-Carlo and computer to simulate the joint network which has the same statistical characteristics with the measured in the field.Thereby it could be done to establish the Marco mechanics parameters of rock mass,including the deformation and strength parameters.
The deformation of rock mass is composed of that of block,discontinuities and the fillings, the latter two play a controlling role.Elastic modulus of deformation modulus and Poisson's ratio are the indexes that describe the rock deformation.The laboratory test and in-site test are usually used to measure the deformation of rock mass in practise,the parameters only is that of rock sample or rock mass around the test point,but not that of rock mass.Due to the limitation of the test method,experts and scholars at home and aboard have put forward many experience estimation methods.At present the main mechanical parameter estimation methods are rock mass quality method(RMR,Q,GSI and RMi,etc)and sonic testing law.In recent years,with the growth of non-linear disciplines,such as fractal geometry,genetic algorithms,neural networks and fuzzy mathematics,they have be used more and more widely to evulate rock mass deformation parameters,and anti-displacement analysis should not be ignored as another method,too.
The earliest rock mass strength theory is the maximum normal stress theory which Rankine proposed at the 18th century.In the past 100 years,rock mass strength theory always is the study focus,and many strength criteria have been made.However rock mass strength theory is not perfect,which results in the experience strength criterions playing more important role,especially Hoek-Brown strength criterion.So the strength parameters become a leading-edge research issues at home and abroad.In the long geological history,many kinds of discontinuities with different shape and size are produced in rock in tectonism.When the external load increases,the nature of rock mass mechanics is controlled by these discontinuities to a certain extent,or that the failure of rock mass is the interaction and the expansion process of discontinuities in essential.Thus it has a great theoretical and engineering significance that rock strength from rock mass failure mechanism. The failure of rock mass is usually composed by a large number of intermittent joints and rock bridges together,and through jointed rock than through intermittent joint rock mass destruction by force and there are great changes in features.Compared with persistent joints,their stress and failure characteristics have changed,the performance is the composite failure surface formed by the original joints and rock bridges expansed from the end of the joints.To a large extent,the deformation,strength and failure mode of rock bridge are controlled by the size,density and spatial distribution of intermittent joints.
It is an issue worth studying that how to evaluate the mechanical parameters of rock mass according to the rock and fracture mechanical parameters,joints' distribution and initial stress conditions.From a macro point of view,rock mass is made up of rock and different structure planes,so the comprehensive strength and deformation parameters are difficult to make certain. However,rock mechanical parameters is the most direct and important basis of geotechnical engineering evaluation and design,it decides whether or not the result is exactly,whether or not make full use of their own rock bearing capacity,or save the work quantity and cost of reinforced and protected project.Whether it is exactly is the key to geotechnical engineering.The most common method is equivalent continuous medium to determine rock mass deformation parameters. Equivalent continuous media method looks rock mass similarly as continuous media,and then obtains the macro deformation parameters of rock mass in accordance with certain equivalent principles,which in essence,is an approximation method.
This paper applies a systematic study way,which combines rock mass mechanics,elastic mechanics and fracture mechanics,does mathematical analysis and numerical analysis,does arch dam and the surrounding geology bodies.The abutment fractured Rock of Yujianhe reservoir arch dam in Guizhou Province is as an example.The paper discusses firstly the features of rock joints on dam area,then the three-dimensional discontinuity network simulation program of fractured rockmass is edited with Monte-Carlo theory and the calculation method of the volume frequency is proposed according to the line frequency of scan line.Secondly the calculation method of complex fractured rock mass equivalent deformation parameters is derived as the premise of strain equivalent.Next,based on the theory of fracture mechanics,Griffith strength theory and Mohr-Coulomb strength theory,the propagation direction of crack-tip,contains tension crack angle and shear crack angle,is determined,as the above,rock bridge failure mechanism is discussed,and then the complex fractured rock mass equivalent shear strength parameters is introduced.Last,with the equivalent continuous medium and finite element method,the arch dam deformation and stress characteristics of Yujianhe reservoir in Guizhou Province.The main researches are as the followings:
1.The average trace length estimate methods of scan line and Kulatilake sampling window are introduced to measured,the random number generation method of some common probability density function(abbreviated by PDF)is provided.The statistic results about the discontinuities geometric parameters in Yujianhe Reservoir Dam Area show that discontinuities space obey negative exponential distribution,the dip is inclined to obey lognormal or normal distribution,the dip angle is subject to lognormal,normal or exponential distribution,trace length do negative exponential or lognormal distribution,gap width do the negative exponential,normal or lognormal distribution,with the function RAND()provided by Microsoft EXCEL 2007 that can generate uniform random number,random number generator procedures of some common PDFs are compiled,at the same time the three-dimensional discontinuity network simulation program of fractured rockmass is edited.
