Introduction to the Special Issue: Nonlinearity and numerical simulation applications in geotechnical engineering
Bingxiang Yuan1 , Yixian Wang2 , Hang Lin3 , Chunshun Zhang4
1School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou, 510006, China
2School of Civil Engineering, Hefei University of Technology, Hefei, 230009, China
3School of Resources and Safety Engineering, Central South University, Changsha, 410083, China
4Department of Civil Engineering, Monash University, Melbourne, Australia
Journal of Vibroengineering, Vol. 21, Issue 4, 2019, p. 816-818.
Accepted 28 June 2019; published 30 June 2019
Special Issue on Nonlinearity and Numerical Simulation Applications in Geotechnical Engineering
In the very early engineering design, engineers simplified the deformation behavior, constitutive model and failure mechanism of rock and soil, which were limited to the scope of linear elasticity. Later, with the development of geotechnical engineering, the scale of engineering became larger and larger, and the problems involved became more and more complicated, and engineering accidents caused by computing defects became more and more serious. Thus, scholars have realized that it is not enough to treat rock and soil simply as a linear elastic material. Nonlinear and numerical simulation is indispensable in geotechnical engineering.
Finite element method is the most widely used numerical simulation method in geotechnical engineering. In recent years, scholars have applied finite element analysis software in slope stability analysis [1-3], tunnel excavation , foundation pit excavation  and other fields. For example, based on the generalized Biot’s dynamic consolidation theory, Zou et al.  analyzed saturated soils by using the polygon scale boundary finite element method, and the results are in good agreement with the computations of finite element method.
The finite difference method is an old numerical simulation method. In the 1980s, the ITASCA company of the United States developed the FLAC program based on the finite difference method. Subsequently, this method is widely used in numerical simulation of geotechnical engineering [7, 8]. Liu et al.  used a finite difference time domain method to establish a three-dimensional hole-bedrock-cave model for sonar detection of karst cavities. Kim and Larson  used FLAC3D to model the initiation and initial evolution of a strike-slip fault, and FLAC3D successfully replicated and created 3D fault zone of strike-slip faults within the entire thickness range of the model. There is also a paper in this Special Issue that utilizes the finite difference method in geotechnical engineering, “Numerical Analysis of Hard Rock Tunnel Excavated by Double Shield TBM based on CWFS model, Diyuan Li, Jing Sun, Quanqi Zhu, Xiangyun Xu, Jian Jiao”. In their article, Flac3D was utilized to evaluate the practicability of DS-TBM (double shield tunnel boring machine) in a deep-buried high geostress tunnel.
Compared with the finite element method, the advantage of the boundary element method is that it can simplify the calculation by dimension reduction. Mostly, the boundary element method is mainly utilized in an excavation of underground engineering , analysis of soil structure interaction [12, 13] and seepage analysis . Based on the boundary element method, Auersch  proposed a method combining the finite element boundary element method to calculate the dynamic interaction between soil mass and flexible structures such as single pile or complete wind tower. Xiao  proposed a boundary element method based on system partition and coupling strategy.
There are two kinds of geotechnical materials targeted by the discrete element method: one is granular geotechnical material, the other is continuum material. The application of the discrete element method on geotechnical engineering was developed in a paper of this Special Issue: “Numerical simulation of hydraulic fracturing in transversely isotropic rock masses based on PFC2D, Lei Xia, Yawu Zeng”. In their article, the bonded-particle element method with embedded smooth joints was applied to establish the transversely isotropic rock masses.
In addition, “Macroscopic and microscopic simulation of silo granular flow based on improved multi-element model, Feng Yong, Yuan Ziran”, a paper about the improvement of discrete element numerical simulation, was also included in this Special Issue. In their article, an improved multi-element model consisting of clump elements and ball elements was proposed.
The fracture mechanics no longer regards materials as a homogeneous continuum, but as composite structures with many defects and cracks. The strength analysis of the material is based on the analysis of these defects and cracks. The optimum penetration depth and the synergistic effect of TBM (Tunnel Boring Machine) rock breaking under the different cutter spacings was investigated by Wang Zhu, Cao Ping, Chen Yu, in their paper “Study on the optimum penetration depth by two TBM cutters under different cutter spacings”. In their article, a series of studies based on fracture mechanics were analyzed through a model test.
