Back analysis technique for mountain tunneling based on the complex variable solution

Abstract

1. IntroductionThe new Austrian tunneling method (NATM) has changed theconcept of mountain tunneling from resisting the passive earthpressure to helping the ground support itself. Consequently, themodern observational method that involves both instrument-basedmonitoring and computer-based back analysis has been widely usedfor the support system design of mountain tunnels [1,2]. It isrelatively easy to collect the displacement (as well as the stress)monitoring data during the construction phase, whereas, the backanalysis technique for mountain tunnels remains a hot researchissue for last two decades and has not yet reach a well agreementamong researchers and practitioners.This article focuses on the back analysis technique for thedynamic design of tunnel support system, which generally consistsof a forward procedure and a backward procedure. The forwardprocedure establishes a mapping from design parameters (not onlyground parameters but also construction parameters) to calculatedresponses (not only ground responses but also structure responses).The backward procedure provides an algorithm to adjust the designparameters so that the discrepancy between the calculated responsesand monitoring data is decreasing. These two procedures are invokediteratively to minimize the discrepancy, and the design parametersafter back analysis can be used to verify or adjust the original designof tunnel support system dynamically.As far as the author’s knowledge is concerned, the backwardprocedure basically can be divided into two categories. Onecategory is the classical optimization theory such as simplexmethod, Levenberg–-Marquardt method and gradient method[3,4]. They are computationally efficient, but have some restrictionon the selection of error functions (e.g. continuity and convexity).Moreover, they have no guarantee of converging to global mini-mum when the forward procedure is highly nonlinear and highlymultimodal. The other category is artificial intelligence theory suchas genetic algorithm, evolution strategies and simulated annealing[5,6]. The advantages and the drawbacks of these methods are justcontrary to the former ones.The forward procedure basically can be divided into threecategories, as far as the author’s knowledge is concerned. The firstcategory is theoretical solution based on the traditional convergence–confinement method [7]. Under the axial symmetry plane strainassumption, the convergence–confinement method relates the defor-mation modulus and the inner pressure to the tunnel convergencesdirectly. The established relationship is a very rough approximationto the real problem, thus it is hardly can be used as the forwardprocedure in the back analysis technique when the boundaryconditions don’t accord with the assumption. The second categoryis 3D or 2D numerical simulation such as finite element method,discrete element method and boundary element method [8–10].They can take the complicated boundary conditions and constitutivelaws into account, and theoretically, can relate any design parametersto any calculated responses when the corresponding monitoring dataare available. But they generally require much more computationalefforts, especially when the convergence of back procedure is slow.The third category is statistical learning such as neural network,support vector machine and radial basis network [11,12]. Thelearning machines are well trained by the examples collected fromprecedent engineering instances or numerical simulations, so thatthey can established relationships between some design parametersand some corresponding responses in the sense of statistics.Contents lists available at SciVerse ScienceDirectjournal homepage:www.elsevier.com/locate/ijrmms