岩土材料工程性质数值试验研究
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摘要
本文选定PFC颗粒流软件作为数值分析平台,fish语言建立了满足一定统计分布的颗粒集聚体,虚拟实现了岩石力学试验。在此基础上,针对岩土材料细观参数的宏观响应、岩土材料内尺度比、尺寸效应、加载率效应、颗粒大小对材料工程性质的影响和岩石材料破裂过程及其分形特性等六个问题设计了专门的数值虚拟试验,分析所得主要结论如下:
1、一个简单的颗粒间力学关系可以反映一个复杂的力学过程。细观参数与宏观参数的关系不是简单求和,是整体与部分的辩证关系,整体的力学行为是部分力学行为的增强和放大。摩擦系数、接触半径乘子、弹性模量等颗粒细观参数对数值试件的影响是全面的,弹性模量的增加,会引起裂纹数量的增加,能量急剧减少,强度没有规律性变化;接触半径乘子的增加会使得材料强度和变形性能均提高,裂纹和能量均有提高;摩擦系数的增加会引起强度和变形性能的提高,裂纹和能量变化不大,但是摩擦能增加明显。细观强度的影响相对独立,只引起了宏观强度的提高,对变形没有影响。
2、通过设计的0.05-2.00mm粒径12种单轴压缩数值试验和巴西圆盘试验计算方案,分析发现岩土材料作为颗粒集聚体,的确存在内尺度比,即最大颗粒与试件直径的比,大于材料固有的内尺度比,则其工程性质出现较大波动;小于该值,则测试结果相对较为稳定。经分析,砂岩的内尺度比约等于0.01。
3、经过用破裂形态、裂纹系统数量和空间位置、应力应变曲线、能量演化等4类手段综合分析设计的不同长径比、不同围压数值试验,发现:通过应力应变曲线、峰值强度、割线模量和试件破坏形态等分析得到岩石几何尺寸最佳长径比在2.5-3.0之间,但存在数据波动和离散问题。而用能量方法分析得到的最佳长径比稳定在3.0。综上,最佳长径比为3.0,能量方法评价尺寸效应稳定性好。端部摩擦效应在低围压下和低长径比下对材料试验结果影响较大;在长径比大于2.5,围压大于10MPa后,端部效应影响相对减弱。低长径比时,材料表现出伪高强度;高长径比时,材料表现出伪高脆性。
4、加载速率越高材料破损过程中不再存在剪切优势带,剪切带等速发展,锥形破坏明显。随着应变速率的提高,岩石的峰值强度提高,变形参数也提高了。材料破损机理在于首先积聚粘结能,克服粘结强度,产生微裂纹,随后在积聚的弹性应变能驱动下扩展贯通,随后摩擦作用开始发挥作用,摩擦能急剧提高。裂纹贯通后,材料本身的强度特性不再起主导作用,局部弱化带主导了材料的后期变形和失稳过程。
5、经过对不同半径、不同数量团簇结构的力学分析发现:团簇数量越多,对材料性质的提高越显著;团簇半径越大、结构体系越稳定,则性质增强效果好。团簇材料的破损机理在于:随着团簇半径的增加,基质所占比例减小,基质中更容易产生微裂纹,但是其绝对数量有限,粘结能地位降低。而应变能则由于团簇强度高,较难以破坏,其主要受力或者传递力,则应变能储能作用增强。破坏经常绕着骨料发生,颗粒越大,越多,由于其竖向密度大,连接较好,侧向连接有限,而且边界作用明显,所以裂纹经常沿垂向发展,径向张开,呈雁行排列。
6、利用数值试验方法,结合图像处理,对不同规格数值试件的破裂体系进行了追踪、描述和研究,发现:岩石破裂体系具有统计自相似性,长径比显著的试件sandbox法测试结果异常值较多,这是方法缺陷。盒计数法对于不同形状数值试件的适应性要比sandbox法好,结果稳定。随着围压增加岩石破裂的分维数减小。加载造成材料劣化,这种性质劣化加剧了初始随机分布损伤的不均匀程度,劣化呈现局部发展,使得裂纹系统变得更为复杂,分数维增加。
The particle flow is selected to do the numerical test. The particle assembly meeting the specified probability distribution is built by program compiled by embedded language of fish. Then, the virtual implementation of rock mechanics experiment is done based on these. Six problems, such as the macro-response of rock and soil material’s micro-parameters, inner scale ratio, size effect, effect of loading rate, engineering characteristics of material affected by particle size and the rupture process of rock with its fractal feature are studied by the specialized numerical virtual test. The main conclusion is drawn as follows.