2.Based on the discontinuity network simulation program,how to ensure the volume frequency of rock mass discontinuity is put forward.Its theory is that given an initialized value to the volume frequency of the joint set,a rock mass sample can be produced with three-dimensional discontinuity network simulation program.Then we can calculate the line frequency of the scan line tend,different line frequency can be obtained by different volume frequency.According to a series volume frequencies and line frequencies correspondent,their relationship function is established.Put the line frequency into the function,we can obtain the actual volume frequency. The total discontinuity volume frequency of rock mass is adding the volume frequency of each set joint.The results show that:①there is a good linear relationship between discontinuity line frequency and volume frequency,namely,the function form is like asλ_v=aλ,where the coefficient a is a constant.②the coefficient is about 2.5～4.0 when trace length obeys negative exponential distribution,while it is approximate 1.0 when the trace length does lognormal distribution.
3.Deformation parameters of fractured rock equivalent.First summarized the test methods and the experience estimation method of rock deformation parameter,and then based on the strain equivalence principle,the formula(4-51)and(4-52)about the equivalent deformation parameter of complex fractured rock mass are derived.Yujianhe reservoir arch dam in Guizhou Province is as an example,with the formulas(4-51),(4-52)and the program of three-dimensional structure plane network simulation,equivalent deformation parameters about 7 kinds of rock mass are all calculated,the scale effect and fluctuation in different scales of equivalent deformation parameter is discussed,the results are,①the bigger rock size is,the smaller the fluctuation of deformation parameter is,namely,the equivalent parameter tend to be stable gradually with the size increasing, and eventually the value is fixed value even though rock mass size is different,②the greater the deformation parameter of structure plane and rock differ,the more equivalent parameters discount, with the structural deformation parameters increased,the sensitivity of equivalent deformation parameter to the structural deformation parameter decreases,even to a certain value,the effect can be ignored.
4.Mechanism of crack propagation.Domestic and foreign scholars have done a great deal of work in mechanism of crack propagation.Based on a summary of previous test and views, combined with the theory of fracture mechanics,the stress field function of single fractured rock mass is derived,and then the tension crack propagation direction in crack tip,which is defined as tensile angle,θ_t,is derived from Griffith strength theory.The tensile angle can be calculated by the formula(5-29).From this formula,we know thatθ_1,which satisfies the equalityβ(θ_1)=0,is the tensile angle if the function G is less than zero,here the direction of tensile crack propagation is accordant with that of the maximum stress.Otherwiseθ_1,which satisfies the equality f(θ_1)=0,is the tensile angle,here there is an angle,β,between the direction of tensile crack propagation and that of the maximum stress.While the shear crack propagation direction,defined with sheared angle,θ_c,could be derived from Mohr-Coulomb strength theory.The angle between the direction of tensile crack propagation and that of the maximum stress isπ/4 +φ/2(whereφis the internal friction angle of intact rock).Promoting to non-penetrative double joint model,three failure modes are induced,namely tension failure,shear failure and tensile-shear damage.
