İstanbul Metro tünellerinin flac bilgisayar programı ile modellenmesi

Abstract

Bu çalışmada İstanbul Metrosu tünellerinde meydana gelebilecek stabilite sorunlarının araştırılması amacıyla Flac bilgisayar programı kullanılarak tünel modelleri hazırlanmıştır. Taksim-Osmanbey hattı üzerindeki formasyon dikkate alınarak jeolojik açıdan iki ayrı durum (en iyi ve en kötü) için hazırlanan modellerle hem tünel kesiti hem de aynaya dik alınan kesit boyunca aşamalı kazı modellenmiştir. Kazı sırasında ve sonrasında göçme meydana gelip gelmeyeceği tünel açılması nedeniyle yüzeyde meydana gelebilecek oturma ve çökmeler araştırılmıştır. Çalışmalarda öncelikle tünel civarındaki oluşacak gerilme ve deformasyon durumunu belirlemek amaçlanmıştır. Çalışmanın birinci bölümünde konunun tanıtımı ve amaçlar belirtilmiştir. İkinci bölümde İstanbul Metrosu Projesinin teknik özellikleri, jeolojisi ve metro güzergahı üzerinde yapılan ölçümler hakkında bilgi verilmiştir. Üçüncü bölümde ise nümerik modelleme teknikleri ve bunların hesaplama yöntemleri tanıtılmıştır. Dördüncü bölüm Flac bilgisayar programının tanıtımı ve sonlu farklar yönteminde kullanılan hesaplama yöntemleri ile ilgili bilgilerden oluşmaktadır. Çalışmanın beşinci bölümünde Flac programının tünel kesitine uygulanması anlatılmış ve elde edilen sonuçlar altıncı bölümde tartışılmıştır. Yapılan incelemelerde tünel kesitlerinde tavan ve yan duvarlarda zamanla oluşan konverjans değerlerinin maksimum 42 mm mertebesinde, süreksizliklere bağlı olarak geliştiği gözlenmiştir. Yüzey nivelmanlanndan alman sonuçlara göre 11 mm'lik maksimum değer gösteren ortalama 1-4 mm mertebesinde oturmalar meydana gelmiştir. Bilgisayar yardımıyla Flac sonlu farklar programı kullanarak yapılan metro modelinde elde edilen sonuçlar en iyi durum için 30 mm ve en kötü durum için 50 mm civarında olmuştur. Bu sonuç tünellerden alınan konverjans değerlerinin değişim aralığında olduğu görülmüştür. Ortamı oluşturan formasyonun kayma modülünün (G) değişimiyle tünel çevresindeki gerilmelerin fazla değişmediği halde deformasyonlar bir kaç misli değişmektedir. Kayma modülü arttıkça deformasyonlar azalmaktadır. Tünel çevresinde oluşan konverjans miktarı en iyi durum için 34 mm civarında olurken daha düşük mekanik parametreler için yapılan hesapta konverjans miktarı 54 mm civarında olduğu görülmektedir. Bununla beraber tünel kaplamasına gelecek yük ise 8 105 Pa olduğu hesaplanmıştır.

