Comparison of displacement field predicted by 2D and 3D finite element modelling of shallow NATM tunnels in clays

Abstract

The 2D load-reduction method for simulating NATM tunnels using plane strain finite elements is evaluated in the paper by comparison with fully 3D simulations. Three real shallow tunnels in urban environment in different stiff clays were simulated. The soil behaviour was described by an advanced non-linear soil constitutive model based on the hypoplasticity theory. Time-dependent behaviour of shotcrete lining was considered in 3D simulations, whereas constant final stiffness was used in the plane strain analyses. The 2D analyses were thus controlled by a single parameter that accounts for 3D effects. It is shown that for an optimum value of this parameter, the displacement field predicted by the 2D method agrees well with the 3D simulations. In some cases only, a discrepancy was observed in the close vicinity of the tunnel. The controlling parameter was, however, found to be dependent on the problem simulated (for the same material) and also on the material properties (for the same tunnelling problem). Considering the material properties, the shear modulus at very small strain was found to be more influential than the shear modulus at large strain. The initial K 0 stress state did not influence the controlling parameter substantially. Vergleich der Prognose des Verschiebungsfeldes durch 2D-und 3D-FE-Modellierungen von seichten Tunneln im TonDie mit finiten Elementen mit ebenem Spannungszustand arbeitende 2D-Lastreduktionsmethode zur Simulierung von NÖT-Tunneln wird im vorliegenden Aufsatz im Vergleich zu vollen 3D-Simulationen bewertet. Es wurden drei existierende oberflächen-nahe Stadttunnel in verschieden festen Tonböden simuliert. Das Bodenverhalten wurde durch ein komplexes, nicht-lineares Bodenmodell auf Basis der Hypoplastizitätstheorie beschrieben. In den 3D-Simulationen wurde das zeitabhängige Verhalten der Spritzbetonauskleidung untersucht, wohingegen in den Analysen der ebenen Spannungszustände die konstante, endgültige Festigkeit des Betons verwendet wurde. Die 2D-Analysen wurden auf diese Weise durch einen einzelnen Parameter bestimmt, der den 3D-Wirkungen Rechnung trägt. Die Untersuchung zeigt, dass für einen Optimalwert dieses Parameters das mittels der 2D-Methode prognostizierte Verschiebungsfeld weitestgehend mit den 3D-Simulationen übereinstimmt. Nur in einigen Fällen war in unmittelbarer Nähe zum Tunnel eine Diskrepanz zu beobachten. Es wurde jedoch festgestellt, dass der bestimmende Parameter von der Art des simulierten Problems abhängt (für dasselbe Material) und auch von den Materialeigenschaften (für dasselbe Tunnelbauproblem). Für die Materialeigenschaften wurde festgestellt, dass der Schubmodul bei sehr kleinen Spannungen eine größere Rolle spielt als bei großen Spannungen. Der anfängliche K 0 -Lastzustand hatte keinen wesentlichen Einfluss auf den bestimmenden Parameter. Introduction3D numerical analysis is becoming an increasingly affordable tool for predicting deformation and stress redistribution induced by tunnelling. As tunnel excavation is clearly a three dimensional problem, conside...

Observed and calculated gravity anomalies above a tunnel driven in clays – implication for errors in gravity interpretation

“…The load reduction parameter was selected so that the numerical model provides predictions of the displacement field around the tunnel similar to those obtained from measurements. This procedure has been shown to provide a good estimate of the displacement field around a tunnel when compared to fully 3D simulations (Svoboda and MaMašín ). The initial conditions of the analyses comprise vertical stresses (calculated from the soil and water unit weight), horizontal stresses (assumed to be equal to the vertical stresses) and the void ratio (estimated using the procedures outlined above).…”

“…The load reduction parameter was selected so that the numerical model provides predictions of the displacement field around the tunnel similar to those obtained from measurements. This procedure has been shown to provide a good estimate of the displacement field around a tunnel when compared to fully 3D simulations (Svoboda and Mašín 2011). The initial conditions of the analyses comprise vertical stresses (calculated from the soil and water unit weight), horizon-• Four undrained triaxial tests with a measurement of pore water pressure (CIUP) on undisturbed soil samples • Two isotropic compression tests on reconstituted soil samples • Five shear-box tests on undisturbed soil samples • Three ring-shear tests on reconstituted soil samples • Two oedometric tests on undisturbed soil samples • One oedometric test on a reconstituted sample.…”

Applying Bayesian approach to predict deformations during tunnel construction

“…This method is briefly discussed in Section 3.1.1. In most practical applications, this method is introduced in the framework of finite element or finite difference method. This, in turn, may prove computationally unfeasible in conjunction with Bayesian updating.…”

Design of underground structures and analysis of self-support capacity

“…Similar incorrect results of displacements could be calculated in case of not optimised number of elements and also line assembling boundary or geometry. In case of very large models, it may be difficult to process because of huge operation that has to be done using computer hardware that an average user does not have [11][12][13].…”