There are still many nonlinearity numerical simulation methods suited for geotechnical engineering which was not mentioned above. The coordination of multiple numerical simulation methods has also become a problem that needs to be solved.
- Oberhollenzer S., Tschuchnigg F., Schweiger H. F. Finite element analyses of slope stability problems using non-associated plasticity. Journal of Rock Mechanics and Geotechnical Engineering, Vol. 10, Issue 6, 2018, p. 1091-1101. [Publisher]
- Dyson A. P., Tolooiyan A. Prediction and classification for finite element slope stability analysis by random field comparison. Computers and Geotechnics, Vol. 109, 2019, p. 117-129. [Publisher]
- Liu Y., Zhang W., Zhang L., et al. Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods. Geoscience Frontiers, Vol. 9, Issue 6, 2018, p. 1657-1664. [Publisher]
- Hounyevou Klotoé C., Bourgeois E. Three dimensional finite element analysis of the influence of the umbrella arch on the settlements induced by shallow tunneling. Computers and Geotechnics, Vol. 110, 2019, p. 114-121. [Publisher]
- Chheng C., Likitlersuang S. Underground excavation behaviour in Bangkok using three-dimensional finite element method. Computers and Geotechnics, Vol. 95, 2018, p. 68-81. [Publisher]
- Zou D., Teng X., Chen K., et al. An extended polygon scaled boundary finite element method for the nonlinear dynamic analysis of saturated soil. Engineering Analysis with Boundary Elements, Vol. 91, 2018, p. 150-161. [Publisher]
- Pasculli A., Calista M., Sciarra N. Variability of local stress states resulting from the application of Monte Carlo and finite difference methods to the stability study of a selected slope. Engineering Geology, Vol. 245, 2018, p. 370-389. [Publisher]
- Yuan B., Sun M., Wang Y., et al. Full 3D displacement measuring system for 3D displacement field of soil around a laterally loaded pile in transparent soil. International Journal of Geomechanics, Vol. 19, Issue 5, 2019, p. 401928. [Publisher]
- Liu L., Shi Z., Peng M., et al. Numerical modeling for karst cavity sonar detection beneath bored cast in situ pile using 3D staggered grid finite difference method. Tunnelling and Underground Space Technology, Vol. 82, 2018, p. 50-65. [Publisher]
- Kim B., Larson M. K. Development of a fault-rupture environment in 3D: A numerical tool for examining the mechanical impact of a fault on underground excavations. International Journal of Mining Science and Technology, Vol. 29, Issue 1, 2019, p. 105-111. [Publisher]
- Beer G., Duenser C. Advanced 3-D boundary element analysis of underground excavations. Computers and Geotechnics, Vol. 101, 2018, p. 196-207. [Publisher]
- Chen D., Dai S. Dynamic fracture analysis of the soil-structure interaction system using the scaled boundary finite element method. Engineering Analysis with Boundary Elements, Vol. 77, 2017, p. 26-35. [Publisher]
- Yuan B., Chen R., Deng G., et al. Accuracy of interpretation methods for deriving p-y curves from model pile tests in layered Soils. Journal of Testing and Evaluation, Vol. 45, Issue 4, 2016, p. 20150484. [Publisher]
- Johari A., Heydari A. Reliability analysis of seepage using an applicable procedure based on stochastic scaled boundary finite element method. Engineering Analysis with Boundary Elements, Vol. 94, 2018, p. 44-59. [Publisher]
- Auersch L. Compliance and damping of piles for wind tower foundation in non-homogeneous soils by the finite-element boundary-element method. Soil Dynamics and Earthquake Engineering, Vol. 120, 2019, p. 228-244. [Publisher]
- Xiao L., Zhao G., Qing H. A compatible boundary element approach with geologic modeling techniques to model transient fluid flow in heterogeneous systems. Journal of Petroleum Science and Engineering, Vol. 151, 2017, p. 318-329. [Publisher]