Numerical modelling in rock engineering and mechanics often requires inputting multiple sets of strength parameters, such as the commonly encountered tensile strength, cohesion, and friction angle. Usually, obtaining these parameters requires performing different types of rock mechanics experiments on certain rock specimens, such as tension tests and triaxial tests, which are time-consuming and labor-intensive. Uniaxial compression testing is simpler and requires less demanding equipment. This paper proposes a solution that relies solely on uniaxial compression testing to obtain multiple sets of rock strength parameters. The basic idea is to treat the process of acquiring multiple parameters as a problem of solving a set of mathematical equations. The uniaxial tests with different geometric specimens provide known quantities and the corresponding equations that link these known quantities (e.g., peak loads) with unknown quantities (e.g., strength parameters). We established three-dimensional numerical tests to represent the relationship between input strength parameters and the peak load. By transforming it into an optimization problem, numerical modelling is embedded into the objective function of the optimization algorithm, thereby achieving the automatic extraction of strength parameters. This method is verified through uniaxial compression tests using red sandstone specimens with various geometries. The results show that by changing the geometry of the rock specimens, multiple sets of strength parameters can be obtained. These parameters are successfully used to predict (extrapolate) peak loads of other geometric specimens. This method holds promise for achieving the automated extraction of material parameters for the numerical modelling of rock.

中文翻译：

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单轴压缩试验提取岩石强度参数的几何变分法


岩石工程和力学中的数值建模通常需要输入多组强度参数，例如常见的抗拉强度、粘聚力和摩擦角。通常，获得这些参数需要对某些岩石试件进行不同类型的岩石力学实验，例如拉伸试验和三轴试验，这些实验非常耗时且费力。单轴压缩测试更简单，并且需要的设备要求较低。本文提出了一种仅依靠单轴压缩试验来获得多组岩石强度参数的解决方案。其基本思想是将获取多个参数的过程视为求解一组数学方程的问题。使用不同几何样本的单轴试验提供了已知量以及将这些已知量（例如峰值载荷）与未知量（例如强度参数）联系起来的相应方程。我们建立了三维数值试验来表示输入强度参数与峰值载荷之间的关系。通过将其转化为优化问题，将数值建模嵌入到优化算法的目标函数中，从而实现强度参数的自动提取。该方法通过使用各种几何形状的红砂岩样本的单轴压缩试验得到验证。结果表明，通过改变岩石试件的几何形状，可以获得多组强度参数。这些参数成功地用于预测（推断）其他几何样本的峰值载荷。该方法有望实现岩石数值模拟的材料参数的自动提取。