Numerical Simulation and Analysis
Going beyond Conventional Failure Thresholds : Exploration of Consequences
In line with the first (and major) objective of the project, the potential consequences of allowing “below ground” support systems (“foundations”) to respond to strong shaking by going beyond conventional failure thresholds has been explored analytically. A new seismic design philosophy, according to which soil “failure”, in the form of foundation uplifting and bearing capacity failure, may be utilized to protect the superstructure, has been introduced. A simple but realistic bridge structure has been used to illustrate the effectiveness of such a new approach. It has been shown that for large intensity earthquakes, exceeding the design limits, the performance of the new design scheme is advantageous, not only avoiding collapse but hardly suffering any inelastic structural deformation. It may however experience increased residual settlement and rotation : a price to pay that must be properly assessed in design.
The effects of sliding at the soil-foundation interface have been explored analytically. A series of parametric analyses have been conducted using as seismic excitation numerous near–fault–recorded severe ground motions and idealised wavelets, bearing the effects of ‘forward-directivity’ and ‘fling-step’. It has been shown that ‘directivity’ and ‘fling’ affected motions containing long-period acceleration pulses and large velocity steps, are particularly “destructive”.
Development of Reliable Analysis Methods : model calibration and validation
A simplified but fairly comprehensive constitutive model for analysis of cyclic response of shallow foundations has been developed. Implementing a kinematic hardening constitutive model with Von Mises failure criterion (readily available in commercial finite element codes) and based on based on the work by Gerolymos and Gazetas (2005, 2006), the model has been made “pressure-sensitive”, and capable of reproducing both the low-strain stiffness and the ultimate resistance of clays and sands. Encoded in ABAQUS through a simple user subroutine, the model has been validated against centrifuge and large-scale model tests of shallow footings on clays and sands under cyclic loading. Requiring calibration of few parameters only, and being easily implemented in commercial FE codes, the model is believed to provide a practically applicable engineering solution. Aiming at further validating the effectiveness of the developed simplified constitutive model, the same model was utilised to simulate a completely different problem: the beyond conventional thresholds dynamic response of reinforced-soil retaining systems.
A phenomenological constitutive model for 1D nonlinear ground response analysis of soil deposits (Gerolymos and Gazetas, 2005) has been calibrated, and validated against more sophisticated constitutive models and numerical tools, and experimental data from centrifuge tests. The sufficiently close agreement of calculated results and experimental measurements gives confidence for using the proposed model. The small number of parameters renders the model easily implemented, yet powerful, able of efficiently reproduce the nonlinear hysteretic behavior of various soils, and simultaneously generating realistic shear modulus reduction and damping ratio curves.
Relevant Publications: A6 [Drosos et al., 2010b].
Parametric Analysis of 1-dof Structures resting on Shallow Foundations
Assuming elastic response of the superstructure, the monotonic, cyclic, and seismic response of shallow foundations was parametrically investigated numerically. Among the key problem parameters were : (a) the static factor of safety FSv ; (b) the distance R of the centre of gravity from the base edge ; (c) the slenderness ratio h/b ; (d) the intensity, frequency content and sequence of pulses of the seismic excitation ; and (e) the natural period of the structure. For FSv > 2, the response is dominated by foundation uplifting, whereas for FSv ≤ 2 bearing capacity failure is fully developed leading to additional settlement of the foundation with permanent rotation. Surprisingly, a non–symmetric over-strength of the foundation was observed for very heavily loaded systems (FSv < 1.5) ─ a novel finding, the appearance of which was interpreted in physical terms.
Other Factors affecting the Performance
A worldwide prevailing fallacy regarding the shape of design response spectra for soft soil has been elucidated, and corrected through the novel idea of a Bi-normalized spectrum. Seismic codes have largely adopted smooth design acceleration spectra, on the basis of statistical processing of a large number of elastic response spectra of actual recordings. Such spectra have an essentially constant acceleration branch (extending to larger periods for softer soil) and a declining acceleration branch. However, their flat shape has no resemblance to an actual soil-amplified spectrum. This unrealistic shape stems from the fact that the spectra of motions recorded on soft soil attain their maxima at different well separated periods, and thereby, averaging them eliminates their peaks and leads to a flat spectrum. Through an extensive parametric study (1008 equivalent linear and 1008 inelastic analyses in total), an attempt was made to derive a more meaningful normalization by dividing the period with the predominant one. This resulted in a bi-normalized spectrum having a peak of Sa/A ≈ 3.75 at T/Tp = 1.