1. A simple mechanics relation between particles can result in a complex response. The relation of micro-parameter and macro-parameter is not a simple summation, which is the dialectical relationship of overall with some. The mechanics behavior of the assembly is the enhancement and enlargement of the particles’mechanics behavior. The effects of friction coefficient, contact radius multiplier and elastic modulus are comprehensive. The increasing of elastic modulus can cause the decreasing of strain, additional fracture, sharp reduction in energy and the irregular vibration of strength. The increase of contact radius multiplier results in the enhancement of material strength and deformation features, increase of rupture number and energy. So is the law of friction coefficient. However, the effect of micro-strength is independent, whose increase only affects the macro-strength.
2. The twelve kinds of computing schemes of uniaxial compression numerical test are designed to analyze the inner ratio of rock and soil material being the maximum of particle diameter divided by the diameter of sample. If the ratio is large than the inherent ratio of material, the engineering features of material appear big vibration. Conversely, the experimental results are stable. It is found that the sandstone’s scale ratio is 0.01 which illustrates the existence of the scale ration in particle assembly material.
3. The numerical test with different height-to-diameter ratio and confining pressure is comprehensively analyzed by means of rupture process, spatial location and number of fracture system, curve of stress and strain, energy evolution methods. It is found that the optimum ratio is 2.5-3.0, obtaining by curve of stress and strain, peak strength, secant modulus and rupture shape of numerical sample methods, that the optimal height-to-diameter ratio drawn by energy method is 3.0, and that the latter method is more stable than the former. End friction effect is apparent under condition of lower confining pressure and height-to-diameter ratio. If the ratio being large than 2.5 and confining pressure large than 10MPa, the end effect is weakened. When the ratio is small value, the material presents the pseudo-high-strength. Conversely, the rock appears false-high-brittle.
4. The priority developing shear zone don’t any longer exist during the rupture process of material because of the increase of loading rate, which makes the shear zone expands with the similar velocity, resulting in cone shape of rupture surface. It is found that the peak strength and deformation parameters of rock are enhanced with the developing of loading rate. The damage and rupture mechanism of material lies in which the cohesion energy is firstly cumulative, then cohesion strength is overcome, the little fracture is produced, the fracture is driven by cumulative elastic strain energy, finally the apparent rupture surface through the sample, when the local weak zone leads the post-peak phase of material’s deformation and instability process. The own strength of material don’t determine the damage process.
5. The computing schemes with different clump radius, number and spatial location or with the same spatial location and number of clumps are designed to study the mechanics behavior of clump structure. It is found that the material features are improved with the increase of clump number and radius. The damage mechanism of material with different dimension clumps lies in which the clump radius increasing can results in the decrease of matrix quantity within the material, rupture is easily produced in matrix, so the number of fracture is lessened and the action of cohesion energy is lowered, conversely the action of the strain energy is enlarged. The clump with high strength isn’t easily damaged, its action is delivering force to matrix. Therefore, damage often happens around the clump. Because the density of clump in vertical direction is large than the horizontal, and the horizontal confining is limit, the rupture often vertically expands and horizontally opens, looking like Yan arrange. 6. The rupture process of numerical samples with different dimension is tracing, describing and studying by means of virtual implementation method and image disposal. It is found that there exists statistical self-similarity in rock rupture system, that the applicability of box-counting-method used to calculate fractal dimension is better than sandbox method, whose computing result often vibrates with the different height-to-diameter of sample, that the fractal dimension is decreasing with the confining pressure and increasing with the loading process, because the loading changes the initial uneven degree of random defects within rock, which limits the deterioration of material features within local zone and worsens the complexity of fractures.