5.Put forward the shear strength parameters estimation method of rock mass with a single set random joint.Supposed there exist single set joint with equal dip angle in two-dimensional rock mass discontinuity network model,its dip angle and trace length obey the random distribution of probability density function.When rock mass is failure,the middle point of the joints,which the failure surface contain,located in the route between the start point and the end point of the failure surface.All rock bridges failure mechanism can be judged by the above content,the angle and the length of each tensile crack or shear crack can be gained.With Lajtai rock bridge failure theory,we can determine the shear resistance and the shear force of every rock bridge and discontinuity,then the total shear resistance and the total shear force can be known,when they are equal,it explains that rock mass is in the critical state.Based on the above assumptions and thought,the estimation procedure of the shear strength is edited.According to a series of critical states of stress and Mohr-Coulomb strength theory,we can ensure the macro shear strength parameters of the jointed rock.Forecast respectively the macro shear strength parameters of the jointed rock when each other group joint is thought alone,and the smallest shear strength is thought as the macro strength of rock mass.Finally,Yujianhe Reservoir arch dam project in Guizhou Province is as an example, the shear strength of rock mass with considered each set joint alone is forecast,and last the smallest shear strength is as that of rock mass.
6.Three-dimensional geological model about Yujianhe Reservoir arch dam project in Guizhou Province is established with continuum medium and finite element method.The deformation and stress of dam are analysis,there are some soft interlayer in T_2s~(3-2),however the REV is big,which leads to determine the equivalent deformation parameter difficult,so this paper analysis the effect of this layer's equivalent deformation parameter to dam's displacement in four conditions.The results show that the dam displacement in the X direction is small,and the deformation parameters and external loads have little effect to the displacement and it can be negligible.To the dam displacement in the Y direction,the impact of hydrostatic pressure in deformation parameters is large than the deformation parameters.
Main results are shows as following:
1.A method to ensure the volume frequency of rock mass discontinuity is put forward.It combines with the discontinuity network simulation.
2.Put forward the shear strength parameters estimation method of rock mass with a single set random joint.It offers reliable source for engineering appliance.
3.Put forword a method to calculate tensile angle and sheared angle.In which tensile angle,θ_t, is derived from Griffith strength theory,while sheared angle,θ_c,is derived from Mohr-Coulomb strength theory.
