同时起爆单排炮孔等效均布荷载的计算方法

Calculation of Equivalent Uniform Load from Simultaneous Initiated Single-row Blast Holes

针对钻孔爆破数值模拟过程中爆破荷载的计算与施加问题,对单排同时起爆炮孔的等效均布荷载计算方法进行了研究。通过理论分析和文献对比,发现许红涛提出的等效均布荷载计算方法存在理论错误。为此,通过对圆孔壁上的径向均布压力的分解与合成,推导了2个相邻炮孔远区介质中垂直于炮孔连线方向的均布应力的计算公式。通过建立脉冲荷载分别作用于含炮孔和无炮孔的长柱有限元模型,对计算模型与许红涛计算模型进行了对比。对比结果表明:当在含炮孔模型的每个炮孔壁上施加峰值为4280 MPa的均布脉冲载荷时,模拟得到炮孔远区指定单元中径向荷载峰值约为120 MPa;当在无炮孔模型平整端面上施加等效均布荷载时,采用计算方法施加的等效均布荷载峰值为111 MPa,模拟得到指定单元中径向荷载峰值约为110 MPa;采用许洪涛计算方法施加的均布载荷峰值为729 MPa,指定单元中径向荷载峰值约为725 MPa。用许红涛模型模拟得到的测点应力峰值是正确解的6倍左右,而用本文模型得到值略低于正确解10%左右。因此,本文提出的炮孔等效均布荷载模型具有更高的计算精度,可用于炮孔远区复杂爆破荷载的近似计算。

Aiming at the problem of calculation and application of blasting load in numerical simulation of blasting,the calculation method of equivalent uniform load from simultaneously initiated single-row holes is studied.Through theoretical analysis and literature comparison,it is found that the calculation method of equivalent uniform load proposed by Xu Hongtao has theoretical errors.Therefore,the formula for calculating the far-field uniform stress perpendicular to the connection direction of two adjacent holes is derived by decomposing and synthesizing the radial uniform pressure on the round hole wall.Then finite element models of long columns with and without blast holes are established to compare with Xu′s calculation model.When a uniform pulse load of 4280 MPa is applied to each hole wall of the model with blast holes,the peak radial load in the designated far-field element from the blast hole is about 120 MPa by using the numerical simulation model in this paper.While the equivalent uniform load is applied on the flat end of the model without blast holes,the peak value of the equivalent uniform load applied by using the proposed calculation method in this paper is 111 MPa,and the peak value of the radial load in the specified element is about 110 MPa.However,the peak value of uniform load applied by using Xu′s calculation method is 729 MPa,and the peak value of radial load in the specified element is about 725 MPa.The stress peak value of the measured point simulated by Xu′s model is about 6 times that of the correct solution,while the value obtained by the proposed model is about 10%lower than that of the correct solution.Therefore,the equivalent uniform load model proposed in this paper has higher calculation accuracy and can be used for approximate calculation of complex blasting load in far field of blast holes.