1、一个简单的颗粒间力学关系可以反映一个复杂的力学过程。细观参数与宏观参数的关系不是简单求和,是整体与部分的辩证关系,整体的力学行为是部分力学行为的增强和放大。摩擦系数、接触半径乘子、弹性模量等颗粒细观参数对数值试件的影响是全面的,弹性模量的增加,会引起裂纹数量的增加,能量急剧减少,强度没有规律性变化;接触半径乘子的增加会使得材料强度和变形性能均提高,裂纹和能量均有提高;摩擦系数的增加会引起强度和变形性能的提高,裂纹和能量变化不大,但是摩擦能增加明显。细观强度的影响相对独立,只引起了宏观强度的提高,对变形没有影响。
2、通过设计的0.05-2.00mm粒径12种单轴压缩数值试验和巴西圆盘试验计算方案,分析发现岩土材料作为颗粒集聚体,的确存在内尺度比,即最大颗粒与试件直径的比,大于材料固有的内尺度比,则其工程性质出现较大波动;小于该值,则测试结果相对较为稳定。经分析,砂岩的内尺度比约等于0.01。
3、经过用破裂形态、裂纹系统数量和空间位置、应力应变曲线、能量演化等4类手段综合分析设计的不同长径比、不同围压数值试验,发现:通过应力应变曲线、峰值强度、割线模量和试件破坏形态等分析得到岩石几何尺寸最佳长径比在2.5-3.0之间,但存在数据波动和离散问题。而用能量方法分析得到的最佳长径比稳定在3.0。综上,最佳长径比为3.0,能量方法评价尺寸效应稳定性好。端部摩擦效应在低围压下和低长径比下对材料试验结果影响较大;在长径比大于2.5,围压大于10MPa后,端部效应影响相对减弱。低长径比时,材料表现出伪高强度;高长径比时,材料表现出伪高脆性。
4、加载速率越高材料破损过程中不再存在剪切优势带,剪切带等速发展,锥形破坏明显。随着应变速率的提高,岩石的峰值强度提高,变形参数也提高了。材料破损机理在于首先积聚粘结能,克服粘结强度,产生微裂纹,随后在积聚的弹性应变能驱动下扩展贯通,随后摩擦作用开始发挥作用,摩擦能急剧提高。裂纹贯通后,材料本身的强度特性不再起主导作用,局部弱化带主导了材料的后期变形和失稳过程。
5、经过对不同半径、不同数量团簇结构的力学分析发现:团簇数量越多,对材料性质的提高越显著;团簇半径越大、结构体系越稳定,则性质增强效果好。团簇材料的破损机理在于:随着团簇半径的增加,基质所占比例减小,基质中更容易产生微裂纹,但是其绝对数量有限,粘结能地位降低。而应变能则由于团簇强度高,较难以破坏,其主要受力或者传递力,则应变能储能作用增强。破坏经常绕着骨料发生,颗粒越大,越多,由于其竖向密度大,连接较好,侧向连接有限,而且边界作用明显,所以裂纹经常沿垂向发展,径向张开,呈雁行排列。
6、利用数值试验方法,结合图像处理,对不同规格数值试件的破裂体系进行了追踪、描述和研究,发现:岩石破裂体系具有统计自相似性,长径比显著的试件sandbox法测试结果异常值较多,这是方法缺陷。盒计数法对于不同形状数值试件的适应性要比sandbox法好,结果稳定。随着围压增加岩石破裂的分维数减小。加载造成材料劣化,这种性质劣化加剧了初始随机分布损伤的不均匀程度,劣化呈现局部发展,使得裂纹系统变得更为复杂,分数维增加。
The particle flow is selected to do the numerical test. The particle assembly meeting the specified probability distribution is built by program compiled by embedded language of fish. Then, the virtual implementation of rock mechanics experiment is done based on these. Six problems, such as the macro-response of rock and soil material’s micro-parameters, inner scale ratio, size effect, effect of loading rate, engineering characteristics of material affected by particle size and the rupture process of rock with its fractal feature are studied by the specialized numerical virtual test. The main conclusion is drawn as follows.