在岩体工程中,根据结构面发育规模,可将其分为五级,各级结构面对岩体力学性质及稳定性所起的作用不同,本文的研究对象是具有随机分布特征的Ⅳ、Ⅴ级结构面,其中Ⅳ级结构面的发育情况,直接反映了岩体的完整性,控制着岩体的强度,它的发育程度、特性和组合状态等都影响到岩体的工程地质特性和受力后岩体变形、破坏的方式。这类结构面的分布极为复杂,但从统计意义上来说,反映岩体结构面分布特征的几何参数服从一定的概率分布规律。目前工程上通常在野外精测线统计的基础上,运用概率统计学的原理,采用Monte-Carlo模拟技术,借助计算机等处理手段,模拟与实测结构面在统计特征上相同的结构面网络,进而可确定一系列具有普遍意义的岩体力学参数,包括岩体变形参数和强度参数。
岩体的变形主要是岩块、不连续面及充填物三者变形的总和,而后两者的变形起着控制作用。常采用弹性模量、变形模量及泊松比等指标表征岩体的变形特性,实际工程中可通过室内试验与现场试验来研究岩体的变形特性,该方法测得的变形参数仅能反映岩样或测试点周围有限范围内岩体的力学特性,不能代表所测岩体的宏观变形参数。由于试验方法存在局限性,国内外专家学者们提出按经验来估算岩体变形参数。主要估算方法有岩体质量计算法(RMR法、Q法、GSI法和RMi法等)和声波测试法等。近年来,随着分形几何、遗传算法、模糊数学和神经网络等非线性学科的发展,使其在岩体参数估算中得到越来越广泛的应用,位移反分析作为另一种力学参数确定方法也不宜忽视。
人们对岩体强度理论的研究,最早始于18世纪Rankine提出的最大正应力理论。在一百多年的发展过程中,岩体强度理论一直是众多专家、学者研究的重点,并已提出许多有应用价值的强度准则。在岩体强度理论还不完善的今天,经验强度准则占据了重要的位置,尤其是Hoek-Brown强度准则。而相关强度参数的确定则成为国内外研究的前缘课题。在漫长的地质历史条件下,岩石受各种各样的构造作用产生了形态各异、大小不等的多种结构面,当外荷进一步作用时,这些岩石力学性质在一定程度上受这些结构面控制,或者说,岩体的破坏实质上是结构面的相互作用与扩展的过程,因而从岩体破坏机理出发研究岩体强度具有重要的理论和工程意义。工程岩体的破坏通常是由大量非贯通节理和岩桥共同破坏组成的,与贯通节理岩体相比,非贯通节理岩体的受力及破坏特征有很大的变化,表现为原生节理和自节理端部扩展的岩桥断面所组成的复合破坏面。而岩桥的变形、贯通破坏模式和强度特性在很大程度上受非贯通节理面的规模、密度和空间分布特征的控制。
如何根据所测岩石和裂隙的力学参数、岩体节理裂隙分布情况及初始应力条件,评价岩体的力学参数是值得研究的问题。从宏观来看,岩体由岩石和不同结构面组成,相互结合后的岩体的综合强度及变形参数很难确定。然而岩体力学参数是岩土工程稳定性评价和设计最直接、最重要的依据,直接决定计算分析成果,关系到能否充分利用岩体自身承载能力、节省岩体加固和支护的工程量及工程费用,因而准确确定岩体力学参数是岩土工程设计的关键。确定岩体力学参数最常用的是等效连续介质法。等效连续介质法是将岩体近似看作连续介质,依照一定的等效原则进行处理而获取岩体的宏观力学参数,它从本质上来说是一种近似处理的方法。
本文运用岩体力学、弹性力学和断裂力学相结合,数理统计分析和数值分析方法相结合,拱坝与周围地质体相结合的系统研究方法,编制了裂隙岩体三维结构面网络模拟程序,提出了结构面体积频率的计算方法;以应变等效原理为前提,推导了复杂裂隙岩体等效变形参数的计算方法,同时基于断裂力学理论、Griffith强度理论和Mohr-Coulomb强度理论,提出裂隙尖端可能扩展方向的确定方法,进而探析岩桥的破坏机理,分析复杂裂隙岩体等效抗剪强度参数的确定方法。最后以贵州省鱼简河水库拱坝坝肩裂隙岩体为研究对象,分析了坝址区岩体节理发育特征,对岩体的宏观变形参数和综合抗剪强度参数进行了估算,并利用有限元软件ANSYS分析了拱坝的变形和应力场特征。论文完成的主要工作包括以下几个方面:
1、介绍了Kulatilake测窗法和测线法平均迹长的估算方法,提供了结构面几何参数几种常见的概率密度函数随机数生成方法。鱼简河水库坝址区岩体发育的结构面几何参数统计结果分析表明,结构面间距服从负指数分布,倾向服从对数正态或正态分布,倾角服从对数正态、正态或指数分布,迹长服从负指数或对数正态分布,隙宽服从负指数、正态或对数正态分布。接着利用Mircosoft EXCEL 2007提供产生均匀随机数的函数RAND(),编写了常见概率密度函数随机数生成程序,最后根据AtuoCAD软件的Visual LISP语言编制了岩体三维结构面网络模拟可视化程序,并应用于鱼简河水库坝址区岩体。
2、基于结构面网络模拟程序,提出岩体结构面体积频率的计算方法。确定任意组结构面体积频率的基本思路为:给该组结构面体积频率赋一初值,根据该值利用岩体三维结构面网络模拟程序,生成一个岩体结构面网络样本,计算该样本在测线走向上的线频率;然后改变该组结构面体积频率大小,按照上述过程再计算该组结构面在测线走向上的线频率,根据一系列体积频率和与之对应的线频率,建立两者之间的函数关系,然后将该组结构面测线走向上的实测线频率带入该函数,即可确定其体积频率。岩体结构面总的体积频率为各组结构面体积频率的代数和。体积频率的分析结果表明:①结构面线频率λ与体积频率λ_v呈现良好的线性关系,可用形如λ_v=aλ(其中a为常数)的函数表示;②当迹长服从负指数分布时,常数a约为2.5～4.0,而当迹长服从对数正态分布时,常数a约为1.0。
3、提出裂隙岩体等效变形参数的估算方法。将岩体变形视为完整岩块变形和结构面变形两部分变形之和,分别研究完整岩块和结构面变形的计算方法,然后利用“应变等效原理”对所有结构面逐一进行等效,最后得到岩体的等效变形参数。复杂裂隙岩体等效变形参数的计算公式为(4-51)和(4-52)。以贵州省鱼简河水库拱坝工程为例,计算了拱坝坝肩共7个岩组的等效变形参数,并分析了它们的力学尺度效应和不同尺度下的波动性,得到两个结论:①岩体尺寸越大,变形参数波动性越小,即岩体变形参数随尺寸增大逐渐趋于稳定,而且最终不同尺寸下的岩体变形参数稳定性为一固定值;②结构面与岩石变形参数差别越大,岩体变形参数折减程度越大,随着结构面变形参数增大,岩体变形参数对结构面变形参数的敏感度降低,达到某一值后,甚至可以不考虑结构面变形参数的影响。