The purpose of this study isto simulate the part of Istanbul subway tunnels, which was completed in april 1994, by using computer programe, in order to gain more understanding on the behaviour of rock mass during excavation and to compare the results of this study with in-situ mesurments. Istanbul subway tunnels run from Taksim to 4th Levent with 7045 km in length, approximately 18-32 m in dept. The investigation shows that approximately %70 of tunnels from Taksim is running through sandstone, mudstone and sheyl. The rock mass rate can be classified as poor to good based on the designation by Bieniawski (1984). The rock mass rate encountered in this partion (Osmanbey-Taksim) of the tunnel can be classified as poor to very poor. The use of numerical techniques for stress analysis can be considered nowadays as a standart practice for the design of complex soil and rock engineering works. In addition to this common use, the numerical techniques may also offer an appreciable help in the interpretation, or back analysis, of the behaviour observed during the construction or during the life of the structure. Most numerical simulation carried out to date have been 2-D analysis using the finite element method. At present, 3-D models cannot be considered as a standart tool for practical tunnel design because of the expenditure with respect to manpower and computer resourses involved. To a large extent their practical application is restricted to investigate specific details, as for example, stresses in the shotcrete lining of tunnel intersections. However tunnelling is definetely a 3-D problem and restricting oneself to two dimensions may lead to significant deviations when compared to actual field behaviour. The following numerical simulation models may be applied to tunnelling: 1 -Finite element method 2-Boundary element method 3-Coupled Finite element method / Boundary element method 4-Finite difference method 5-Discrete element method The :Finite element method is still the most widely used and probably the most versatile method for analysing tunnelling problems. With this method, the domain to be analysed has to be subdivided into a number of subdomains (the finite element) which are connected at discrete points (nodal points). Within each element, a variation of the displacements (in terms of the nodal values) is assumed. Stresses XII inside the elements are derived from displacements and the accuracy of the results depends, not only on the discretisation, but also on the order of the function used to describe the displacements (shape function). The stresses thus obtained do not in general satisfy the conditions of equilibrium, especially at the interfaces between finite elements. In geotechnical problems the rock /soil mass has no cleary defined boundaries and therefore artificial boundary conditions have to be applied. The main advantages and disadvantages may be summarized as follows: Main advantages: - The nonlinear material behaviour can be considered for domain analysed. - The modelling of excavation seqences, including the appropriate timing of shotcrete placement, is straightforward. - Closely spaced parallel, unfilled sets of joints are efficiently modelled by applying a homogenisation technique. - Time dependent material behaviour may be introduced so ageing and creep of shotcrete may be considered. - The method has been extensively applied to solve practical problems so a lot of experience is available already. Main disadvantages: - The valune of the domain analysed has to be discretised, high pre and postprocessing efforts required. - Due to large equation systems run times and/or disk storage requirements may become excessive. - Distinct fault zones is an arbitrary position with respect to the tunnel axis are very diffucult to model. - Infinite and semi infinite domains are difficult to deal with and artificial boundary conditions have to be applied. Significant advances have been made recently in the develepment of the boundary element method and, as a consequence, this method provides a viable alternanive to the finite element methpd. To be able to solve the boundary problem numericaly, the surface of the domain is divided into small sub surfaces (boundary elements) inside which a variation of the boundary conditions (displacements, boundary stresses) is assumed. There is no difficulty in dealing with problems where the domain extends to infinity and the discretisation effort is reduced by an order of magnitude because only surface of excavations need to be discretised. The main advantages and disadvantages may be summarized as follows: Main advantages: - Pre and postprocessing is reduced by an order of magnitude. - The surface discretisation leads to smaller equation systems and less disk storage requirements. - Computation time is usually significantly shorter than for comparable F.E.M. analyses. - Results of analyses can be obtained at any location by postprocessing. XUl - Distinct faults can be modelled much more efficiently than with finite element method because the method works with tractions rather than nodal forces. The nonlinear behaviour of the foult can be included in the analysis. - Stresses and displacement on the surfaces of excavations are much more accurate than those obtained by the finite element method. - Unlike the finite element method stresses and displacements inside the region satisfy the conditions of equilibrium and compatibility exactly. Main disadvantages: - Except for interfaces only elastic material behaviour can be considered with surface discretisation. - A detailed modelling of excavation sequences and support measures is very difficult and not feasible. - The standart formulation is not suitable for highly jointed rocks when joints are randomly distributed. However, the posibility exists of implementing a fundemental solution for anisotropic material. - Up to now, the method has not been used very often for solving tunnelling problems, therefore considerably less experience is available than with finite element models. It may be concluded that the best analysis procedure is a combination of Finite element and Boundary Element methods because all the advantages of both methods can be exploited leaving almost no disadvantages. Indeed efficient numerical models can be obtained by for example discretising the soil/rock in the vicinity of the tunnel with finite elements and representing the far field by boundary elements. One disadvantages however remains : namely the cumbersum modelling of fault zones intersecting the tunnel axis in arbitrary directions. Finite element programs are more common in engineeriig than finite difference program. Flac, however, has several advantages over finite element programs. It handles large grid distortions (geometric nonlinearity) and nonlinear material models in almost the same calculation time a small strain linear problems. Futhermore the explicit formulation and mixed discretization scheme ensure that plastic collapse and flow are modeled very accurately. The usual drawbacks of the explicit formulation (small time step and choice of damping) are overcome by automatic inertia scaling and automatic damping. The explicit method is ideal for geomechanics problems that cosist of several stages (loading, excavation, etc.) because it modules the stages sequentially in the same way that they occur in reality. Material models: - Isotropic and anisotropic elastic - Elasto-plasticity (Mohr-Coulomb yield criterion with or without tension, non- associated flow rule, large or small strain) - General strain softening/hardening - Every element may have different model or property; a contiuous gradient in properties may be specified. XIV Flac is explicit finite difference code which simulates the behaviour of structures built of soil, rock or other materials which may undergo plastic flow when their yield limit is reached. Materials are represented by zones, or elements, which form a grid that is adjusted by the user to fit the shape of the object to be modeled. Each element follows a prescribed linear or nonlinear stress/strain law in response to the applied forces and boundary restraints. If stresses are high enough to cause the material to yield and flow, the grid actually deforms and moves with the material it represents. The explicit method makes use of the idea that, for small timesteps, a disturbance at a given gridpoint is experienced only by its immediate neighbors. For each timestep, the equations of motion are solved for each gridpoint inthe mesh. The strains are used in the constitutive law to determine the corresponding stress increment for the zone. The timestep must be chosen carefully to avoid numerical instability in the solution. This study concerns with the stress analysis of İstanbul subway tunnels which is excavated in rock (Fig.l). The analysis presented here considers the lining as a shotcrete and includes gravitational loading of the surrounding rock mass. Jf \y 4f 4" w w v v s]/ \ Figure 1. Cross Section of Tunnels and Model Boundaires The objectives of this analysis are to simulate stress relaxation in the rock after excavation and prior to liner installation and to examine rock stresses after the lining is installed. The circuler water tunnels have an axcavated radius of 3.5 m and the monolithic liner is 45 cm thick. It is assumed thet the rock is at equilibrium under gravity loading prior to making the excavation. Further, it is assumed that there is sufficient time delay between excavation and liner installation to permit the perturbed stress field to come to equilibrium. The following properties describe the rock behavior: Elastic modulus (E) : 300 - 500 kg/cm2 Poisson's ratio (v) : 0.18 - 0.22 Friction angle ((()) : 27 - 30° XV For this study, the rock is assumed to be a homogeneous isotropic material with no anisotropy (bedding or jointing). The vertical in-situ stress is assumed to increase hydrostatically with depth as the sum of the water weight and the buoyant rock weight. Depth stress gradients are assumed linear. Gravity is specified in the analysis. The results have been plotted in chapter 5. Figures 5.4 and 5.6 show principal stress plots after stress equilibrium for both the far field and near field cases. It is seen that the major principal stress is vertical as expected, these stresses increase with depth. These plots demonstrate that the problem has been initiaized properly. The next plots, Figures 5.5 and 5.7 are of the displacement after the excavation is made.