The combined effects of earthquake-triggered landslides and topography-affected ground shaking on foundation-structure systems founded near slope crests was investigated. Plane-strain nonlinear finite element dynamic analyses were performed, investigating the effects of : (i) foundation type (isolated footings versus a rigid raft), and (ii) on the position of the sliding surface relative to the structure. It was shown that a frame structure founded on a properly designed raft could survive the combined effects of slope failure and strong seismic shaking, even if the latter is the result of a strong base excitation amplified by the soil layer and slope topography.
Relevant Publications: A11 [Kourkoulis et al., 2010a].
Faulting-induced deformation loading has been investigated as an example of loading that unavoidably leads soil-foundation systems far “beyond” conventional failure thresholds. The response of slab foundations subjected to thrust faulting were parametrically investigated, showing that the design of structures to withstand such extreme seismic stressing is feasible. Foundation and superstructure distress was shown to stem mainly from loss of support. A simplified design method was developed, calling for conventional static analysis of a slab on Winkler supports, “simulating” the faulting-induced deformation by removing Winkler springs from equivalent area(s) of loss of support.
Relevant Publications: A4 [Anastasopoulos et al., 2009c].
Effect of the Structure Type
Apart from 1–dof elastic oscillators and bridge piers the analysis methodology has been extended to moment–resisting frames. For this purpose, an idealized, simple but realistic, 1-bay 2-storey reinforced concrete (RC) structure has been used as an example. The problem was analyzed employing the finite element (FE) method, taking account of material (soil and superstructure) and geometric (uplifting and P-Δ effects) nonlinearities. It was shown that the axial forces N acting on the footings and the M/Q (moment to shear) ratio fluctuate substantially, leading to significant changes of footing M−θ (moment-rotation) response. The seismic performance was explored further through dynamic time history analysis, using a wide range of seismic motions. It was shown that the performance of both alternatives can be acceptable for moderately strong seismic shaking, within the design limits. For very strong seismic shaking, well in excess of the design, the performance of the rocking−isolated system was found to be advantageous : while the conventional system may collapse or sustain non-repairable damage, the rocking−isolated frame would survive sustaining repairable but non-negligible damage to its beams and non-structural elements (infill walls, etc.).
Numerical Modelling in 3D
A numerical study was conducted to investigate the response of shallow rigid foundations carrying a 1-dof structure and resting on inelastic clayey soil through a tensionless but rough interface. The system was modelled in 3D employing the finite element method. Three types of lateral loading were applied : (a) static displacement–controlled loading at the mass centre monotonically increasing up to overturning ; (b) cyclic displacement–controlled loading at the mass center ; and (c) seismic excitation (dynamic time history analysis with three different accelerograms). The analysis accounts for uplifting of the footing from the base and generation of bearing–capacity failure mechanisms in the soil, during large amplitude rotations. The detrimental effect of the slenderness of the structure to increase the overturning moment on the foundation due to the large displacement of its mass (P–δ effects) is also accounted for. The results for the foundation response are presented mainly in the form of moment–rotation and settlement–rotation curves. A number of key problem parameters were identified and explored. The results revealed a remarkable sensitivity of system response to the static factor of safety. 3D results were compared to 2D analysis results, allowing for definition of a proper equivalence between a strip and a square foundation.
Relevant Publications: C4 [Panagiotidou et al., 2010]
The response of structure–foundation systems under faulting induced deformation loading has also been investigated for 3-dimensional problems such as that of the interaction of a dip-slip fault rupture with a rigid, square in plan, caisson. The mechanisms of normal and reverse fault rupture interaction with caisson foundations, were investigated applying an integrated approach using centrifuge model tests and 3D finite element analysis. A series of centrifuge model tests were first conducted at the University of Dundee. Nonlinear 3-D numerical simulation of the problem was then developed and adequately validated. Depending on its position relative to the fault, the caisson was found to interact with the rupture. Acting as a kinematic constraint, the caisson “forces” the rupture to divert on either one, or both, of its sides, thus sucessfully sustaining loading that is substantially beyond conventional failure thresholds.