Performance analysis of empirical models for predicting rock mass deformation modulus using regression and Bayesian methods

Deformation modulus of rock mass is one of the input parameters to most rock engineering designs and constructions.The field tests for determination of deformation modulus are cumbersome,expensive and time-consuming.This has prompted the development of various regression equations to estimate deformation modulus from results of rock mass classifications,with rock mass rating(RMR)being one of the frequently used classifications.The regression equations are of different types ranging from linear to nonlinear functions like power and exponential.Bayesian method has recently been developed to incorporate regression equations into a Bayesian framework to provide better estimates of geotechnical properties.The question of whether Bayesian method improves the estimation of geotechnical properties in all circumstances remains open.Therefore,a comparative study was conducted to assess the performances of regression and Bayesian methods when they are used to characterize deformation modulus from the same set of RMR data obtained from two project sites.The study also investigated the performance of different types of regression equations in estimation of the deformation modulus.Statistics,probability distributions and prediction indicators were used to assess the performances of regression and Bayesian methods and different types of regression equations.It was found that power and exponential types of regression equations provide a better estimate than linear regression equations.In addition,it was discovered that the ability of the Bayesian method to provide better estimates of deformation modulus than regression method depends on the quality and quantity of input data as well as the type of the regression equation.

Failure mode and strength anisotropic characteristic of stratified rock mass under uniaxial compressive situation

A stratified rock mass model was founded by FLAC3D. The failure mode and anisotropic characteristic of strength for stratified rock mass were analyzed. The analysis results show that the numerical simulation can visually reflect the failure modes of rock samples under different inclination angles β of structural plane. The stiffness of rock sample before peak strength changes in the compressive procedure. With the increase of β, the compressive strength σc of rock sample decreases firstly and then increases; when β is in the range of 20°-30° and 80°-90°, σc has the largest sensitivity to β; while β falls in the range of 30°-70°, σc varies little. When φ j<β<90°. (φj is friction angle of structure plane), the results obtained from numerical simulation and theoretical analysis are in almost the same values; while β≤φ j or β=90°, they are in great different values. The results obtained from theoretical analysis are obvious larger than those from numerical simulation; and the results from numerical simulation can reflect the difference of compressive strength of rock samples for the two situations of β≥φj and β=90°, which is in more accordance with the real situation.

Elasto-plastic Analysis of Circular Tunnels in Jointed Rock Masses Satisfy the Hoek-Brown Failure Criterion

The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is il-lustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and dis-placement fields under axisymmetrical and asymmetric stress conditions. For the same rock masses and under axisym-metrical stress conditions,the radius of the plastic zone in terms of Hoek-Brown criterion is generally an approximation of the radius in terms of the Mohr-Coulomb criterion. The radius in terms of the Hoek-Brown criterion is larger under low stress conditions. For poor quality rock masses (GSI<25),measures (such as grouting,setting rock bolts,etc.) that improve the GSI of rock masses are effective in improving the stability of tunnels. It is not advisable to improve the sta-bility of the tunnels by providing a small support resistance p through shotcrete,except for very poor quality jointed rock masses. Without reference to the quality of the rock mass,the disturbance factor D should not less than 0.5. Meas-ures which disturb rock masses during tunnel construction should be taken carefully when the tunnel depth increases.

Fuzzy Random Reliability Analysis of Blocky Rock-Mass in Slopes

Slope stability assessment is a geotechnical problem characterized by many sources of uncertainty. In clas- sical reliability analysis, only the randomness of uncertainties is taken into account but the fuzziness of them is ignored. In this paper, a fuzzy probability approach and a fuzzy JC method are presented for the reliability analysis. The two methods have been applied to stability analysis of a certain slope of permanent ship lock in the Three-Gorges Project. The results obtained from these two methods are basically the same. However, compared with the fuzzy probability means, the fuzzy JC method can reflect the real situation better because it uses a fuzzy-based analysis applied to not only limit state equation but also mechanical parameters.

Two-and three-dimensional stability analysis of underground storage caverns in soft rock(Cappadocia, Turkey) by finite element method

Engineering design in soft rocks and its stability analysis exerts many challenges to rock engineers. Many engineering works in Turkey’s Cappadocia region must face and tackle the existing sites covered by the soft rocks. This study is aimed to examine the stability condition of a typical underground storage cavern(USC) excavated in a soft rock in this region. For this purpose, two-and threedimensional stability analyses of the USCs were performed using the finite element method(FEM).Because of the inherent difficulty in characterizing soft/weak rock masses in the region using traditional classification systems, the stability of a typical USC was evaluated by representing the rock mass condition with two distinct scenarios in FEM analysis.While these structures were unstable according to the 2D analysis conducted in RS2 software in the worstcase scenario, they were stable in the 3D analysis using RS3 software in both scenarios. Besides,feasible cover depths were examined to assess their possible effects on the factor of safety and deformation measurements. It was found that 15 m seems to be an optimal depth for excavating a typical USC in the soft rocks exposed in the region. The 3D FEM results provide valuable information to optimize the future planning and preliminary design of USCs.

