Numerical simulation on uniaxial compressive mechanical properties of karstified rock mass in epikarst zone
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摘要: 研究表层喀斯特带溶蚀岩体的力学特性，有助于岩溶区边坡稳定性分析。本文以表层岩溶带溶蚀特征为依据，设定溶蚀率和溶蚀均匀系数作为溶蚀特征参数。基于元胞自动机算法思路，在颗粒离散元软件中构建不同溶蚀特征的岩体模型。对溶蚀岩体进行单轴压缩数值试验，检测岩体加载过程中声发射事件。试验结果表明：溶蚀岩体加载过程可分为：（1）压密阶段；（2）弹性变形阶段；（3）稳定破裂发展阶段；（4）不稳定破裂发展阶段；（5）峰后缓慢软化阶段；（6）峰后快速软化阶段。随溶蚀率增加，岩体弹性变形阶段曲线缩短，岩体抗压强度降低；岩体由脆性破坏逐渐转为延性破坏；同时，溶蚀率增加，岩体抗压强度下降速率由最初快速降低转为缓慢降低，最终收敛。溶蚀均匀系数增加，不稳定破裂阶段曲线增长，岩体由局部破坏转为整体性破坏。研究发现溶蚀岩体单轴抗压强度与溶蚀特征参数呈负指数关系，该关系式可用作溶蚀岩体强度取值，实际工程中应增加溶蚀均匀系数对岩体质量的影响。溶蚀岩体裂纹扩展机理有助于边坡失稳机理研究。Abstract:
The research of mechanical properties of karstified rock mass is helpful to the study of slope stability, foundation bearing capacity and mechanism of karst-induced disasters in karst area. However, it is difficult to obtain suitable rock samples for mechanical tests of karstified rock mass, or there exist experimental results with large differences. Nowadays, many scholars have studied mechanical properties by numerical simulation and have achieved greatly. In this kind of research, the stochastic method to simulate the karstification process is mainly adopted, whose algorithm is relatively simple but with less accurate response to the kasitified characteristics of rock mass, thus leading to the limitations of the results. Relevant literature shows that the epikarst zone presents characteristics of negative exponential relationship between the dissolution rate and depth, uneven distribution of dissolved pores caused by the difference of dissolution morphology, and more vertical karstification than horizontal karstification. In this study, two parameters of the karstification characteristics—the dissolution rate (the quantitative index of dissolution degree of rock mass) and dissolution uniformity coefficient (representing the uneven distribution of dissolution fractures)—have been set to analyze its characteristics in the epikarst zone. According to the characteristics of limestone joint in a typical karst area in Guizhou, the equivalent model of jointed rock mass has been established by using the Flat Joint Model (FJM), Smooth Joint Model (SJM) and Discrete Fracture Network (DFN). Based on the cellular automata algorithm and the dissolution of the equivalent model of jointed rock mass, the kastified rock mass model with different dissolution rates and different dissolution uniformity coefficients has been obtained. According to the numerical uniaxial compression test and the acoustic emission events in the process of loading rock mass. A total of 48 groups of test samples were collected in terms of 8 grades of dissolution rate and 6 groups of dissolution uniformity coefficient. The results show that the loading process of karstified rock mass can be divided into six stages: (1) stage of compaction; (2) stage of elastic deformation; (3) stage of stable fracture development; (4) stage of unstable fracture development; (5) stage of post-peak strain softening; (6) stage of post-peak rapid strain softening. The karstification reduces the cementation between rock masses and destroys the skeleton of rock mass, which leads to the following effects. With an increase of dissolution rate, the uniaxial compressive strength decreases. The curve shortens at the stage of elastic deformation. The number of acoustic emission events decreases significantly when the rock mass is damaged. The failure mode of rock mass gradually changes from brittle failure to ductile failure. The strength after failure mainly comes from the locking effect of rock bridge and the friction between fracture surfaces. At the same time, with the continuous increase of dissolution rate, the compressive strength of rock mass declines from rapid to slow rate. The higher the dissolution uniformity coefficient is, the smaller size the dissolution pore and the more uniform distribution of dissolution fractures may become. Under these conditions, the formation and penetration of macro cracks need to go through a longer process, and the curve of unstable fracture development increases. The internal stress of rock mass is more divergent, and the rock mass changes from local failure to overall failure. The fitting of uniaxial compressive strength and karstification characteristic parameters (k, U) indicate their negative exponential relationship, and the exponential constant C is related to the uniformity coefficient u. The relationship can be used as the basis for determining the strength of karstified rock mass. In practical engineering, the deformation state of karstified rock mass can be judged according to this acoustic emission characteristics, and thus corresponding treatment measures can be taken. In the evaluation of rock mass quality, the dissolution uniformity coefficient can be used as an auxiliary evaluation basis, in addition to the dissolution rate as the main feature of dissolution development. -
图 1 平直节理模型与光滑节理模型示意图
Figure 1. Schematic diagram of flat joint model and smooth joint model
图 3 数值实验及拟合参数标定关系式
Figure 3. Relationship between numerical test and fitting microscopic parameter calibration
图 4 溶蚀转化过程及最小、大溶蚀均匀系数示意图
Figure 4. Karstification and the minimum and maximum of dissolution uniformity coefficient
图 5 加载条件下溶蚀岩体应力应变曲线、声发射特征
Figure 5. Stress-strain curve and acoustic emission characteristics of karstified rock mass on loading
图 6 岩体变形破坏过程及各阶段裂纹扩展
Figure 6. Deformation and failure process of rock mass and crack propagation
图 7 溶蚀岩体破坏后微裂纹分布图
Figure 7. Distribution of microcracks after the damage of karstified rock mass
图 8 不同溶蚀均匀系数下溶蚀率与单轴抗压强度关系图
Figure 8. Relationship between uniaxial compressive strength and dissolution rate in terms of different dissolution uniformity coefficients
表 1 岩体宏观力学参数
Table 1. Macro-mechanic parameters of rock mass
参数类型 力学参数属性 参数值 岩块 密度ρ /g·cm−3 2.50 单轴抗压强度σc /MPa 57.5 抗拉强度σt /MPa 3.50 压拉强度之比σc/σt 16.40 弹性模量E /GPa 22.10 泊松比ν 0.19 结构面参数 内聚力C /MPa 0.08 内摩擦角φ /° 49.00 
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表 2 岩体细观强度参数
Table 2. Micro-mechanic parameters of rock mass
参数类型 细观参数/单位 参数值 颗粒尺寸 半径比 R* 1.66 最小半径Rmin 0.01 平直节理模型
(Flat Joint Model)杨氏模量Ec /GPa 35.0 刚度比K* 2.00 抗拉强度σt /MPa 6.00 粘聚力c /MPa 35.0 内摩擦角φ /° 0.00 内摩擦系数μ 0.50 光滑节理模型
(Smooth Joint Model)法向刚度Kn /GPa·m−1 30.00 切向刚度Ks /GPa·m−1 20.00 内摩擦系数μ 0.60 内摩擦角ϕb /° 49.70 剪胀角ψ /° 5.00 抗拉强度σc /MPa 0.00 黏聚力cb /MPa 0.15
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表 3 岩体结构面几何参数
Table 3. Geometric parameters of structural plane of rock mass
结构面名称 倾角 迹长 间隔 分布 平均值/标准差 分布 参数/(下、上限指数) 分布 P10密度（条/m） 节理面J1 正态 82.26/2.83 幂律 2.5/（0.15、2） 均匀 8 层面 正态 3.12/0.16 / 全贯通 均匀 4
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