土体中水力劈裂大规模数值模拟及应用

doi:10.16183/j.cnki.jsjtu.2024.180

摘要/Abstract

摘要：

在岩土工程领域,分析土体水力劈裂规律和机理具有重要意义,可为劈裂注浆脉体的扩散和分布规律研究提供依据,指导实际工程.通过使用块对角预处理、预处理的对称拟最小残量(PSQMR)迭代法及改进的稀疏矩阵矢量乘并行算法,开发土体中水力劈裂三维有限元程序,可实现大规模Biot固结有限元计算.实现了基于中央处理器(CPU)串行计算和图形处理器(GPU)并行计算平台的有限元求解,大幅提高计算规模,在个人计算机上可进行工程尺度的大规模有限元计算.通过数值模拟、试验模拟和理论分析与计算结果的对比,验证了所述计算方法的正确性,为研究土体中水力劈裂提供了有力的数值模拟工具.

关键词: 水力劈裂, 块对角预处理, 预处理的对称拟最小残量迭代法, 稀疏矩阵, 并行计算

Abstract:

In the field of geotechnical engineering, it is of great significance to analyze the law and mechanism of soil hydraulic fracturing, which can provide a basis for the study of the diffusion and distribution of splitting grouting veins and guide practical engineering. In this paper, a three-dimensional finite element program is developed by using block diagonal preprocessing, preconditioned symmetric quasi-minimal residual (PSQMR) iterative method, and improved sparse matrix vector multiplication parallel algorithm, which enables large-scale Biot consolidation finite element calculation, realizing the finite element solution based on CPU serial computing platform and GPU parallel computing platform, greatly improving the calculation scale, and accomplishing large scale finite element calculation on personal computer. By comparing the numerical simulation results, experimental simulation results, and theoretical analysis with the calculation results, the correctness of the calculation method is verified, which provides a numerical simulation tool for the study of hydraulic fracturing in soil.

Key words: hydraulic fracturing, block diagonal preprocessing, preconditioned symmetric quasi-minimal residual (PSQMR) iterative method, sparse matrix, parallel computing

中图分类号:

TU432

王风, 陈铁林, 樊容, 李跃鹏. 土体中水力劈裂大规模数值模拟及应用[J]. 上海交通大学学报, 2026, 60(3): 463-472.

WANG Feng, CHEN Tielin, FAN Rong, LI Yuepeng. Large-Scale Numerical Simulation and Application of Hydraulic Fracturing in Soil[J]. Journal of Shanghai Jiao Tong University, 2026, 60(3): 463-472.

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参数	取值
C/kPa	60
ϕ/(°)	30
K	50
K_u	100
n_s	0.6
R_f	0.95
K_b/kPa^-1	20
m_c	0.5

出浆口	起裂压力/kPa,终压/kPa
出浆口	1号孔	2号孔	3号孔	4号孔
a	175,120	181,129	181,123	188,143
b	169,109	146,115	159,118	209,137
c	152,113	157,119	166,143	186,126
d	141,103	145,110	172,137	209,122