Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 11, No. 1, 2024 

 

274 

Tunnel	excavation	based	on	FLAC3d	numerical	
simulation	
Shihao Guo1, *, Bangbang Mu2, Mingyang Zhao3, Huiyan Wang4 

1 School of Energy Science and Engineering, Henan Polytechnic University, China 
2 School of Energy Science and Engineering, Henan Polytechnic University, China 
3 School of Energy Science and Engineering, Henan Polytechnic University, China 
4 Vocational and Technical Education Center, Tangyin County, Anyang City, Henan Province, China 
* Corresponding author: Guo Shihao (Email: 1809175902@qq.com) 

 

Abstract: A semi-circular arch straight wall tunnel with a span of 10m, a side wall height of 5m and a buried depth of 500m 
is excavated in a class IV surrounding rock. Assuming that the surrounding rock is an ideal elastoplastic material, the following 
problems are analyzed by using finite element or finite difference method: the arch roof subsidence and the horizontal 
convergence of the side wall after tunnel excavation under the action of gravity stress field and the size of the plastic zone in the 
surrounding rock. If the lateral pressure coefficient is 0.5-3, the effects of structural stress on the subsidence of the tunnel arch, 
the horizontal convergence of the side wall and the plastic zone are analyzed. If the bolt support is adopted after excavation, the 
system bolt shall be laid on the tunnel arch and side wall. The bolt shall be a full-length metal bolt, perpendicular to the tunnel 
wall, with a spacing of 1.5m, a length of 3.0m, and a diameter of 25mm. The thickness of shotcrete is 100mm, the number is 
C20, and the supporting effect is analyzed. 

Keywords: Numerical simulation; FLAC3d; Tunnel excavation. 
 

1. Introduction 
The finite element calculation method is often used in the 

numerical analysis of engineering structures, and FLAC3D is 
different from other finite element programs in that it uses the 
finite difference method [1-4]. In the finite difference method, 
the system of fundamental equations and boundary conditions 
(generally differential equations) are approximately 
expressed by difference equations (algebraic equations), i.e., 
they are replaced by algebraic expressions of field variables 
(stress, displacement) at discrete points in space [5-9]. These 
variables are non-deterministic within the unit, so that the 
problem of solving differential equations can be replaced by 
solving algebraic equations, and the finite difference equation 
can be regenerated relatively efficiently at each calculation 
step [10-13]. In the finite element method, implicit and matrix 
solutions are often used, while the finite difference method is 
usually used to solve algebraic equations using explicit and 
time-recurring methods [14,15]. The FLAC3D program has 
powerful post-processing capabilities that allow users to 
create and output multiple forms of graphics directly on the 
screen or as files, as well as to combine several variables in 
the same graph for research and analysis as needed [16]. 

2. Modeling 
Since the radius of the tunnel is 5m, and the radius of the 

tunnel is 6 times as the affected area of the surrounding rock 
according to experience, so 30m is taken as the boundary, and 
the side length of the mesh is 0.5m, so we only need to analyze 
the force and displacement on the x-z plane, and the specific 
model is shown in the figure. 

 

 
Figure 1. Model of the tunnel before excavation 

 

 
Figure 2. Model of the tunnel after excavation 

3. Tunnel Excavation 
Format and save your graphic images using a suitable 

graphics processing program that will allow you to create the 
images as PostScript (PS), Encapsulated PostScript (EPS), or 
Tagged Image File Format (TIFF), sizes them, and adjusts the 
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the following you will be able to submit the graphics without 
converting to a PS, EPS, or TIFF file: Microsoft Word, 
Microsoft PowerPoint, Microsoft Excel, or Portable 
Document Format (PDF). 

The M-C model was used for surrounding rock, and the 



 

275 

parameters were selected as follows: rock density (kg/m3) 
=2200; Acceleration of gravity (kg/N) =10; Volume modulus 
(Pa)=5e10; Shear modulus (Pa)= le10; Friction Angle =30°; 
Cohesion (N)=18e7; Tensile strength (N/m2) =1e7. The stress 
applied at the Z=30m plane is yh=22000x(500-
30)=10.34e6N/m². 

