GPU-Accelerated Anisotropic Random Field and Its Application in the Modeling of a Diversion Tunnel
Abstract
:1. Introduction
2. Methodology
2.1. Basic Theory of Random Fields
2.2. Parameter Definitions for Random Fields
2.3. Anisotropic Random Field
2.4. GPU-Accelerated Anisotropic Random Fields
3. Simulation of the Red Layer in Central Yunnan
3.1. Geological Background
3.2. Modeling and Analysis Process for Red-Bedded Soft Rock Tunnels in Central Yunnan
4. Analyses on the Influence of the Law of Anisotropic Random Fields on the Safety Factor
4.1. Simulation Conditions and Method
4.2. Simulation Results and Analysis
5. Conclusions
- (1)
- The focus of this paper is on the covariance matrix decomposition method, which can be used to obtain stable independent random fields through Cholesky decomposition. However, due to the large number of grids and correlation matrix arrays, the method can result in slow calculations. To address this issue, the paper proposes a GPU acceleration technology, which enables the parallel operation of local matrix decomposition and overall serial calculations. By combining the advantages of the GPU, the proposed method efficiently generates random fields.
- (2)
- In this study, numerical simulation of the excavation stability of hydraulic tunnels was carried out for the anisotropic random field of red-bedded soft rocks in central Yunnan. The Mohr–Coulomb model was chosen for the rock material, and the internal friction angle and cohesion were set as random parameters, while other parameters were defined as constants. The safety factors of the anisotropic random field with different rotation angles are compared. The distribution of the plastic zone after excavation has a significant relationship with the random parameters of the anisotropic random field. When the stronger or weaker random parameters are located in the surrounding rock of the cavern, it will cause the change in the radius of the plastic zone. The overall safety factor of the anisotropic random field is relatively stable, with an average value of about 2, which mainly depends on the strength of the random parameters of the rock mass. Based on the random fluctuation of the value suggested in the engineering report, the simulation result is safe.
Author Contributions
Funding
Conflicts of Interest
References
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Threshold of Correlation Function | Cohesion (MPa) | Friction Angle (°) | Young’s Modulus (GPa) | Poisson’s Ratio | Density (kg/m3) | Geostress (MPa) |
---|---|---|---|---|---|---|
0.5 | 0.1–0.4 | 25–35 | 20 | 0.25 | 2500 | 14.5 |
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Ding, Y.; Zhu, G.; Meng, Q. GPU-Accelerated Anisotropic Random Field and Its Application in the Modeling of a Diversion Tunnel. Sustainability 2023, 15, 6573. https://doi.org/10.3390/su15086573
Ding Y, Zhu G, Meng Q. GPU-Accelerated Anisotropic Random Field and Its Application in the Modeling of a Diversion Tunnel. Sustainability. 2023; 15(8):6573. https://doi.org/10.3390/su15086573
Chicago/Turabian StyleDing, Yu, Guojin Zhu, and Qingxiang Meng. 2023. "GPU-Accelerated Anisotropic Random Field and Its Application in the Modeling of a Diversion Tunnel" Sustainability 15, no. 8: 6573. https://doi.org/10.3390/su15086573