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Evaluation and Application of Numerical Computation Software in Stability Analysis of Tunnel Engineering Ruilang CAO，Lifeng ZHENG State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, China

Key words：Tunneling engineering; Numerical simulation; Finite element method; Finite difference method

Abstract: Numerical software is widely used in stability analysis of tunnel engineering, but difference among different software has always been the focus of attention. This paper presents a comparative study of the most commonly used numerical software in tunnel engineering calculations, including ABAQUS, ANSYS, MIDAS-GTS and FLAC3D. With the same tunnel boundary conditions, geological parameters and numerical model adopted, the results of four kinds of software on the deformation of the surrounding rock, the stress of the lining and the distribution of the yielding area are compared. The results show that: 1) The deformation and change trend of the surrounding rock are basically the same, only that the results of MIDAS-GTS are slightly larger than others (2) The calculation of lining stress differs very little from each other and distributes irregularly (3) FLAC3D takes into account the effect of the stress path on the plastic state, the distribution of plastic zone calculated by that differs a little larger than others 4) Overall, the stability of the tunnel project reflected by results of four software is relatively similar, all four software can be used for engineering practice.

Key words: Tunneling engineering; Numerical simulation; Finite element method; Finite difference method

1 Introduction Tunnel engineering possesses the characteristics of strong complexity and particularity. Empirical method is used to predict the stability of the surrounding rock and the stress of the lining structure will be constrained by the number of statistical samples, the difference of the tunnel size and surrounding rocks. And theoretical method can only be applied to the circular section tunnel. Numerical analysis method is increasingly valued by tunnel engineering researchers for its convenient and fast features. At present, the numerical method of tunnel engineering is mainly based on finite element method and fast Lagrangian difference method. ,Lots of software are developed based on these two methods, and many research results have been obtained. Jia et al. [1] analyzed the mechanical failure behavior of tunnels under different angles of jointed rock mass; Funatsu et al. [2] analyzed the effect of prestressed support structure on tunnel stability; Lee et al. [3] simulated elastic plastic analysis of soft rock wall in circular tunnel Hejazi et al. [4] analyzed the effect of constitutive model on underground engineering,; Azadi et al. [5] analyzed the seismic performance of shallow-buried tunnels in liquefiable sites; Deb et al. [6] analyzed The effect of prestressed anchor on stratum deformation in tunnel excavation; Fernadez et al. [7] simulated the hydraulic conductance during tunnel excavation. The research above shows that the numerical simulation method can be applied to a variety of complex geological conditions as well as shapes and sizes of the tunnel, the calculation process is convenient, fast, while intuitive contours of stress, strain can be extracted. Therefore, numerical simulation will continue to play an important role in future study of tunnel stability.

Although numerical software has been widely used in the stability analysis of tunnel engineering, almost little research about difference of the calculation results among software is done. In this paper, the comparative study of the most commonly used numerical software in tunnel engineering is carried out, and the difference evaluation is made to provide a comprehensive understanding and grasp of the reliability and accuracy. It is important source of reference. for the selection of numerical software for tunnel engineering 2 Numerical calculation software and its characteristics With the development of mathematics, mechanics theory and computer technology, numerical analysis methods have been applied in engineering geology and geotechnical engineering, and widely used as an important tool to solve such engineering problems in complex media and boundary conditions. A study is conducted by retrieving articles for tunnel engineering stability analysis involving numerical software; The results show that the following numerical software is the most widely used ones: FLAC3D (27934 related papers or patents); ABAQUS (18237); MIDAS-GTS (9266), ANSYS (8513). The characteristics of the four software are listed in Table 1:

3 Numerical calculation case and model In the four numerical software comparative analysis, the same tunnel size, grid division of model, surrounding rock and structural support parameters, construction conditions are adopted. Surrounding rock is of Class IV, the tunnel is circular and radius is 3.05m. The excavation method is full-section excavation. In order to make the calculation results more representative, both cased with initial support and without initial support of are simulated, each step of the construction footage is1m and tunnel is buried in depth of 250m, In initial support conditions, the initial support lags a distance of 3 m behind excavation face. In the model, the Z axis is the direction of the tunnel axis, the X axis is along left to right direction, and the Y axis is the vertical direction. The numerical model geometry is: x × y × z = 60m × 60m × 20m. Numerical calculation model and data monitoring line layout are shown in Figure 1, model grid in various software are consistent. The physical and mechanical properties of surrounding rock and support are shown in Table 2.