4、裂纹扩展机理的探讨。通过对前人试验和观点的总结,结合断裂力学理论,推导了单裂隙岩体周围应力场函数的表达式,依据Griffith强度理论确定了裂隙尖端张裂纹的可能扩展方向,即张裂角θ_t,确定张裂角的公式为(5-29)。由该公式可知,若函数G＜0,则等式β(θ_1)=0成立时,θ_t=θ_1,此时张裂纹扩展方向与最大主应力方向一致,若函数G＞0,则等式f(θ_1)=0成立时,θ_t=θ_1,此时张裂纹扩展方向与最大主应力存在一个夹角,夹角大小为β;依据Mohr-Coulomb强度理论确定了裂隙尖端剪裂纹的可能扩展方向,即剪裂角θ_c,剪切裂纹方向与最大主应力方向的夹角为π/4+φ/2(φ为岩石的内摩擦角)。任何情况下,张裂角和剪裂角都满足关系式(5-30)。将此结论推广到非贯通双节理中,归纳了非贯通双节理岩桥的三种破坏模式,即拉破坏、剪切破坏和复合拉剪破坏。
5、提出了含单组随机节理岩体的抗剪强度参数估算方法。假设二维岩体结构面网络模型内发育有一组等倾角的节理,该节理的间距和迹长服从某概率密度函数随机分布规律,岩体破坏时破坏面涉及到的节理的中心点都落在破坏面始末点的连线上。相邻节理之间的岩桥破坏机理可根据上述结论进行判断,同时可计算相应的张裂纹和剪裂纹的倾角和长度。根据Lajtai岩桥破坏理论,可确定各段节理面和岩桥的抗剪力和剪切力,从而可计算破坏路径上总抗剪力和剪切力,两者相等时即为岩体破坏的临界条件,根据上述假设和原理编制了岩体抗剪强度计算程序。根据一系列临界应力条件,按照Mohr-Coulomb强度理论,可确定考虑该组节理岩体的宏观抗剪强度参数。分别预测每一组结构面单独存在时岩体的抗剪强度,取最小抗剪强度作为岩体的综合强度。最后以贵州省鱼简河水库拱坝工程为例,对坝址区岩体抗剪强度进行了预测。
6、以贵州省鱼简河水库拱坝工程为例,建立了该拱坝工程的三维地质模型,利用有限元方法,分析了该拱坝坝体的应力场和变形场的分布特征,由于地层T_(2s)~(3-2)岩体有多层软弱夹层,其变形参数难以准确确定,故分析了该层岩体变形模量在不同工况下对坝体的变形的影响分析。结果表明,坝体在x方向的位移较小,且受变形参数和外部荷载的影响甚微,可以忽略不计,坝体在Y方向的位移受静水压力的影响较大,其次为地层T_(2s)~(3-2)变形参数的影响。
本文的主要创新性成果有:
1、提出了岩体结构面体积频率的一种计算方法。该方法能与岩体结构面网络模拟有机结合。
2、提出了复杂裂隙岩体等效变形参数和含单组随机节理岩体的抗剪强度参数的确定方法。为工程应用提供了可靠的依据。
3、提出了裂隙尖端张裂纹和剪裂纹可能扩展方向的确定方法。依据Griffith强度理论提出了裂隙尖端张裂纹的可能扩展方向,依据M0hr-Coulomb强度理论确定了裂隙尖端剪裂纹的可能扩展方向。
It is because of a lot of different scale discontinuities that many scholars have always been concerned on mechanics parameters of complexity rock mass over the years.Generally most of rock-forming minerals can be considered to be linear elastic body,but rock is a multi-mineral polycrystalline,some crystal doesn't grow entirely.In addition,structure of rock have shortcomings in one way or another,such as not-detailed grain,subtle cracks,porosity,weak surface,etc.and those make the deformation characteristics of rock different from that of minerals in the loading.To rock mass,its deformation characteristics are more complex because there are many natural discontinuities,such as joints,fissures,faults etc.Because of these discontinuities the macro-mechanical parameters of rock mass show asymmetrical,anisotropic and size effect characteristics.Rock equivalent of rock mechanics parameters are concerned with the roughness, size and gap width,the occurrence and distribution density of discontinuities.So rock discontinuities should be analysis firstly.
In geotechnical engineering,discontinuities can be divided into five classes by their growth scale.Each class discontinuities play the different role in mechanical properties and stability rock mass,and the object of this paper is theⅣandⅤ-class structure plane,which obey random distribution.The growth degree ofⅣ-class structure plane reflect directly the integrity of the rock mass and control the rock mass strength,its growth extent,characteristics and composition affect the engineering geological characteristics,deformation and failure mannal of rock mass.The distribution of such discontinuities is extremely complicated,however their geometric parameters is subject to certain probability distribution in statistical.Nowadays fracture network simulation technique is the common method that applies statistical probability theory,a Monte-Carlo and computer to simulate the joint network which has the same statistical characteristics with the measured in the field.Thereby it could be done to establish the Marco mechanics parameters of rock mass,including the deformation and strength parameters.