Numerical simulation on deformation character of surrounding rock masses of Changjiashan tunnel through the gob of coalmine

Based on the construction project of the Changjiashan tunnel of the freeway,the variety rule of surrounding rock masses of the tunnel through the gob of coalmine wasstudied by using of finite element methed(FEM).The status of the stress and strain,thevariety of the plastic area were simulated in the whole rock mass before and after thetunnel was excavated.The characters of stress and deformation of surrounding rockmasses were analyzed when the tunnel was built.It concluded from the numerical simula-tion that the influence on the tunneling is great when the tunnel passing through the gob ofcoalmine is excavated,and the relative measures should be taken.

Stability of High Slope Interbedded Strata with Low Dip Angle Constituted by Soft and Hard Rock Mass

Slopes consisting of interbedded strata of soft and hard rock mass, such as purplish red mudstone and grey brown arkosic sandstone of Jurassic age, are very common in Sichuan basin of China. The mudstone is soft while the sandstone is hard and contains many opening or closing joints with a high dip angle. Some are nearly parallel and the others are nearly decussated with the trend of the slopes. Many natural slopes are in deformation or sliding because of those reasons. The stability of cutting slopes and supporting method to be taken for their stability in civil engineering are important. In this paper, the stability and deformation of the slopes are studied. The methods of analysis and support design principle are analyzed also. Finally, the method put forward is applied to study Fengdian high cutting slope in Sichuan section of the express way from Chengdu to Shanghai. The results indicate that the method is effective.

Geotechnical investigations and remediation design for failure of tunnel portal section： a case study in northern Turkey

Mass movements are very common problems in the eastern Black Sea region of Turkey due to its climate conditions, geological, and geomorphological characteristics. High slope angle, weathering, dense rainfalls, and anthropogenic impacts are generally reported as the most important triggering factors in the region. Following the portal slope excavations in the entrance section of Cankurtaran tunnel, located in the region, where the highly weathered andesitic tuff crops out, a circular toe failure occurred. The main target of the present study is to investigate the causes and occurrence mechanism of this failure and to determine the feasible remedial measures against it using finite element method(FEM) in four stages. These stages are slope stability analyses for pre-and postexcavation cases, and remediation design assessments for slope and tunnel. The results of the FEM-SSR analyses indicated that the insufficient initial support design and weathering of the andesitic tuffs are the main factors that caused the portal failure. After installing a rock retaining wall with jet grout columns and reinforced slope benching applications, the factor of safety increased from 0.83 to 2.80. In addition toslope stability evaluation, the Rock Mass Rating(RMR), Rock Mass Quality(Q) and New Austrian Tunneling Method(NATM) systems were also utilized as empirical methods to characterize the tunnel ground and to determine the tunnel support design. The performance of the suggested empirical support design, induced stress distributions and deformations were analyzed by means of numerical modelling. Finally, it was concluded that the recommended stabilization technique was essential for the dynamic long-term stability and prevents the effects of failure. Additionally, the FEM method gives useful and reasonably reliable results in evaluating the stability of cut slopes and tunnels excavated both in continuous and discontinuous rock masses.

Simulation of failure process of jointed rock

A modified discontinuous deformation analysis (DDA) algorithm was proposed to simulate the failure behavior of jointed rock. In the proposed algorithm, by using the Monte-Carlo technique, random joint network was generated in the domain of interest. Based on the joint network, the triangular DDA block system was automatically generated by adopting the advanced front method. In the process of generating blocks, numerous artificial joints came into being, and once the stress states at some artificial joints satisfy the failure criterion given beforehand, artificial joints will turn into real joints. In this way, the whole fragmentation process of rock mass can be replicated. The algorithm logic was described in detail, and several numerical examples were carried out to obtain some insight into the failure behavior of rock mass containing random joints. From the numerical results, it can be found that the crack initiates from the crack tip, the growth direction of the crack depends upon the loading and constraint conditions, and the proposed method can reproduce some complicated phenomena in the whole process of rock failure.