 

 
Figure 3. Model of the tunnel when it is not excavated 

 

 
Figure 4. The plastic zone of the cavity after excavation 

 

 
Figure 5. Displacement contour in the Z direction after excavation 

 

 
Figure 6. Displacement contour in the X direction after excavation 

 
Figure 7. Displacement curve in the Z direction after excavation  

 

 
Figure 8. Displacement curve in the X direction after excavation 

 

 
Figure 9. Stress in the Z direction after excavation 

 

 
Figure 10. Stress in the X direction after excavation 

 
It can be seen that the vault sinks 4.775mm without support 

after excavation, the horizontal convergence of the side wall 
is 2.996mm, and the plastic zone of the surrounding rock is 
shown in the figure above. 

4. The Influence of Side Pressure 
Coefficient 

The plastic zones after excavation with different side 
pressure coefficients are shown in the figure below: 

 
 
 
 



 

276 

 
Figure 11. λ=0.5 

 

 
Figure 12. λ=1 

 

 
Figure 13. λ=1.5 

 

 
Figure 14. λ=2 

 

 
Figure 15. λ=2.5

 
Figure 16. λ=3 

 
With the increase of the lateral pressure coefficient, the 

plastic zone of the tunnel top and the side wall is gradually 
increasing, and the vault expands more, when the lateral 
pressure coefficient is 2.5, the plastic zone expands sharply 
and cannot be self-stable.  

The displacement contours in the Z direction after 
excavation with different lateral pressure coefficients are 
shown in the figure below: 

 

 
Figure 17. λ=1.5 

 

 
Figure 18. λ=2 

 

 
Figure 19. λ=1.5



 

277 

 
Figure 20. λ=2 

 

 
Figure 21. λ=2.5 

 

 
Figure 22. λ=3 

 
The displacement curves in the Z direction of the vault after 

excavation with different lateral pressure coefficients are 
shown in the following figure: 

 

 
Figure 23. λ=0.5 

 
Figure 24. λ=1 

 
Figure 25. λ=1.5 

 

 
Figure 26. λ=2 

 

 
Figure 27. λ=2.5 

 

 
Figure 28. λ=3 

 
The stress contour diagram in the Z direction after 

excavation with different lateral pressure coefficients is 
shown in the figure below: 

 

 
Figure 29. λ=0.5



 

278 

 
Figure 30. λ=1 

 

 
Figure 31. λ=1.5 

 

 
Figure 32. λ=2 

 

 
Figure 33. λ=2.5 

 

 
Figure 34. λ=3 

 
The displacement contours in the X direction after 

excavation with different lateral pressure coefficients are 

shown in the figure below: 
 

 
Figure 35. λ=0.5 

 

 
Figure 36. λ=1 

 

 
Figure 37. λ=1.5 

 

 
Figure 38. λ=2 

 

 
Figure 39. λ=2.5



 

279 

 
Figure 40. λ=3 

 
The displacement curves in the X direction of the vault 

after excavation with different lateral pressure coefficients are 
shown in the figure below: 

 

 
Figure 41. λ=0.5 

 

 
Figure 42. λ=1 

 

 
Figure 43. λ=1.5 

 

 
Figure 44. λ=2 

 
Figure 45. λ=2.5 

 

 
Figure 46. λ=3 

 
The stress contour diagram in the X direction after 

excavation with different lateral pressure coefficients is 
shown in the following figure: 

 

 
Figure 47. λ=0.5 

 

 
Figure 48. λ=1 

 

 
Figure 49. λ=1.5 



 

280 

 
Figure 50. λ=2 

 

 
Figure 51. λ=2.5 

 

 
Figure 52. λ=3 

 
It can be seen that with the increase of the lateral pressure 

coefficient, the vertical displacement of the vault and the 
horizontal displacement of the side wall increase 
correspondingly, and the horizontal displacement increases 
faster than the vertical displacement. The plastic zone 
increases with the increase of the lateral pressure coefficient, 
and the plastic zone at the vault increases more. This indicates 
that the horizontal tectonic stress has a great influence on the 
horizontal displacement of the side wall and the plastic zone 
of the vault. 