The deformation of rock mass is composed of that of block,discontinuities and the fillings, the latter two play a controlling role.Elastic modulus of deformation modulus and Poisson's ratio are the indexes that describe the rock deformation.The laboratory test and in-site test are usually used to measure the deformation of rock mass in practise,the parameters only is that of rock sample or rock mass around the test point,but not that of rock mass.Due to the limitation of the test method,experts and scholars at home and aboard have put forward many experience estimation methods.At present the main mechanical parameter estimation methods are rock mass quality method(RMR,Q,GSI and RMi,etc)and sonic testing law.In recent years,with the growth of non-linear disciplines,such as fractal geometry,genetic algorithms,neural networks and fuzzy mathematics,they have be used more and more widely to evulate rock mass deformation parameters,and anti-displacement analysis should not be ignored as another method,too.
The earliest rock mass strength theory is the maximum normal stress theory which Rankine proposed at the 18th century.In the past 100 years,rock mass strength theory always is the study focus,and many strength criteria have been made.However rock mass strength theory is not perfect,which results in the experience strength criterions playing more important role,especially Hoek-Brown strength criterion.So the strength parameters become a leading-edge research issues at home and abroad.In the long geological history,many kinds of discontinuities with different shape and size are produced in rock in tectonism.When the external load increases,the nature of rock mass mechanics is controlled by these discontinuities to a certain extent,or that the failure of rock mass is the interaction and the expansion process of discontinuities in essential.Thus it has a great theoretical and engineering significance that rock strength from rock mass failure mechanism. The failure of rock mass is usually composed by a large number of intermittent joints and rock bridges together,and through jointed rock than through intermittent joint rock mass destruction by force and there are great changes in features.Compared with persistent joints,their stress and failure characteristics have changed,the performance is the composite failure surface formed by the original joints and rock bridges expansed from the end of the joints.To a large extent,the deformation,strength and failure mode of rock bridge are controlled by the size,density and spatial distribution of intermittent joints.