Figure 1, Numerical calculation model and data monitoring line layout

Table 2 The physical and mechanical properties of surrounding rock and support Parameter	Rock mass (the mesh number is 85932)	Lining (the mesh number is 1920) Deformation modulus	Poisson ratio	Internal friction angle	Cohesion	Density	Deformation modulus	Poisson ratio	Density Symbol	Er	μr	βr	Cr	ρr	Ec	μc	ρc Unit	GPa	-	°	MPa	Kg/m3	GPa	-	Kg/m3 Value	1.0	0.32	32	0.2	2400	15	0.167	2600

4 Calculation result Surrounding convergence of tunnel is the relative displacement value of two fixed point connections in opposite direction around the tunnel, which is the most intuitive performance of the deformation caused by tunnel excavation. As shown in Fig. 2, the convergence rules of FLAC3D, ABAQUS, ANSTS and MIDAS-GTS are basically the same.

(a)FLAC3D                            (b)ABAQUS (c) ANSYS                           (d) MIDAS-GTS Fig. 2 Vertical displacement of tunnel surrounding rock Figure 3 shows the longitudinal curves of tunnel surrounding rock deformation. At first, the surrounding rock deformation is very small. Then, the longitudinal deformation of the surrounding rock which is plotted as the process curve increases with the increasing distance of the palm surface. Finally, the deformation of the surrounding rock tends to be stable when the distance reaches a certain value (generally 3 times tunnel diameter). Coordinates of the Z axis (unit: m)                                    Coordinates of the Z axis (unit: m)   (a) Tunnel crown                            (b) Tunnel wall Fig.3 Longitudinal curves of tunnel surrounding rock deformation

By Comparing the surrounding rock deformation of monitoring line A and monitoring line B, the study shows that the results of the four kinds of software reflect the same deformation trend (see figure 4). Moreover, the values in Monitoring line B are basically consistent Coordinates of the A axis (unit: m)                       Coordinates of the B axis (unit: m)    (a) Line A                            (b) Line B Fig. 4 Monitoring value of surrounding rock deformation Difference among the values of the stress calculated by the four numerical software are small: the maximum value is 20.48MPa by FLAC3D, the minimum value of 17.23MPa by ANSYS, difference between the two is about 15% (Figure 5), The calculation accuracy can meet the engineering application requirement.

(a) FLAC3D（Unit：Pa）                (b) ABAQUS（Unit：Pa） (c) ANSYS（Unit：Pa）            (d) MIDAS-GTS（Unit：MPa） Fig.5 Compressive stress distribution of tunnel lining As is shown by distribution pattern of plastic area in surrounding rock (Fig. 6) The results of ABAQUS, ANSYS and MIDAS-GTS are consistent, and the maximum depth of plastic zone is 0.5m-1.2m.. Figure 6 shows the plastic zone distribution of the surrounding rock of the tunnel. The plastic zone of the four software calculations is slightly different in depth and range. Plastic zone distribution calculated by FLAC3D differentiates quite large compared with other, 2 times larger than the yield range of other. This is mainly because criteria of plastic zone in FLAC3D is rather special, it not only takes into account the plastic yield criterion of the material, but also consider the effect of the stress path on the plastic state. Flac3D divides the plastic zone type into Shear-n, Shear-p, Tension-n and Tension-p, while the plastic regions of other software are reduced to the same type. Calculation results of the stability of the surrounding rock are shown in Table 3. Overall, the four software results reflect the stability of the tunnel project is relatively similar, and can be used for engineering practice. (a)FLAC3D       (b)ABAQUS       (c) ANSYS       (d) MIDAS-GTS Fig. 6 Distribution pattern of plastic zone in surrounding rock Table 3 Calculation results of stability of tunnel surrounding rock

Working condition	Software	Displacement of rock mass/cm	Plastic zone/m	Lining stress /MPa Inflected arch	Side wall	Crown	Depth	Tensile	Compressive With support	FLAC3D	3.08	3.01	2.63	1.28	-0.35	-20.48 ABAQUS	2.57	2.50	2.11	0.60	-0.45	-19.62 ANSYS	3.00	2.91	2.52	0.87	-0.39	-17.23 MIDAS-GTS	3.77	3.52	3.18	0.60	-0.30	-17.78 Without support	FLAC3D	4.14	3.93	3.48	1.27	-	- ABAQUS	3.5	3.32	2.82	0.29	-	- ANSYS	3.52	3.68	3.07	0.42	-	- MIDAS-GTS	5.22	4.64	4.39	0.57	-	-

5 Conclusions In this paper, Application of four software (ABAQUS, ANSYS, MIDAS-GTS and FLAC3D )in tunnel engineering stability analysis is evaluated: The results show that: 1) the morphological and changing trend of the surrounding rock is basically the same, only that the calculation results of MIDAS-GTS are large in the value; 2) the difference of the stress among four is small, and the distribution rule is same; 3) FLAC3D takes into account the effect of stress path on the plastic state, and its calculated law of the plastic zone of the surrounding rock is different from that of other software. 4) Overall, the stability of the tunnel project reflected by four software is relatively similar, all four can be used for engineering practice.