基于颗粒破碎尺寸效应的岩堆体剪切强度理论研究

Shear strength of coarse granular materials, widely used in civil works, is seldom measured because of severe practical experimental limitations. The lack of knowledge in shear strength of coarse granular materials often leads to severe accidents including failures in civil works built by coarse granular materials. This project presents an original method for evaluating the shear strength of coarse granular materials, based on fractal crushing of particles in coarse granular materials. Shear strength is defined as the friction stress at contact points due to particle mobile. Contact points between particles in granular materials are fractally distributed in shear plane. According to fractal distribution of contact points between particles, the shear strength envelope of granular materials can be deduced, and expressed by a power function, in which parameters are expressed by fractal dimension of the particle distribution, the particle tensile strength and inner friction angle of granular materials. According to fractal particle crushing of granular materials, the size effect of particle tensile strength can be derived. Through the size effect relation operating on the shear strength envelope, it is possible to determine the shear strength of a coarse-grained granular material from the measured shear properties of a finer-grained granular material made of the same mineral and having parallel particle size distributions. In this project, the method is explicitly proved, taking into account the statistical distribution of the crushing strength of particles with different sizes, within materials that can be considered as physically similar, particularly having parallel grain size distributions. A wide set of independent experimental results is shown to validate the method consistently.

随着土地资源越来越稀缺，岩堆体地基将在我国今后的工程实践中经常遇到，岩堆体的剪切强度是地基承载力和稳定性分析的最基本参数，在工程设计中首当其冲地需要。以往确定含巨砾岩堆体的剪切强度是进行缩尺处理，根据缩尺后试料的剪切强度外推估算岩堆体剪切强度，外推估算遇到缩尺试料选择难、拟合参数离散等难题。本项目在建立颗粒破碎的分形模型和假设剪切强度为颗粒间的摩擦力的基础上，建立岩堆体剪切强度理论，导出颗粒破碎强度的尺寸效应，由此根据细颗粒岩堆体的剪切强度计算含巨砾岩堆体的剪切强度，并采用颗粒破碎强度和岩堆体剪切强度试验数据验证提出的剪切强度理论，颗粒破碎强度采用单颗粒压缩试验确定，剪切强度通过不同尺寸的直剪仪和三轴仪测量。本课题提出的剪切强度理论中的计算参数包括颗粒破碎的分维、破碎强度和细粒料的内摩擦角，计算参数物理意义明确，参数取值范围确定，确定方法规范，易于实际工程应用，并用试验数据进行广泛验证。

粗粒岩堆体在自然界及工程中很常见，具有压缩性小、强度高、填筑密度大、透水性强、固结速度快等工程特点，因此粗粒岩堆体常作为填料广泛应用于沟塘回填、铁路公路地基、水利大坝等工程中。粗颗粒容易发生破碎，引起颗粒粒径、级配改变，影响岩堆体的剪切强度。本项目通过粗颗粒的冲击破碎试验和单颗粒压缩破碎试验，证明颗粒破碎符合分形模型，揭示颗粒破碎强度的尺寸效应；基于颗粒接触点分布的分形模型，假设剪切强度是颗粒接触面上的摩擦力，导出用正应力幂函数表示的粗粒土剪切强度公式，幂函数的指数是颗粒破碎分维的函数，采用粗颗粒材料的直剪试验结果验证了岩堆体的剪切强度理论。另外，采用离散单元法模拟了粗颗粒压缩破碎过程和直剪试验，从微观解释了粗颗粒破碎模式，验证了单颗粒压缩破碎强度和岩堆体的剪切强度理论，取得以下成果：.（1）建立颗粒破碎的分形模型，提出颗粒破碎分维的确定方法.基于Steacy和Sammis（1991）颗粒破碎的分形模型，揭示了颗粒破碎分形理论的物理机理，提出筛分法确定颗粒破碎分维。选取了大理岩、垃圾炉渣和生物质炉渣进行冲击破碎试验，采用筛分试验分析了三种材料颗粒破碎后的分布特征，计算了颗粒破碎的分维。.（2）提出“真分维”和“似分维”的概念，揭示了“似分维”演化规律.颗粒破碎分维随着破碎应力和破碎能量增加而增加，颗粒完全破碎后的粒径分布的分维趋于定值，为2.6左右。将颗粒破碎过程中变化的分维称为颗粒破碎的“似分维”，简称分维；分维的极限值称为“真分维”。揭示了颗粒破碎几率与破碎（似）分维的关系，建立了分维与破碎应力和破碎能量的对数正相关关系。随着破碎能量和破碎应力增加，颗粒破碎几率增大，破碎分维增加。.（3）揭示了颗粒破碎强度的尺寸效应，建立了破碎强度与粒径的理论关系.基于颗粒破碎的分形模型，揭示了颗粒破碎强度随粒径增加而减小的规律。根据颗粒破碎面的分形模型，建立了颗粒破碎强度与颗粒粒径的理论关系，提出了颗粒破碎强度的计算方法。根据单颗粒压缩破碎试验，将单颗粒压缩试验的力－位移曲线分为三种类型，并与颗粒形状建立联系。.（4）提出了Weibull的计算公式，修正了Weibull统计理论.假设固体颗粒是D维的分形体，基于颗粒破碎强度的尺寸效应，提出Weibull模量m的计算公式，对颗粒破碎几率的Weibull理论进行修正。.（5）揭示了粗颗粒料剪切强度幂律的机理，建立了粗颗粒料剪切强度