Seismic analysis of the zaouiat ait mellal twin tunnels of Agadir motorway (Morocco)

. Underground structures, such as tunnels, are vital for ensuring all kinds of transportation; and being buried under the surface makes them exposed to soil dynamics. Added to the moderate seismic activity in Morocco, the stability of tunnels is put to the test. This paper examines the interaction between the ZAM (Zaouit Ait Mellal ) twin tunnels between the cities of Marrakesh and Agadir, using the Difference Element Method provided by FLAC 2D software. The acceleration is introduced as the one related to the historic event of El centro 1940 with free-field boundary conditions in the numerical model, with three configurations: tunnel 1 without tunnel 2, tunnel 2 without tunnel 1 and tunnel 1 with tunnel 2. The results of the simulations indicate that the differences values of the maximum displacement, axial force and bending moment on structural elements are very noteworthy from the configuration of the tunnel (single) to the twin tunnels in order to prove the interaction between these latter under seismic loading.


Introduction
In recent years, Morocco has experienced considerable development in infrastructure with the implementation of large projects such as road and rail networks and underground structures. However, the latter, in particular tunnels built in areas exposed to seismic activities must be particularly and essentially resistant to soil dynamics. This fact is illustrated in many cases of tunnel damage due to seismic events, such as the ones observed during the 1995 Kobe earthquake in Japan at the Daikai subway station [1][2], the 1999 Chi Chi earthquake in Taiwan investigated by Wang et al [3], which showed the 49 tunnels of 57 (in total) sustained damage from this earthquake and the 1999 Kocaeli earthquake in Turkey at of the Bolu tunnel [4]. The importance and cost of the underground RC structures require an accurate analysis of the seismic behavior of structural systems, including the ground environment. Although several studies have investigated the seismic performance of tunnels [5][6][7][8][9], little research has been conducted in northern Africa and Morocco.
Historically Morocco had experienced a very violent earthquake in 1960 in the city of Agadir of magnitude 5.7 on the Richter scale and which caused 12000 of deaths and 70 % of the infrastructures are destroyed [10], For this reason, we chose the ZAM twin tunnels which are between Marrakech and Agadir motorway. This article presents a seismic analysis of the ZAM twin tunnels, using the numerical simulation of the explicit finite difference method provided by FLAC 2D (Fast Lagrangian Analysis of Continua) (FLAC 2005 ) [11], software by introducing the data of El centro 1940 earthquake to see his impact between the tunnels on the maximum displacements in different points on structural elements, for that we chose 3 configurations as follows: -Tunnel 1 without tunnel 2 -Tunnel 2 without tunnel 1 -Tunnel 1 with tunnel 2 2 Data and Material The ZAM is the first twin tunnel motorway across the Atlas mountains, this tunnel is located between Marrakech and Agadir cities with total length of 546 (m), the RC tunnels lining is of horseshoe shape of 11 m wide x 9 m height without equipment and the distance between the tube centrelines is 26,5 (m).

Geology
The tunnel crosses a sedimentary rock formation from the Eocene and cretaceous periods, predominantly limestone ( Figure 1), from the top to the bottom, the materials are as follow: -Marls and marly limestone Massive brown limestone (type I) -Massive limestone locally vacuolar and siliceous ( type II and IIII) -Limestone with fragmented nodules ( type IV and V) -Partially fractured to fractured light brown limestone (type VI) -Marly limestone and grey-brown marls (type VII) Table 1 summarized the properties of the soil layers following these distributions as mentioned in the longitudinal geotechnical profile ( Figure 1) used in the numerical model, which are Young's modulus (E), Poisson's ratio (ν), Cohesion ( c ) , Friction angle (φ) , Dilation angle (ψ) and unit weight (γ).

Numerical modeling
Analyses are conducted using the difference element method. The model is created with the FLAC 2D code on cross section of 89 m wide x 111 m height, the tunnel lining as elastic linear material using ''liner '' and ''beam'' structural elements : and the different layers of soil are considered as a linear elastic-perfectly plastic material that follows the Mohr-Coulomb criterion. For the boundary conditions, we applied an absorbing boundaries at the sides of the model to minimize the seismic waves reflection in dynamic loading. FLAC employs a special lateral boundary known as free field as shown in figure 2.

Fig .2.Constitutive model in FLAC with free-field boundaries
Concerning the dynamic Input, we have applied in the base of the model an acceleration time history of El centro 1940 earthquake ( Figure 3) like an approximate way. This earthquake had a moment magnitude of 6.9 and a maximum perceived intensity of X (Extreme) on the Mercalli intensity scale (table 2). It was the first major earthquake to be recorded.

Results and discussion
The numerical simulation under seismic loading have been done, and the results are in terms of maximum displacement, Axial force and bending moment in the structure elements at dynamic time of 8.14 s, due to the location of the Peak Ground Acceleration value in the accelerograms in the range [0s, 8s].The estimation of these parameters around the tunnel requires special attention because it has a major influence on the design of lining, also for the verification of stability.   The compared values of the maximum displacement in table 3 show that differences up to 0.6% in tunnel 1 and 1.43% in tunnel 2.
The maximum values of the axial forces and the bending moment respectively show that differences are down to 20.10 % and to 10.08 % in the tunnel 1 also those differences are up to 18.62% and to 22.65% in the tunnel 2. These differences are justified by the interaction between the twin tunnels under seismic loading of El Centro earthquake in order to prove the efficiency of the proposed numerical model. However, the maximum values of the displacement, axial force and the bending moment during construction and service of the tunnel would be under the maximum calculated.

Conclusions
In this paper, the numerical simulations under seismic loading of El centro 1940 earthquake for the ZAM twin tunnels of Agadir motorway in Morocco have been used for the three configurations : tunnel 1 without tunnel 2 ,tunnel 2 without tunnel 1 and tunnel 1with tunnel 2, using the differences element method provided by the FLAC 2D code. The model was built with linear elastic-perfectly plastic soil with an absorbing boundary for a good estimation of the interaction between the twin tunnels through the calculation of the maximum displacement, axial force and bending moment on the structure elements. The comparative study shows that the maximum value differences are very noteworthy between the different configurations ,especially for the axial force and bending moment: Displacements, the differences up to 0.6% in tunnel 1 and 1.43% in tunnel 2. Axial force -The differences down to 20.10 % in tunnel 1 -The differences up to 18.62% in tunnel 2 Bending moment: -The differences down to 10.08 % in tunnel 1 -The differences up to 22.65 % in tunnel 2

Prospects
This study will allows us to: -Evaluate the tunnel's performance under seismic conditions in terms of stress and strain to choose the support type of the twin tunnels and comparing with the type used in situ.
-Determine the damage that will affect the twin tunnels during a real seismic activity with suggested solutions