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Theoretical basis for evaluating the deformability of rock blocks
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-07-26 , DOI: 10.1002/zamm.201900066
Rubén Galindo 1 , Alcibiades Serrano 1 , José Sánchez 1
Affiliation  

A theoretical basis for evaluating the deformability of rock blocks is presented in this study and is used to derive an equation that governs the relationship between the normal force applied and the displacement produced. This relationship depends on the distribution of forces in the contact; therefore, it depends on the load process acting at the asperities of the rock block. Most previous studies do not take into account the crushing effect of the contact points and do not address large pressures. However, this effect is more crucial when the material is thicker. The interpretation of the deformability tests with coarse granular materials is difficult because the stresses within the material are not known but are estimated from boundary conditions. The load is distributed in a general situation between asperities in an elastic state, asperities in a plastic state and the body of the block. A mathematical model based on a suitable geometrical characterization of the roughness of the surface of the rock block, height and radius, and well‐known mechanical principles is developed. This model makes it possible to evaluate partially the force‐displacement relationship of particle breakage tests. The main objective is to obtain the stress‐strain relationship of rock blocks considering the influence of roughness on its surface. The described theoretical formulation is applied to the rockfill of the dock of the Minerales harbor (Huelva). Their strength characteristics and deformation modulus are known, and the distribution of roughness on its surface is obtained using a specialized scanner on one of the block samples. From these results, the arrangement of the irregularities and the parameters of this developed mathematical model are applied to obtain adequate predictions and behavior patterns of particle breakage tests. The developed model adequately reproduces the different behaviors of the force‐displacement relationship depending on the fragility index (FI). Realistic values of this index make it possible to obtain adequate predictions.

中文翻译:

评价岩石块体变形性的理论基础

这项研究为评估岩石块的可变形性提供了理论基础,并用于推导一个方程,该方程可控制法向力与所产生位移之间的关系。这种关系取决于接触中力的分布。因此,这取决于作用在岩石块凹凸上的加载过程。以前的大多数研究都没有考虑接触点的挤压作用,也没有解决较大的压力。但是,当材料较厚时,此效果更为关键。用粗粒状材料来解释形变测试是困难的,因为材料中的应力是未知的,而是根据边界条件估算的。一般情况下,负载是在弹性状态的凹凸之间分配的,凹凸不平处于可塑性状态,且块体。基于岩石块表面粗糙度,高度和半径的适当几何特征以及众所周知的机械原理,建立了数学模型。该模型可以部分评估颗粒破损测试的力-位移关系。主要目的是考虑到岩石表面粗糙度对岩石块的应力-应变关系的影响。所描述的理论公式适用于Minerales港口(韦尔瓦)码头的堆石场。它们的强度特性和变形模量是已知的,并且使用专门的扫描仪在块样品之一上获得其表面上的粗糙度分布。根据这些结果,不规则的排列和该发达的数学模型的参数可用于获得足够的颗粒破损测试预测和行为模式。开发的模型根据脆弱性指数(FI)充分再现了力-位移关系的不同行为。该指数的实际值可以获取足够的预测。
更新日期:2020-07-26
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