# A Gene Expression Programming Model for Predicting Tunnel Convergence
## 1 Introduction  
Avoiding transportation problems and heavy traffic has led to the development of underground roads in metropolises. There are several ways to excavate tunnels in urban areas; among them, the New Austrian Tunneling Method (NATM), is the most preferred method, especially when dealing with soft grounds. In this method, the strength of the surrounding ground is used to the greatest extent possible to strengthen the tunnel structure. The excavation takes place sequentially, thus taking advantage of the ground conditions. In addition, a support system is installed, as needed. The temporary support system usually includes one or two layers of shotcrete, reinforced with steel wire mesh, if necessary. The final permanent support system is commonly a cast-in-place concrete lining, placed over a waterproofing membrane. Tunnel stability, ground displacements induced by tunneling, and the performance of the support system, are some of the issues that must be taken into consideration forthe successful design and implementation of a NATM tunnel [1]. The ground movements, induced by tunneling, affect the safety of adjacent underground structures and surface buildings [2]. Therefore, it is necessary to predict the ground displacements and their effects on the existing buildings, throughout the tunnel route [3]. In this regard, ground displacements at the surface and subsurface around the tunnel are frequently measured during and after construction. Convergence monitoring, as a simple measurement, provides valuable data on the deformation around the tunnel and tunnel wall. The instrumentation and monitoring of underground structures is of great importance, on account of the uncertainties in the mechanical behavior of the ground. In addition the implementation impacts of an underground structure on the adjacent structures increase the complexity of the design and necessitate a more precise monitoring plan. This is of even higher importance when underground structures are excavated in shallow urban environments. Instrumentation tools are used to precisely quantify certain parameters of structural behavior and to monitor their rate of change [4]. Depending on the use and importance of an underground structure, various instrumentation tools are used to monitor the behavior of the underground structure and its surrounding ground. In-situ measurements during the construction process of a tunnel are a very useful tool for measuring the tunnel stability. Various techniques are now available for measuring stress and displacement in underground spaces. Among them, the best and most appropriate technique that can measure displacements, are convergence meters. In practice, obtained convergence data, during and after tunneling, are used for a wide variety of decision-making aims [5]. Due to the ease of use of convergence meters and the reliability of the obtained data, the displacement measurements can be used to obtain the stress distribution around the tunnel. Accordingly, a method has been proposed for tunnel stability evaluation based on the obtained strains and therefore, stress analysis is thus not required [6]. Convergence of a tunnel is the amount of closure on the tunnel walls, which is due to the loss of the stress-strain equilibrium state of the surrounding soil or rock mass, resulting in a redistribution of stress around the excavation [7; 8; 9; 10]. An important application of convergence measuring is demonstrated in the convergence-confinement method. This method calculates the load applied to the support system, installed behind the tunnel face, and provides insight in relation to the interaction between tunnel lining and the surrounding ground [11; 12; 13; 14; 15]. The convergence-confinement method has been used in several researches; investigating active grouted rock-bolts in tunnel stability [16], design of active grouted rock-bolts in tunnel stability [17] and analysis of the interaction between the lining of a tunnel boring machine (TBM) tunnel and the ground [18].