一维轴对称杆件爆源模型及其在台阶爆破模拟中的应用

为了解决在实体炮孔建模时需要加密网格、计算量大等问题，提出了一种一维轴对称爆源模型：利用一维线状杆件表述炮孔及炸药，实体单元表述周围岩体，通过杆件节点与实体单元的拓扑关系，将杆件节点上的爆生气体压力施加至周围实体单元上，并根据实体单元的体应变计算出杆件节点处的横截面变化情况，从而实现模拟炸药与周围岩体的相互作用。通过与实体炮孔模型的数值对比分析，发现压力衰减指数为1.25时，一维轴对称爆源模型获得的径向质点峰值振动速度（peak particle velocity, PPV）衰减规律及振动速度时程曲线与实体炮孔模型基本一致，证明了该模型在模拟爆破问题中的精确性。针对混凝土块动态爆破破坏特性的研究，通过与文献对比分析，进一步验证了该模型的正确性。为验证该一维轴对称爆源模型在台阶爆破模拟中的应用，以鞍钢露天铁矿台阶爆破开采为研究对象，建立了5排50炮孔三维台阶爆破概化模型，模拟了爆区内露天边坡的损伤破坏状态。数值计算结果表明，爆区内拉伸破坏为主，并且除了离爆源较近的第一个测点外，其余测点处的振动速度峰值大小及其随距离的变化规律与现场实测数据基本一致，证明了所提爆源模型在三维台阶爆破远场模拟的可行性。

A one-dimensional axisymmetric explosive model and its application in bench blasting simulation

The bench blasting technology is widely applied in mining, transportation and civil construction excavations, in which numerical simulation plays an increasingly important role in the selection and optimization of parameters. In order to solve the problems of dense mesh and large amount of calculation in solid hole modelling, a one-dimensional axisymmetric explosive model is proposed. In this model, the rock mass to be exploded is divided into larger solid mesh elements, and the blast hole is simplified into a bar and inserted into the designated position of the rock mass to be exploded. The bar is divided into several elements, and the classic Landau model is introduced into the bar elements. The gas expansion pressure is calculated according to the volume of the bar element. By determining the topological relationships between bar nodes and solid elements, if the bar node is located in the interior (3D) or surface (2D) of a solid element, the solid element is used as the force transfer object of the bar node, and the explosive gas pressure on the bar node is applied to the solid element. At the same time, the constitutive model is applied for solid elements according to the specific material, so as to calculate the body strain of the solid element. The bar element only expands radially is assumed, so the cross-sectional change at the bar node can be calculated according to the strain of the solid element body, which is used to calculate the explosive gas pressure at the next moment. Through numerical comparison with the entity bore hole model, when the pressure attenuation index is 1.25, the radial peak particle velocity attenuation law and vibration velocity time history curve obtained by the one-dimensional axisymmetric explosion source model are basically consistent with the entity blast-hole model, which proves the accuracy of the model in blasting simulation. Aiming at the study of dynamic blasting damage characteristics of concrete blocks, the correctness of the model is further verified by comparing with the literature. Based on the blasting technology in Angang open-pit mine, a generalized three-dimensional bench blasting model with 5 rows and 50 bore holes was set up to simulate the damage and failure status in the blasting area. The numerical calculation results show that the tensile failure is the dominant in the blasting area, and the peak particle velocity and its variation with distance at monitor points except the first point near the blasting source is well fitted with the test data, which proves the feasibility of the proposed model in the far-field simulation of three-dimensional bench blasting.