节理化炭质页岩地层隧道围岩大变形及控制技术研究

某高速铁路XHS隧道穿越节理化炭质页岩地层,在施工过程中围岩大变形、失稳坍塌现象显著,现场采用强支护和仰拱加深等措施后围岩变形控制效果不佳。针对XHS隧道节理化炭质页岩地层地质条件,结合现场监测手段、离散-连续耦合数值模拟分析围岩大变形及破坏特征,基于数值模拟提出以采取地层预加固为主的围岩变形控制措施,并通过现场试验探讨该控制措施的应用效果。研究结果表明:隧道开挖后,围岩变形具有变形量大、变形速率快的特点,围岩拱部沉降量大于水平收敛量且变形具有非对称的分布特征;受三台阶法多次开挖扰动影响,围岩卸荷范围动态发育并不断向全环扩展,松动区逐渐由浅部围岩向深部转移,并呈现出非对称的破坏特征,最终引发围岩大变形;采取地层预加固后,模型中围岩变形和松动区范围明显减小,围岩非对称变形破坏也得到了有效控制;在采用地层预加固、管棚超前支护、三台阶临时仰拱法开挖的控制措施后,围岩变形得到控制,施工效果良好,隧道恢复正常施工,保证了隧道的顺利贯通;以地层预加固为主的控制措施是此类节理化炭质页岩地层围岩变形控制的有效手段。

程潮铁矿崩落法开采对上覆岩体变形的影响研究

针对程潮铁矿开展工程地质调查,采用离散元分析软件UDEC建立其二维地质剖面模型,在假设其上部水平矿房未开采的条件下,模拟了程潮铁矿无底柱分段崩落法开采-480m、-500m相邻分段的过程,研究单一分段及相邻分段开采导致的围岩“冒落带、导水裂隙带”的分布规律及范围,探索程潮铁矿单分段矿房开采时其上覆岩体形成的导水裂隙带高度范围y随采长x的变化函数,分析无底柱分段崩落法不同分段矿房开采对于上覆岩体变形及影响机理,为类似开采技术条件矿山安全生产提供参考。

焦家金矿破碎岩体变形破坏规律研究

焦家金矿-570~630 m中段矿(岩)体节理裂隙发育,易出现楔形不稳定结构,进而发生岩体冒落。对岩体进行了地质钻孔、结构面条件调查等得出,焦家金矿岩体较为破碎,节理发育,节理产状分布范围广。对开采扰动下巷道收敛变形规律进行研究与总结,并通过雷达测试分析焦家金矿巷道破坏深度,损伤深度基本保持在2 m,存在较多的结构弱面,需及时采取加固措施。此研究对该处矿体的支护等做出合理规划,进一步指导采场结构参数的合理选取,以确保该矿段的安全生产。对类似矿山破碎矿体的治理条件有一定的借鉴意义。

深埋软岩隧道围岩稳定性分析与防护措施研究

深埋软岩隧道初支大变形问题是隧道建设常见难题之一。针对西南地区某在建铁路隧道出现初支开裂变形及拱顶坍塌等问题,进行围岩内部位移监测及初支变形监测,并结合隧祉区情况对隧道灾害成因进行分析。研究结果表明:根据围岩深部位移曲线斜率,判断出围岩松动圈范围处于6.0~7.0 m;围岩前期变形速率快,水平收敛值明显大于拱顶沉降值,最大变形在上台阶收敛处,为93.2 mm,其主要原因是区域构造应力作用影响;初始在前期释放迅速,初支-围岩接触压力在空间上分布各不相同,围岩压力大小并不直接影响围岩变形情况;对已发生大变形区域采用径向注浆加固,对未开挖段落将超前小导管支护改为T76超前管棚注浆支护,有效控制了大变形持续发展,可为深埋软岩隧道断层破碎带处开挖前后大变形防护提供参考。

西延高铁隧道缓倾层状岩体破坏机理及防治措施

针对西延高铁新延安隧道侏罗系下统页岩夹砂岩缓倾层状岩体初支变形及破坏问题,采用workbench静态结构及特征值屈曲模块进行支护结构建模,对初支结构破坏机理进行分析,对支护措施进行优化研究。研究表明:(1)缓倾层状岩体隧道围岩及支护结构变形破坏,主要受缓倾层状岩体岩性及缓倾层理构造等地质因素影响;(2)支护结构的破坏模式为支护结构面内屈曲,在围岩压力达到初支结构材料承载极限时出现失稳,压力继续增加时呈现压溃破坏;(3)缓倾层状岩体隧道围岩变形复杂,隧道开挖后围岩变形时间长,宜采用刚性支护,采用型钢支护相较于原设计的格栅支护在缓倾层状岩体变形控制及承载方面更合理。

Simulation of blast induced crater in jointed rock mass by discontinuous deformation analysis method

Rock blasting is a dynamic process accom panied with the propagations of shock waves and the dispersion of the explosion gas.This paper adopts the discontinuous deformation analysis(DDA)method to simulate the rock blasting process.A dynamic parameter adjustment and the non-reflecting boundary condition are implemented in the DDA method.The sub-block DDA method to simulate fracture problems is used.The blasting process in jointed rock mass is simulated by application of the explosion gas pressure on the expanding borehole walls and induced connected fracture surfaces around the boreholes.The blast craters with different overburdens are derived.The whole process including the explosion gas dispersion,borehole expansion,rock mass failure and cast,and the formation of the final blasting piles in rock blasting are well reproduced numerically.Parametric study for different overburdens is carried out,and the results are analyzed and discussed.

