We present a full waveform inversion algorithm of downhole array seismogram recordings that can be used to estimate the inelastic soil behavior in situ during earthquake ground motion. For this purpose, we first develop a new hysteretic scheme that improves upon existing nonlinear site response models by allowing adjustment of the width and length of the hysteresis loop for a relatively small number of soil parameters. The constitutive law is formulated to approximate the response of saturated cohesive materials, and does not account for volumetric changes due to shear leading to pore pressure development and potential liquefaction. We implement the soil model in the forward operator of the inversion, and evaluate the constitutive parameters that maximize the cross-correlation between site response predictions and observations on ground surface. The objective function is defined in the wavelet domain, which allows equal weight to be assigned across all frequency bands of the non-stationary signal. We evaluate the convergence rate and robustness of the proposed scheme for noisefree and noise-contaminated data, and illustrate good performance of the inversion for signal-to-noise ratios as low as 3. We finally employ the proposed scheme to downhole array data, and show that results compare very well with published data on generic soil conditions and previous geotechnical investigation studies at the array site. By assuming a realistic hysteretic model and estimating the constitutive soil parameters, the proposed inversion accounts for the instantaneous adjustment of soil response to the level and strain and load path during transient loading, and allows results to be used in predictions of nonlinear site effects during future events.

The paper studies the stability of unsupported tunnel faces by analyzing the results of a large number of 3D numerical analyses of tunnel faces, in various ground conditions and overburden depths. The analyses calculate the average face extrusion (Uh) by averaging the axial displacement over the tunnel face. Limiting face stability occurs when the average face extrusion becomes very large and algorithmic convergence becomes problematic. Using the results of the analyses, a dimensionless "face stability parameter" is defined, which depends on a suitable combination of ground strength, overburden depth and tunnel width. The face stability parameter correlates very well with many critical tunnel face parameters, like the safety factor of the tunnel against face instability, the average face extrusion, the radial convergence of the tunnel wall at the excavation face, the volume loss and the deconfinement ratio at the tunnel face. Thus, semi-empirical formulae are proposed for the calculation of these parameters in terms of the face stability parameter. Since the face stability parameter can be easily calculated from basic tunnel and ground parameters, the above critical tunnel parameters can be calculated, and conclusions can be drawn about tunnel face stability, volume loss and the deconfinement ratio at the excavation face which can be useful in preliminary tunnel designs.

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The paper studies the stability of unsupported tunnel faces by analyzing the results of a large number of 3D numerical analyses of tunnel faces, in various ground conditions and overburden depths. The analyses calculate the average face extrusion (Uh) by averaging the axial displacement over the tunnel face. Limiting face stability occurs when the average face extrusion becomes very large and algorithmic convergence becomes problematic. Using the results of the analyses, a dimensionless “face stability parameter” is defined, which depends on a suitable combination of ground strength, overburden depth and tunnel width. The face stability parameter correlates very well with many critical tunnel face parameters, like the safety factor of the tunnel against face instability, the average face extrusion, the radial convergence of the tunnel wall at the excavation face, the volume loss and the deconfinement ratio at the tunnel face. Thus, semi-empirical formulae are proposed for the calculation of these parameters in terms of the face stability parameter. Since the face stability parameter can be easily calculated from basic tunnel and ground parameters, the above critical tunnel parameters can be calculated, and conclusions can be drawn about tunnel face stability, volume loss and the deconfinement ratio at the excavation face which can be useful in preliminary tunnel designs.

Pre-support of tunnel excavation faces using fiberglass nails or forepoling umbrellas aims to improve face stability in cases where an unsupported excavation face will develop uncontrollably large face extrusion, leading to face instability. The paper presents the results of a large set of parametric 3D numerical analyses of tunnel face excavation by the Finite Element Code Simulia Abaqus, using various degrees of reinforcement by fiberglass nails or forepoling umbrellas. The analyses use the average face extrusion as a measure of face stability, considering that face instability is associated with large face extrusions while the safety factor against face instability can be correlated with lower face extrusions in case of pre-supported tunnel faces. The results of the analyses are normalized and a set of semi-empirical formulae and design graphs are produced to calculate the safety factor of supported tunnel faces against instability and other useful quantities in tunnel design (average face extrusion, volume loss and deconfinement coefficient) as a function of ground strength, overburden depth and amount of face reinforcement. The analyses show that tunnel face reinforcement with FG nails is much more effective and less costly in securing face stability than the use of forepoling umbrellas. It is shown that even a coarse grid of FG nails can achieve better results than very heavy forepoling, and the difference in effectiveness is more pronounced in weaker ground and or deeper tunnels.