Macroelement modelling for the mechanical response of granular soil and layered sites improved with granular columns
Abstract
The scope of the doctoral dissertation is the development of a macro-element model for the mechanical response of granular soil and layered sites improved with granular columns.The model is based on the plasticity constitutive model for sand Ta-Ger expressed in a one dimensional p-q, εvol-εq space form, slightly revised from its initial formulation, which exhibits remarkable versatility in representing complex patterns of sand cyclic behavior, such as stiffness decay and decrease in strength due to build-up of pore-water pressure. The calibration of the model parameters was based on a procedure that targeted to the optimum performance in both drained and undrained load conditions by simultaneously matching the response in terms of: (a) the cyclic resistance ratio curves as per the NCEER/NSF methodology, and (b) widely-used experimental shear modulus and damping ratio curves available in the literature. The calibration was executed for various sand relative densities and under various levels of effective stress. The methodology under drained loading conditions was based on matching model response with the (G-γ), (ξ-γ) curves suggested by: i) Ishibashi and Zhang (1993), ii) Vucetic and Dobry (1991) and iii) Darendeli et al. (2001). Under undrained loading conditions, the correlation for the reference cyclic resistance ratio from SPT data by Idriss & Boulanger (2004, 2008) was combined with (a) the empirical formula of Seed & Idriss 1982), that relates the earthquake magnitude to the equivalent number of uniform cycles of the seismic motion, (b) the magnitude scaling factors (MSFs) proposed by i) Idriss (1995) and ii) Andrus and Stokoe (1997), that associates the reference cyclic resistance ratio with the actual one and (c) the correction factor for overburden stress Kσ suggested by the NCEER (1996, 1998) workshops. A simplified version of the developed p-q version of Ta-Ger model was used to represent the behavior of clay in cyclic loading, based on the assumption of zero incremental volumetric strains and relating Ms with the undrained strength Su. The calibration procedure was based on matching two families of (G-γ), (ξ-γ) curves: i) the Ishibashi and Zhang (1993) and ii) the Vucetic και Dobry (1991). The model was then implemented through an explicit finite difference algorithm into an in-house computer code which performs integration of the wave equations to obtain the non-linear response of the soil, under both drained and undrained conditions of loading. The accuracy of the algorithm was verified through comparison with analytical solutions for the amplification function of soil deposits with linearly increasing Vs (Gazetas, 1982), subjected to vertically propagating shear waves. The capability of the model in simulating the seismic response of horizontally layered deposits was validated against two centrifuge experiments (Hashash et al, 2015). The tests involved a 26m thick profile of dry stiff Nevada sand with Dr=60%, subjected to two levels of seismic excitation at its base. The computed response was reasonably compared to the measured one. The case history of Port Island vertical array records in the 1995 Kobe earthquake was then employed to verify the versatility of the model to predict the dynamic response of saturated soil. The accordance of the model response and the in situ records in terms of acceleration time histories at 0m, -16m, -32m and -83m and surface spectrum was quite satisfactory. Field investigations along with previous simulations of the seismic response of the site indicated that liquefaction must have occurred at the gravelly sand layer above the shallow alluvial clay and the sandy layer below it. This was confirmed by the present analysis, where pore water pressure generation took place at the specific layers. Thus, it can be inferred that the developed model was satisfactory in reproducing the observed response. The developed numerical non-linear ground response analysis algorithm was then reformulated in order to take into consideration the simultaneous dissipation of the excess pore water pressure through soil grains. The differential equation that describes the one-dimensional, vertical, soil consolidation was approached with the finite differences technique and its solution was verified against Terzaghi’s analytical solution. The model validation against the case history of the Port Island array from the Kobe 1995 earthquake was repeated, considering the simultaneous vertical soil consolidation. The model was then applied to estimate the elastic response spectra at the surface of soil profiles with liquefiable layers (ground type S2) as per EC8:2004. The investigation study involved the ground response analysis of diverse soil profiles, all including a liquefiable zone, excited with a suite of earthquake motions at their base. The acceleration time histories were extracted from the PEER Ground Motion Database having characteristics compatible with the NGA-estimated response spectrum at the bedrock and with key seismological parameters such as the earthquake magnitude Mw and horizontal distance from the fault RJB. Two different methods were applied regarding the selection of base excitations: amplitude scaled records (to match a target response spectrum) and spectral matched records. From the results an idealized response spectrum was deduced in terms of the design spectrum parameters S, η, ΤΒ and TC. It was shown that the idealized ground surface response spectrum was marginally sensitive to the method of base excitation selection. Finally, the developed numerical algorithm was applied for the simulation of the seismic response of liquefiable sandy sites improved with vertical drains. The differential equation of soil consolidation was reformulated to account not only for the vertical water flow up to the ground surface, but also for the axisymmetric water flow, through the ground towards the drain. The mechanical interaction between the drain material and the surrounding soil in case of stone columns / gravel piles, is possible to be taken into consideration, by increasing the overall strength of the composite gravel pile-surrounding soil material. The proposed numerical algorithm was validated against a set of non-linear, dynamic, three dimensional, numerical analyses that were carried out in the finite differences program FLAC3D (Itasca, 2006) and concerned a thin liquefiable sand layer of Dr=60% encased between clayey layers, in order to establish purely horizontal flow towards the drains, improved with drains of radius Rd=0.5m and a center-to-center distance (2 Re) equal to 2.8m (Bouckovalas et al., 2011). The comparison of the results was satisfactory. Show more
Publication status
publishedContributors
Examiner: Gerolymos, Nikos
Publisher
National Technical University of AthensOrganisational unit
03655 - Anagnostou, Georgios / Anagnostou, Georgios
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