断层蠕滑作用下活动断裂带地应力分布研究

采用非连续变形分析(DDA)方法研究断层蠕滑过程中嘉黎活动断裂带区域应力分布的变化规律。结果表明,断层蠕滑会导致岩体中应力明显增长,随着深度的增加应力有相近的变化趋势;断层破碎带中的应力普遍低于两侧岩体中的应力;断层蠕滑会使岩体内发育大量裂隙,造成破碎岩体中应力分布不连续;断层破碎带及其两侧岩体中出现应力集中的区域在不同深度下的分布有一定的相似性。

岩石圆盘径向压缩破坏的Voronoi子块体单元DDA方法模拟

非连续变形分析(DDA)方法是计算离散可变形块体系统力学行为的数值计算方法,可通过子块体单元DDA方法模拟岩石的开裂破坏。考虑到Voronoi多边形颗粒与细观尺度下岩石矿物晶粒形态的相似性,提出一种基于随机圆的Voronoi颗粒单元模型生成方法;并通过完整及带预制裂纹岩石圆盘径向压缩破坏的模拟,验证岩石破裂问题Voronoi子块体单元DDA模拟方法的适用性。结果表明,当子块体单元数较小时,圆盘表现出更高的整体强度;随着子块体单元数的增大,起裂处位置更接近真实,开裂破坏路径更清晰;子块体单元数较大时不同倾角预制裂纹圆盘破坏的模拟结果与实验结果高度吻合,并能有效反映圆盘中心加工小孔对开裂破坏路径的影响。使用Voronoi子块体单元DDA方法能够有效模拟岩石的开裂破坏过程,为进一步开展基于Voronoi颗粒单元模型的岩石开裂破坏模拟创造了条件。

Discontinuous deformation and displacement analysis: From continuous to discontinuous

A discontinuous deformation and displacement(DDD) analysis method is proposed for modelling the rock failure process. This method combines the rock failure process analysis(RFPA) method(based on finite element method) and discontinuous deformation analysis(DDA) method. RFPA is used to simulate crack initiation, propagation and coalescence processes of rock during the small deformation state. The DDA method is used to simulate the movement of blocks created by the multiple cracks modelled by the RFPA. The newly developed DDD method is particularly suitable for modelling both crack propagation and block movement during the rock failure process because of the natural and convenient coupling of continuous and discontinuous deformation analyses. The proposed method has been used to simulate crack initiation, propagation and coalescence within a slope as well as the block movement during the landslide process. Numerical modelling results indicate that the proposed DDD method can automatically simulate crack propagation and block movement during the rock failure process without degrading accuracy.

分段黏结非连续变形分析方法及其在砂岩破裂分析中的应用

深部采煤面临高地温、高地压、高岩溶水压及开采扰动的综合影响,岩石的非连续变形及破裂行为也比浅部更为复杂,开发模拟岩石破裂行为的数值计算方法,进行从实验室尺度到工程现场尺度的分析是研究岩石破裂相关灾害规律和机理的重要手段。非连续变形分析方法 (Discontinuous Deformation Analysis,DDA)在接触理论、块体积分、计算收敛中具有严格的数学基础,采用子块体剖分和黏结处理的DDA模型可以有效模拟岩石及裂隙岩体从连续弹性变形到渐进断裂和完全破断的全过程。基于边-边黏结效应分段线性表征的朴素思想,提出分段式边-边黏结模型,将线性及非线性黏结本构关系通过分段中心点处的成对罚弹簧进行等效表征,嵌入三角形剖分的非连续变形分析求解框架内,实现模拟岩石断裂的优化DDA模型。通过简支梁中心受压、单轴压缩、巴西劈裂案例的变形、应力结果分析,验证了优化模型的准确性,获得了边-边黏结模型中分段数目、黏结刚度比、切向法向刚度比等参数的合理取值范围;通过完整及带孔洞的砂岩试样的单轴压缩试验,阐明了块体弹性模量、泊松比等变形参数及黏结单元抗拉强度、黏聚力、内摩擦角等强度参数的赋值方法,验证了优化模型在应力-应变曲线,裂纹起裂位置捕获的准确性;通过含单裂隙及组合裂隙的砂岩巴西圆盘劈裂试验的分析,验证了优化模型在裂纹起裂、裂纹扩展、多裂纹交汇等复杂裂隙扩展问题中的适用性;采用分段式边-边黏结的优化模型可推广用于包含复杂裂隙网络的岩体破坏规律和机理的分析。