 
Table 1. Statistical table 

Lateral 
pressure 

coefficient
（λ） 

0.5 1 1.5 2 2.5 3 

Vault vertical 
displacement 

(mm) 
2.861 2.988 4.217 6.222 8.142 1.198 

Horizontal 
displacement 
of side wall 

(mm) 

2.052 3.253 4.949 7.200 9.963 1.319 

5. Bolt Support After Tunnel 
Excavation 

The calculation result after support is as follows: 

 
Figure 53. Plastic zone before support  

 

 
Figure 54. Plastic zone after support 

 

 
Figure 55. Stress of the bolt  

 

 
Figure 56. Relative position of the bolt and the plastic zone 

 

 
Figure 57. X-direction displacement contour after support  

 



 

281 

 
Figure 58. Z-direction displacement contour after support   

 

 
Figure 59. Stress contour in the X direction after support  

 

 
Figure 60. Stress contour in the Z direction after support   

 

 
Figure 61. Displacement curve in X direction after support  

 

 
Figure 61. Displacement curve in Z direction after support 

 
As can be seen from the figure, the plastic zone after 

support is obviously much smaller than that without support, 
and the stress of the surrounding rock after support is 
improved, and the vertical displacement and horizontal 
displacement are reduced. A turning point can be clearly seen 
in the displacement curve, which is caused by the restriction 
of the deformation of the surrounding rock after the 
application of the initial support, which prevents the further 
deformation of the surrounding rock. 

 
Table 2 Comparison table before and after support 

 Vault vertical 
displacement X0 

(mm) 

Horizontal 
displacement of 

side wall Z0 (mm) 
Pre-support 3.181 5.199 

After supporting 1.622 3.625 

6. Conclusion  
After in-depth study of FLAC3D numerical simulation of 

tunnel excavation process, we draw the following conclusions: 
(1) During tunnel excavation, the stress distribution of 

surrounding rock changes significantly. At the beginning of 
excavation, the stress concentration around the tunnel is 
obvious, especially at the top and bottom of the tunnel, there 
are relatively concentrated tensile stress and compressive 
stress. With the progress of excavation, the stress gradually 
tends to be stable, but there is still a phenomenon of stress 
concentration in some areas, and special attention should be 
paid to the support design in these areas. 

(2) FLAC3D simulation results show that the surrounding 
rock has obvious displacement and deformation after tunnel 
excavation. Among them, the subsidence deformation at the 
top and bottom of the tunnel and the convergence deformation 
of the side wall are the main deformation forms. These 
deformations are affected by many factors, including 
geological conditions, excavation methods, support measures, 
etc. Through reasonable support design and construction 
scheme, the displacement and deformation of surrounding 
rock can be effectively controlled. 

(3) Numerical simulation results show that the stress and 
displacement deformation of surrounding rock are effectively 
controlled after adopting reasonable support measures. The 
supporting structure can effectively share the stress of 
surrounding rock, reduce the phenomenon of stress 
concentration, and limit the displacement and deformation of 
surrounding rock. Therefore, in the process of tunnel 
excavation, it is very important to select the appropriate 
supporting structure types and parameters. 

Based on the above conclusions, we suggest that geological 
conditions and construction conditions should be fully 
considered in the process of tunnel excavation, and 
appropriate excavation methods and support measures should 
be selected. At the same time, on-site monitoring and data 
analysis should be strengthened to discover and deal with 
possible safety hazards in a timely manner. In addition, the 
construction scheme and support design should be 
continuously optimized to improve the safety and economy of 
tunnel excavation. 

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