1. A simple mechanics relation between particles can result in a complex response. The relation of micro-parameter and macro-parameter is not a simple summation, which is the dialectical relationship of overall with some. The mechanics behavior of the assembly is the enhancement and enlargement of the particles’mechanics behavior. The effects of friction coefficient, contact radius multiplier and elastic modulus are comprehensive. The increasing of elastic modulus can cause the decreasing of strain, additional fracture, sharp reduction in energy and the irregular vibration of strength. The increase of contact radius multiplier results in the enhancement of material strength and deformation features, increase of rupture number and energy. So is the law of friction coefficient. However, the effect of micro-strength is independent, whose increase only affects the macro-strength.
2. The twelve kinds of computing schemes of uniaxial compression numerical test are designed to analyze the inner ratio of rock and soil material being the maximum of particle diameter divided by the diameter of sample. If the ratio is large than the inherent ratio of material, the engineering features of material appear big vibration. Conversely, the experimental results are stable. It is found that the sandstone’s scale ratio is 0.01 which illustrates the existence of the scale ration in particle assembly material.
3. The numerical test with different height-to-diameter ratio and confining pressure is comprehensively analyzed by means of rupture process, spatial location and number of fracture system, curve of stress and strain, energy evolution methods. It is found that the optimum ratio is 2.5-3.0, obtaining by curve of stress and strain, peak strength, secant modulus and rupture shape of numerical sample methods, that the optimal height-to-diameter ratio drawn by energy method is 3.0, and that the latter method is more stable than the former. End friction effect is apparent under condition of lower confining pressure and height-to-diameter ratio. If the ratio being large than 2.5 and confining pressure large than 10MPa, the end effect is weakened. When the ratio is small value, the material presents the pseudo-high-strength. Conversely, the rock appears false-high-brittle.
4. The priority developing shear zone don’t any longer exist during the rupture process of material because of the increase of loading rate, which makes the shear zone expands with the similar velocity, resulting in cone shape of rupture surface. It is found that the peak strength and deformation parameters of rock are enhanced with the developing of loading rate. The damage and rupture mechanism of material lies in which the cohesion energy is firstly cumulative, then cohesion strength is overcome, the little fracture is produced, the fracture is driven by cumulative elastic strain energy, finally the apparent rupture surface through the sample, when the local weak zone leads the post-peak phase of material’s deformation and instability process. The own strength of material don’t determine the damage process.
5. The computing schemes with different clump radius, number and spatial location or with the same spatial location and number of clumps are designed to study the mechanics behavior of clump structure. It is found that the material features are improved with the increase of clump number and radius. The damage mechanism of material with different dimension clumps lies in which the clump radius increasing can results in the decrease of matrix quantity within the material, rupture is easily produced in matrix, so the number of fracture is lessened and the action of cohesion energy is lowered, conversely the action of the strain energy is enlarged. The clump with high strength isn’t easily damaged, its action is delivering force to matrix. Therefore, damage often happens around the clump. Because the density of clump in vertical direction is large than the horizontal, and the horizontal confining is limit, the rupture often vertically expands and horizontally opens, looking like Yan arrange. 6. The rupture process of numerical samples with different dimension is tracing, describing and studying by means of virtual implementation method and image disposal. It is found that there exists statistical self-similarity in rock rupture system, that the applicability of box-counting-method used to calculate fractal dimension is better than sandbox method, whose computing result often vibrates with the different height-to-diameter of sample, that the fractal dimension is decreasing with the confining pressure and increasing with the loading process, because the loading changes the initial uneven degree of random defects within rock, which limits the deterioration of material features within local zone and worsens the complexity of fractures.
引文
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