It is an issue worth studying that how to evaluate the mechanical parameters of rock mass according to the rock and fracture mechanical parameters,joints' distribution and initial stress conditions.From a macro point of view,rock mass is made up of rock and different structure planes,so the comprehensive strength and deformation parameters are difficult to make certain. However,rock mechanical parameters is the most direct and important basis of geotechnical engineering evaluation and design,it decides whether or not the result is exactly,whether or not make full use of their own rock bearing capacity,or save the work quantity and cost of reinforced and protected project.Whether it is exactly is the key to geotechnical engineering.The most common method is equivalent continuous medium to determine rock mass deformation parameters. Equivalent continuous media method looks rock mass similarly as continuous media,and then obtains the macro deformation parameters of rock mass in accordance with certain equivalent principles,which in essence,is an approximation method.
This paper applies a systematic study way,which combines rock mass mechanics,elastic mechanics and fracture mechanics,does mathematical analysis and numerical analysis,does arch dam and the surrounding geology bodies.The abutment fractured Rock of Yujianhe reservoir arch dam in Guizhou Province is as an example.The paper discusses firstly the features of rock joints on dam area,then the three-dimensional discontinuity network simulation program of fractured rockmass is edited with Monte-Carlo theory and the calculation method of the volume frequency is proposed according to the line frequency of scan line.Secondly the calculation method of complex fractured rock mass equivalent deformation parameters is derived as the premise of strain equivalent.Next,based on the theory of fracture mechanics,Griffith strength theory and Mohr-Coulomb strength theory,the propagation direction of crack-tip,contains tension crack angle and shear crack angle,is determined,as the above,rock bridge failure mechanism is discussed,and then the complex fractured rock mass equivalent shear strength parameters is introduced.Last,with the equivalent continuous medium and finite element method,the arch dam deformation and stress characteristics of Yujianhe reservoir in Guizhou Province.The main researches are as the followings:
1.The average trace length estimate methods of scan line and Kulatilake sampling window are introduced to measured,the random number generation method of some common probability density function(abbreviated by PDF)is provided.The statistic results about the discontinuities geometric parameters in Yujianhe Reservoir Dam Area show that discontinuities space obey negative exponential distribution,the dip is inclined to obey lognormal or normal distribution,the dip angle is subject to lognormal,normal or exponential distribution,trace length do negative exponential or lognormal distribution,gap width do the negative exponential,normal or lognormal distribution,with the function RAND()provided by Microsoft EXCEL 2007 that can generate uniform random number,random number generator procedures of some common PDFs are compiled,at the same time the three-dimensional discontinuity network simulation program of fractured rockmass is edited.
2.Based on the discontinuity network simulation program,how to ensure the volume frequency of rock mass discontinuity is put forward.Its theory is that given an initialized value to the volume frequency of the joint set,a rock mass sample can be produced with three-dimensional discontinuity network simulation program.Then we can calculate the line frequency of the scan line tend,different line frequency can be obtained by different volume frequency.According to a series volume frequencies and line frequencies correspondent,their relationship function is established.Put the line frequency into the function,we can obtain the actual volume frequency. The total discontinuity volume frequency of rock mass is adding the volume frequency of each set joint.The results show that:①there is a good linear relationship between discontinuity line frequency and volume frequency,namely,the function form is like asλ_v=aλ,where the coefficient a is a constant.②the coefficient is about 2.5～4.0 when trace length obeys negative exponential distribution,while it is approximate 1.0 when the trace length does lognormal distribution.
