Study On The Equivalent Mechanical Parameters Of Complicated Fractured Rock Mass And Their Engineering Application

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 theâ…£andâ…¤-class structure plane,which obey random distribution.The growth degree ofâ…£-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:â‘ there 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.â‘¡the 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,â‘ the 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,â‘¡the 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 thatθ₁,which satisfies the equalityβ(θ₁)=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.Otherwiseθ₁,which satisfies the equality f(θ₁)=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 isÏ€/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 T₂s^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.