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Research Journal of Mining Volume 1 (2017) Issue 1 Pages 1-11

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NUMERICAL MODELLING FOR CIRCLE TUNNEL UNDER STATIC

AND DYNAMIC LOADS FOR DIFFERENT DEPTH

Jaafar Mohammed1)

1) Department of Geotechnics and Underground Engineering, Faculty of Civil Engineering, VŠB- Technical University of Ostrava, L. Podéště 1875, 708 33, Ostrava-Poruba, Czech Republic, Email:

[email protected]

Abstract: The aim of this paper is to analyse the effects of internal and seismic loads on the stability of circle tunnels at different depth using response spectrum. A full 3D numerical model using the finite element software program MIDAS GTS NX is established. It is often assumed that the effect of earthquakes on underground structures such as tunnels is negligible but the results of this study show that the stress caused by seismic loads can be harmful to the tunnel stability [22].Most of the researcher explains that shallow tunnels suffer higher damage compared to deep structures. During the Shield TBM excavation, it is assumed that the excavation pressure and the Jack thrust are applied on the shield excavation face the Shield external pressure and segment external pressure are applied around that face. This work study a 3D numerical modelling was prepared to simulate the static and dynamic behavior of circular tunnels, were undertaken to investigate the seismic tunnel response conditions to compare the results in the displacement, stresses, forces and bending moments acting in the tunnel lining .

Key words: Tunnel, FEM, Static , Dynamic, Internal Forces,Deep and Shallow Tunnel

1 INTRODUCTION

A tunnel is an underground structure which has different uses. After tunnel modelling

using MIDAS GTS NX, it is run to analyse the tunnel stability in static and dynamic conditions

by calculated the value of each mesh node based on 3D finite element method to simulate the

effect of loads on tunnel stability. The TBM method used depends on such factors as the ground

conditions, length, diameter and depth of the tunnel, etc.

Designing tunnel linings are usually performed accounting for the static cases of loading

only, without considering the effect of earthquakes. Earthquake loads on tunnels are

unpredictable due to the special nature of earthquakes. [29]

During service time, a tunnel could be exposed to dynamic loads. While tunnels

generally performed better than above ground structures during earthquakes, damage to some

of important structures during previous earthquake events highlights the need to account for

seismic loads in the design of underground structures. [26]

Static and dynamic analysis using finite element method were undertaken to investigate

the seismic tunnel response conditions to compare the results with the displacement, stresses,

forces and bending moments acting in the final tunnel lining. In static analysis, when analyzing

a model with infinite material such as ground, boundaries are set far enough from main analysis

area. But in dynamic analysis since effect of waves reflection occurs, if boundaries are set in

the same way as static analysis, big error may occur. (MIDAS GTS NX manual).

Static and dynamic plane strain finite element (FE) analyses were undertaken to

investigate the seismic tunnel response at two sections and to compare the results with the post-


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earthquake field observations. The predicted maximum total hoop stress during the earthquake

exceeds the strength of shotcrete in the examined section. The occurrence of lining failure and

the predicted failure mechanism compare very favourably with field observations. [35]

The sizing of the lining of a tunnel requires to consider not only the static loads

transmitted from the surrounding rock, but also the effects of earthquakes on the stresses and

strains of the lining.[31]

� Sheared off lining: it occurs for tunnel passing through active faults.

� Slopes failure induced tunnel collapse: it occurs when the tunnel runs parallel to slopes

generating landslides passing through the lining;

� Longitudinal cracks: it occurs when the tunnel is subjected to higher deformations due

to surrounding ground;

� Traverse cracks: it occurs when the tunnel has weak joints;

� Inclined cracks: it occurs for a combination of longitudinal and transversal cracks;

� Extended cracks: it occurs when there is the partial collapse of linings for seismic

intense deformation;

� Wall deformation: it occurs when there is a transverse reduction due to the invert

collapse;

� Spilling of lining: it occurs when the transversal section completely collapses.

2 DEFINITION OF GROUND AND STRUCTURAL MATERIALS

This paper studies the 3D model with gravity in Z direction and using SI unit system

(KN, m). The studied parameters of soft rock included modeled of Elasticity model (E=20000

KN/m2) , diameter of tunnel (D=6 m), and 0.3m thickness of concrete lining ,distance between

the external diameter of tunnel and ground surface varying ( for deep tunnel, h=78.4 m and

shallow h=38.4 m), tunnel had 47 stage sets. Automatic ground boundary condition for static

case and ground surface spring to support the bottom for response spectrum; applied loads [self-

weight, Drilling or excavation pressure (200kN/m2), and the Jack thrust (- 4500kN/m2, are

applied on the shield excavation face. The Shield external pressure (50kN/m2) and Segment

external pressure (1000kN/m2) are applied around that face. Design Response Spectrum of

UBC (1997) is used as seismic response spectrum. The model has (x=100, z=80, y=80) m.

Tab. 1 Ground Materials

Name Soft Rock Segment

Material Isotropic Isotropic

Model Type Elastic Elastic

Elastic Modulus (E) [KN/m2] 20000 20000000

Poisson’s Ratio (ν) 0.4 0.2

Unit Weight (γ) [KN/m3] 18 24

Ko 0.5 1

Drainage Parameters Drainage Drainage

Non-Linear - -

Tab. 2 Structure Materials

Name Steel Grout

Material Isotropic Isotropic


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Model Type Elastic Elastic

Elastic Modulus (E) [KN/m2] 25000000 15000000

Poisson’s Ratio (ν) 0.25 0.3

Unit Weight (γ) [KN/m3] 78 23

Tab. 3 Ground Properties

Name Soil Segment Steel Grout

Type 3D 3D 2D- Plate 2D - Plate

Material Soil Segment Steel Grout

3 RESPONSE OF UNDERGROUND STRUCTURES TO EARTHQUAKES

Studies realized in the past have shown that underground structures are less vulnerable

to earthquakes respect to structures built at surface, but the associated risk may be high, since

even a low level of damage could affect the serviceability of a wide network. However

underground structures cannot be considered completely exempt to the effects of ground

shaking.