3.Deformation parameters of fractured rock equivalent.First summarized the test methods and the experience estimation method of rock deformation parameter,and then based on the strain equivalence principle,the formula(4-51)and(4-52)about the equivalent deformation parameter of complex fractured rock mass are derived.Yujianhe reservoir arch dam in Guizhou Province is as an example,with the formulas(4-51),(4-52)and the program of three-dimensional structure plane network simulation,equivalent deformation parameters about 7 kinds of rock mass are all calculated,the scale effect and fluctuation in different scales of equivalent deformation parameter is discussed,the results are,①the bigger rock size is,the smaller the fluctuation of deformation parameter is,namely,the equivalent parameter tend to be stable gradually with the size increasing, and eventually the value is fixed value even though rock mass size is different,②the greater the deformation parameter of structure plane and rock differ,the more equivalent parameters discount, with the structural deformation parameters increased,the sensitivity of equivalent deformation parameter to the structural deformation parameter decreases,even to a certain value,the effect can be ignored.
4.Mechanism of crack propagation.Domestic and foreign scholars have done a great deal of work in mechanism of crack propagation.Based on a summary of previous test and views, combined with the theory of fracture mechanics,the stress field function of single fractured rock mass is derived,and then the tension crack propagation direction in crack tip,which is defined as tensile angle,θ_t,is derived from Griffith strength theory.The tensile angle can be calculated by the formula(5-29).From this formula,we know thatθ_1,which satisfies the equalityβ(θ_1)=0,is the tensile angle if the function G is less than zero,here the direction of tensile crack propagation is accordant with that of the maximum stress.Otherwiseθ_1,which satisfies the equality f(θ_1)=0,is the tensile angle,here there is an angle,β,between the direction of tensile crack propagation and that of the maximum stress.While the shear crack propagation direction,defined with sheared angle,θ_c,could be derived from Mohr-Coulomb strength theory.The angle between the direction of tensile crack propagation and that of the maximum stress isπ/4 +φ/2(whereφis the internal friction angle of intact rock).Promoting to non-penetrative double joint model,three failure modes are induced,namely tension failure,shear failure and tensile-shear damage.
5.Put forward the shear strength parameters estimation method of rock mass with a single set random joint.Supposed there exist single set joint with equal dip angle in two-dimensional rock mass discontinuity network model,its dip angle and trace length obey the random distribution of probability density function.When rock mass is failure,the middle point of the joints,which the failure surface contain,located in the route between the start point and the end point of the failure surface.All rock bridges failure mechanism can be judged by the above content,the angle and the length of each tensile crack or shear crack can be gained.With Lajtai rock bridge failure theory,we can determine the shear resistance and the shear force of every rock bridge and discontinuity,then the total shear resistance and the total shear force can be known,when they are equal,it explains that rock mass is in the critical state.Based on the above assumptions and thought,the estimation procedure of the shear strength is edited.According to a series of critical states of stress and Mohr-Coulomb strength theory,we can ensure the macro shear strength parameters of the jointed rock.Forecast respectively the macro shear strength parameters of the jointed rock when each other group joint is thought alone,and the smallest shear strength is thought as the macro strength of rock mass.Finally,Yujianhe Reservoir arch dam project in Guizhou Province is as an example, the shear strength of rock mass with considered each set joint alone is forecast,and last the smallest shear strength is as that of rock mass.
6.Three-dimensional geological model about Yujianhe Reservoir arch dam project in Guizhou Province is established with continuum medium and finite element method.The deformation and stress of dam are analysis,there are some soft interlayer in T_2s~(3-2),however the REV is big,which leads to determine the equivalent deformation parameter difficult,so this paper analysis the effect of this layer's equivalent deformation parameter to dam's displacement in four conditions.The results show that the dam displacement in the X direction is small,and the deformation parameters and external loads have little effect to the displacement and it can be negligible.To the dam displacement in the Y direction,the impact of hydrostatic pressure in deformation parameters is large than the deformation parameters.
Main results are shows as following:
1.A method to ensure the volume frequency of rock mass discontinuity is put forward.It combines with the discontinuity network simulation.
2.Put forward the shear strength parameters estimation method of rock mass with a single set random joint.It offers reliable source for engineering appliance.
3.Put forword a method to calculate tensile angle and sheared angle.In which tensile angle,θ_t, is derived from Griffith strength theory,while sheared angle,θ_c,is derived from Mohr-Coulomb strength theory.
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