Article
Hoek-Brown Failure Criterion-Based Creep Constitutive Model
and BP Neural Network Parameter Inversion for Soft
Surrounding Rock Mass of Tunnels
Chao Chen, Tianbin Li *, Chunchi Ma * , Hang Zhang , Jieling Tang and Yin Zhang
Citation: Chen, C.; Li, T.; Ma, C.;
Zhang, H.; Tang, J.; Zhang, Y.
Hoek-Brown Failure Criterion-Based
Creep Constitutive Model and BP
Neural Network Parameter Inversion
for Soft Surrounding Rock Mass of
Tunnels. Appl. Sci. 2021, 11, 10033.
https://doi.org/10.3390/
app112110033
Academic Editor: Nikos D. Lagaros
Received: 16 August 2021
Accepted: 19 October 2021
Published: 26 October 2021
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4.0/).
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, College of Environment and
Civil Engineering, Chengdu University of Technology, Chengdu 610059, China; xchenchaox@126.com (C.C.);
zhanghang_nn720@163.com (H.Z.); tangjieling@stu.cdut.edu.cn (J.T.); zhangyin0503@gmail.com (Y.Z.)
* Correspondence: ltb@cdut.edu.cn (T.L.); machunchi17@cdut.edu.cn (C.M.)
Abstract:
This paper summarizes the main factors affecting the large deformation of soft rock tunnels,
including the lithology combination, weathering effect, and underground water status, by reviewing
the typical cases of largely-deformed soft rock tunnels. The engineering geological properties of
the rock mass were quantified using the rock mass block index (RBI) and the absolute weathering
index (AWI ) to calculate the geological strength index (GSI). Then, the long-term strength
σ
r
and the
elastic modulus
E
0
of the rock mass were calculated according to the Hoek–Brown failure criterion
and substituted into the creep constitutive model based on the Nashihara model. Finally, the creep
parameters of the surrounding rock mass of the Ganbao tunnel were inverted and validated by
integrating the on-site monitoring and BP neural network. The inversion results were consistent
with the measured convergence during monitoring and satisfied the engineering requirements of
accuracy. The method proposed in this paper can be used to invert the geological parameters of the
surrounding rock mass for a certain point, which can provide important mechanical parameters for
the design and construction of tunnels, and ensure the stability of the surrounding rock mass during
the period of construction and the safety of the lining structure during operation.
Keywords:
tunnel engineering; soft rock; creep parameter; parameter inversion; BP neural network
1. Introduction
Tunnel projects in western China often encounter soft rocks with well-developed
bedding, such as carbonaceous phyllite, sericite phyllite, schist, carbonaceous slate, sandy
slate, and carbonaceous shale. Under high in situ stress, the laminated soft surrounding
rock masses are vulnerable to large and rapid deformation and local destruction [
1
–
3
]. In
these conditions, tunnels frequently suffer from large deformation hazards.
Laminated rock mass, frequently seen in engineering practice and presenting oriented
grouped bedding, has more heterogeneous mechanical properties than normal rock mass.
Many researchers have developed constitutive models for laminated surrounding rock
masses. For instance, Jia et al. [
4
] applied the microscopic element method with the
constitutive model based on damage mechanics and statistical theory to the simulation
of rock tunnel stability using the finite element method (FEM). Li et al. [
5
] developed a
three-dimensional creep constitutive model for transversely isotropic rock mass, based
on the Burgers viscoelastic model. Li et al. [
6
] proposed three basic creep patterns of
shale and a general methodology for developing the anisotropic creep model. These
constitutive models have been used to probe the deformation and failure characteristics
of laminated rock masses with varied dip angles. However, research on the constitutive
theory of laminated surrounding rock masses in tunnels is fairly limited and cannot
provide the theoretical guidance for the engineering design of actual tunnels. In terms
of the mechanisms of laminated rock mass deformation, previous studies have mainly
Appl. Sci. 2021, 11, 10033. https://doi.org/10.3390/app112110033 https://www.mdpi.com/journal/applsci