A careful review of the seismic damages suffered by underground facilities shows that

most tunnels were located in the vicinity of causative faults. The characteristics of ground

motion in the vicinity of the source can be different from that of the farfield.

The ground motion is characterized by strong, coherent (narrow band) long period

pulses and is severely affected by the rupture mechanism, the direction of rupture propagation

relative to the site, and possible permanent ground displacements resulting from fault slip.

The seismic analysis of underground structures is a complex process because involves

the interaction between several disciplines as soil, rock and structural dynamics, structural

geology, seismotectonics and engineering seismology.

The difference between underground structures and surface facilities from the seismic

effects point of view are due, since the overall mass of the structure is usually small compared

with the mass of the surrounding soil and the overall confinement provides high level of

radiation damping. The response of an underground structure to a seismic event is basically

governed by the behavior of the surrounding ground and not by the inertia characteristics of the

structure itself, as the response to such event is substantially depending on the induce ground

deformation.

4 SIMULATION AND CALIBRATION OF THE NUMERICAL MODEL

Static and dynamic analyses has been carried out on the 3D model of the tunnel

structural complex using the MIDAS GTS NX software to investigate the control of tunnel

deformation observed during tunnelling using TBM under earthquake load.

Eigenvalue analysis is used to analyze the inherent dynamic properties of the

ground/structure, and this can be used to obtain the natural mode (mode shape), natural period

(natural frequency), modal participation factor etc. of the ground/structure. These properties are

determined by the mass and stiffness of the structure. In other words, if a structure is

determined, the natural frequency and vibration mode (natural mode) are also determined and

the number of properties is the same as the degree of freedom of the structure. For real cases,

the structure does not vibrate at a single mode shape and multiple modes overlap to display a

complex vibration shape. (MIDAS GTS NX manual)


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Fig.1 Schematic of Slurry Shield TBM and pressure components (a portion of image courtesy

of Herrenknecht) (after Zili LI, et al, 2015).

Fig.2 Mesh Tunnel profile

Fig.3 The static and dynamic case: Max. Displacement [m]


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Fig.4 The static and dynamic case: Shell Element forces [KN/m]

Fig.5 The static and dynamic case: Bending Moment XX [KNm/m]

Fig.6 The static and dynamic case: Shell Element Stresses - Shear MAX [KN/m ^2]


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Fig.7 The Max. Displacement for Shield at #10 in static case for Deep Tunnel

Fig.8 The S-Max. Shear Max. for Shield at #1 in static case for Deep Tunnel

Fig. 9 Total displacement at shallow tunnel


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Fig. 10 Total displacement at deep tunnel

In Figure 9 and 10, the displacement in static and dynamic conditions is shown. Due to

the application of the static stress the displacement state of tunnel periphery is changed, and the

displacement in tunnel to the down is more than to the up side, therefore the balance is disrupted

and the potential of instability increases, otherwise the result show that the applied dynamic

stress is not negligible for underground structure , but it is less than that on the surface structure.

Fig.11 Modified Response Spectrum using UBC(1997); Damping Ration = 0.05; Seismic

Coefficient : Ca = 0.06 Cv = 0.06; Normalized Acceleration

Fig.12 Modified Time History Load Function using The Generate Earthquake Acceleration

Record: 1940, EI Centro Site, 270 Deg.; Peak = 0.3569 g and Duration = 53.72 Sec.


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Fig.13 An example of using the value from Eigenvalue to get the Damping Ratio.

Tab. 4 The result of static analysis for all depth showing the Maximum value

Tab. 5 The result of Dynamic analysis for all depth showing the Maximum value

5 CONCLUSION

It is very important to adequately predict and control ground during the design and

construction of tunnels in urban areas especially at / near earthquake zone. They provide very

good results when tunnelling conditions are well known especially when using numerical

analysis.

The paper includes the study of the behavior of tunnel lining due to internal and seismic

load by calculating the (Displacement, S- MAX Shear, Shear Force and Bending Moment) in

the ground materials (soft rock) during the various stages of construction effected on tunnel

lining.

For static case the maximum value was taken from the last stage, and for dynamic it was

taken from the response spectrum.

During the Shield TBM excavation, it is assumed that the excavation pressure and the

Jack thrust are applied on the shield excavation face. The Shield external pressure and segment

external pressure are applied around that face.

The affect of tunnel under different loads like internal , seismic load and etc. depend on

several state and parameters ,one of this state is the depth of tunnel under ground surface, also

the static and dynamic analysis had different simulation as showing in the tables (4 and 5) and

figures (3 - 6) which show the result of this analysis.

In Figure 9 and 10, the displacement in static and dynamic conditions is shown. Due to

the application of the static stress the displacement state of tunnel periphery is changed, and the

displacement in tunnel to the down is more than to the up side, therefore the balance is disrupted

and the potential of instability increases, otherwise the result show that the applied dynamic

stress is not negligible for underground structure , but it is less than that on the surface structure.


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