Multiscale structural analysis of circular arches and segmental tunnel rings: nonlinear hybrid analysis of displacement-monitored experiments and pre-design considerations

Abstract

This thesis is devoted to the development of methods facilitating structural analysisof circular arches and segmental tunnel rings. These methods are based on transferrelations representing analytical solutions of the linear theory of circular arches. Theemployed analytical solutions refer to dead load, ground pressure, uniform temperaturechanges, point loads, and discontinuities of the kinematic variables at the joints.Discontinuities, such as the ones resulting from the point loads and the discontinuitiesof the kinematic variables at the joints, are accounted for by means of the Heavisidefunction. After verification of the correct implementation of the transfer relations intothe available numerical computing environment, they are used for structural analysisof (i) arch bridges made of steel and (ii) tunnel rings made of steel-reinforced concretesegments, whereby the main focus is on the second application.As for segmental tunnel rings, the central aim of the present thesis is the developmentof hybrid methods for multiscale structural analysis of real-scale bearing-capacitytests which were carried out at Tongji University, Shanghai, China. The term “hybrid”expresses the use of two types of input for the computational structural analyses:(i) point loads which were prescribed during the experiments, and (ii) the discontinuitiesof the kinematic variables at the joints, which were measured during testing. The term“multiscale” refers to multiscale models for the stiffness, strength, and the softening ofconcrete. These modern material models resolve the micrstructure of concrete down tothe nanometric scale.The first one of the developed hybrid methods accounts for linear-elastic behaviorof the tunnel segments. A 7 x 7 transfer matrix allows for the mechanical treatmentof the entire segmental tunnel ring. As for the analyzed real-scale test, this transfermatrix contains 42 sets of analytical solutions: 24 of them refer to the 24 point loads,the remaining 18 to the discontinuities of the 3 kinematic variables at all of the 6 joints.The linear hybrid method is used for the analysis of a real-scale test on a segmentaltunnel ring, all the way up to the elastic limit of the segments. This elastic limit isreached when tensile cracking of one of the segments starts.The second one of the developed hybrid methods accounts for the nonlinearitiesresulting from bending-induced tensile cracking of the segments. They are subdividedinto elements of a length equal to the crack spacing. The elements are either intact orcontain one central crack band, flanked by lateral undamaged domains. A multiscalemodel for tensile softening of concrete is used to describe the progressive deteriorationof the crack bands. The nonlinear hybrid method is used for the analysis of a real-scaletest on a segmental tunnel ring, all the way up to the bearing capacity of the structure.Hybrid analysis of segmental tunnel rings is elegant, because measured discontinuitiesof the kinematic variables at the joints are used as input, which eliminates the needto model the nonlinear behavior of the joints. Still, hybrid methods require measurementdata from structural monitoring. Such data are generally not available. This wasthe motivation to develop a method for structural analysis of segmental tunnel rings,for which monitoring data are not available.The third one of the developed methods refers to the combination of linear transferrelations with interface laws, describing the nonlinear behavior of the joints. Theyaccount for (i) loss of initial full-face segment-to-segment contact by means of partialsegment-from-segment separation, (ii) compressive crushing of the concrete, and(iii) tensile yielding of the steel bolts, connecting neighboring segments. The developed nonlinear interface model and the corresponding method for structural analysis are validatedby comparing computed results with measurements from independent bearingcapacity tests on bolted joints and on a segmental tunnel ring, respectively.The following conclusions are drawn: (i) Bending-induced tensile cracking of thesegments and the corresponding crack opening displacements can be predicted reliablyby modern multiscale models for tensile softening of concrete. This is beneficial for thedurability assessment of segmental tunnel rings, as required for serviceability design.Nonetheless, consideration of tensile cracking is of minor importance for quantificationof the internal forces and the displacements of segmental tunnel rings. These two aspectscan be estimated reliably by means of transfer relations based on linear-elasticbehavior of the segments. (ii) The nonlinear behavior of the joints governs the structuralperformance of segmental tunnel rings. Thereby, the relative rotation angles atthe joints are of prime importance. They result, first and foremost, from the bendingmoments and the normal forces transmitted across the joints, but there are strong indicationsof a second contribution that affects the relative rotation angles such that theyresult in rigid body motions of the segments. (iii) The bearing capacity of segmentaltunnel rings is characterized by the development of a kinematic mechanism, resultingfrom plastic hinges at several joints. Thus, the bearing capacity of segmental tunnelrings can be estimated reliably based on a combination of linear transfer relations andrealistic failure envelopes for the joints. (iv) Viscoelastic material behavior of concreteresults in time-dependent behavior of the joints. Under constant external loading, therelative rotation angles at the joints are increasing progressively, without approachingan asymptotic limit. Consequently, the ovalization displacements of segmental tunnelrings are increasing progressively, while the internal forces practically remain the same.(v) Steel bolts, connecting neighboring segments, are significantly improving the serviceabilityof segmental tunnel rings, because they ensure the position stability of thelining, even if significant bending-induced segment-from-segment separation takes place.In case of strongly anisotropic ground pressure, the bolts result in a significant increaseof the bearing capacity of segmental tunnel rings, because they contribute significantlyto the bending moments, required for overall structural equilibrium.