Influence of Segmental Joints in the Segmental Circular Tunnel Lining under the Impact of Earthquakes

At present, the underground construction system is developing very strongly in the world and in Vietnam. In particular, the metro tunnel system was developed very rapidly due to its ability to serve in the urban transport system. Most tunnels in the metro system today use the segmental tunnel lining, which has segmental joints in the segmental tunnel lining due to its advantages. Tunnels these have circular cross section are very popular in metro tunnels system. In this paper, the methods of calculating the impact of earthquake on tunnels lining in the case of the tunnel has lining continuous or segmental (with segmental joints between segments of lining tunnel) have been used to comparisons of internal forces, displacement of tunnel lining in two cases under the impact of earthquake and comments about effects of segmental joints in the segmental tunnel lining. This paper is used as a case study for the Hanoi metro tunnel. Keyword Tunnel, segmental lining, earthquake, joints, effect, earthquake.

Some characteristics of the strongest earthquakes that can occur in the Hanoi area are [15]: -Earthquake has got magnitude maximum M W of 6.5; -Distance from the epicentre of the earthquake, that has got magnitude maximum to Hanoi centre is 20 to 50 km and peak ground acceleration a max = 0.2 g.
Parameters of layers soils in Hanoi centre, where has got the metro tunnel, these have been determined through extensive in situ and laboratory tests (in Table I).  [10] In 1993, Wang given this method that could calculation for the tunnel lining continuous under the impact of the earthquake. In this method, has got two case of, in the first case: full -slip at the soil -lining tunnel's, the internal forces on the tunnel lining can be written:

A. Wang's Method
W h e r e 1 12(1 ) In case no-slip at the soil -lining tunnel's, only the normal forces (T) can be expressed by Wang [1993]: (1 ) In 2013, Kouretzis el al proposed an equation of the maximum bending moment in lining tunnel under no slip condition when effect dynamic loading, this to improve the Wang's method.
Where max  -the maximum free field seismic shear stress, max  -density of the surround ground, max G -the maximum ground shear modulus, max V -the peak seismic velocity due to shear wave propagation.
Where K 1 is full-slip lining response coefficient; K 2 is no-slip lining response coefficient; F is flexibility ratio of tunnel lining; C is compressibility ratio of tunnel lining; E s is Young's modulus of tunnel lining; ν s is Poisson's ratio of tunnel lining; R is tunnel radius; t is thickness of tunnel lining; J s is inertia moment of tunnel lining per unit length of the tunnel (per unit width); ν l is Poisson's ratio of ground mass surrounding the tunnel lining; E is Young's modulus of ground mass surrounding the tunnel lining; G is shear modulus of ground mass surrounding the tunnel lining; ; I is moment of inertia of the tunnel lining; γ max is maximum free-field shear strain; θ is angle measured counter-clockwise from spring line on the right; T is normal forces and M is bending moment in the tunnel lining. B. Penzien's Method [11]- [12] Penzien&Wu (1998) and Penzien (2000) given similar analytical solutions for the internal forces on the tunnel lining. In case full-slip condition at the soil-lining: 3 2 12 With the case of no-slip condition: 3 2 24 (3 4 ) (1 ) C. HRM Method [1], [16]- [18] Method HRM is a direct method. This is part of the numerical method, method HRM used to Matlab program to construction model of tunnel lining and environment ground surrounding tunnel [16]- [17]. This method simulates the interaction between the lining and ground surrounding the tunnel through a number of independent "Winkler" type springs. The method HRM requires the definition of the active loads that apply directly to the support structure. These loads can be estimated using different methods of Mashimo and Ishimura [18].
Note: In case of the tunnel has got impact of the earthquake, method HRM needed to adjust: all the external loads are rotated counter-clockwise by 45 0 and the horizontal loads are in opposite directions.

D. 2D Numerical Method
The soil environment around the tunnel and the tunnel lining behave linearly and elastically. In this method, has not got effect of gravity and drained conditions. A time history analysis has carried out using data of El Centro earthquake [19] (with characteristics of the El Centro earthquake almost identical to characteristics of the strongest earthquake that can occur in the Hanoi) -M w = 6.5 richter (in Fig. 2). 2D numerical method be calculation for case no-slip at the soil -lining tunnel's.  Make comparisons of results obtained by different methods (in Table II). It was found that with the first three methods, Wang's analytical method, Pezien and Wu's analytical method, and 2D numerical method using Abaqus program, the results were quite close to each other and the deviation was not large. With the HRM method, in the case of the tunnel lining continuous, the internal forces obtained on the tunnel lining is not significantly different from the results of the above three methods, however. In the case of the segmental tunnel lining with the presence of segment joints in the tunnel lining, the internal forces on the tunnel lining significantly reduced, which is typical of the stresses on the tunnel lining. The displacement of this tunnel lining also increased compared to the case the tunnel lining is continuous.  Similarly, compared with the stress value on the tunnel lining. The maximum stress on the tunnel lining continuous of the Wang's method was not significantly different from the maximum stress on the tunnel lining continuous in the Pezien's method (difference of 2.328%), with the HRM method, the difference between the maximum stress in the tunnel lining continuous is 2.577%, the difference in the maximum stress of the Wang's method with the 2D numerical method -used Abaqus program is only 1.546%. However, when comparing the maximum stress value in the tunnel lining continuous of the Wang's method with the maximum stress in the segmental tunnel lining of the HRM method, the difference value is quite large, up to 12.94%. With a comparison of displacement values of the tunnel lining, there is a significant difference for displacements -d max of the tunnel lining is 42.85% in two cases: the tunnel lining continuous (d max = 2.8 mm) and the segmental tunnel lining with segmental joints (d max = 4 mm), could give conclusions: Under the effect of segmental joints, the segmental tunnel lining is much more flexible, thereby reducing the maximum bending moment in the tunnel lining and reducing the maximum stresses on the tunnel lining under the impact of the earthquake.

V. CONCLUSIONS
In this paper, by using different methods to calculate the impact of earthquakes on the tunnel lining, in the case of the tunnel lining continuous and cases of the segmental tunnel lining with segmental joints. Comparison of the results obtained in each method to evaluate the effects of segmental joints in the tunnel lining when the tunnel lining is affected by the earthquake. The paper used the data of a tunnel's cross section of the Hanoi metro system, with the El Centro's earthquake data (that could be as the maximum magnitude earthquake possible in the Hanoi) to use the calculation of the internal force on the tunnel lining in cases the tunnel lining continuous and the segmental tunnel lining with segmental joints. With the results obtained, recognize the positive effects of segmental joints to the operation of the tunnel lining under the impact of the earthquake. These segmental joints increase the flexibility of the tunnel lining under impact of the earthquake. The presence of segmental joints in the tunnel lining reduces the maximum bending moments on the tunnel lining, thus reducing the maximum stress values present on the lining when the tunnel lining is affected by the earthquake.