Exact seismic response of smooth rigid retaining walls resting on stiff soil

The assessment of forces exerted on walls by the backfill is a recurrent problem in geotechnical engineering, owing to its relevance for both retaining systems and underground structures. In particular, the work by Arias and colleagues, and later also the one by Veletsos and Younan, among others, becomes pertinent when considering pressure increments on underground structures triggered by seismic events. As a first step, they studied the response of a rigid retaining wall resting on rigid bedrock subjected to SV waves, introducing some simplifying assumptions. This paper presents the exact solution to this reference problem. The solution is given in horizontal wavenumber domain; hence, it comes in terms of inverse Fourier transforms, which can be approximated numerically in Mathematica , which in turn are verified against finite‐element simulations. Specific features of this exact solution that were not captured by prior engineering approximations are highlighted and discussed

On the fundamental resonant mode of inhomogeneous soil deposits

The problem of estimating seismic ground deformation is central to state-of-practice procedures of designing and maintaining infrastructure in earthquake-prone areas. Particularly, the problem of estimating the displacement field in a soft shallow layer overlying rigid bedrock induced by simple shear wave excitation has been favored by engineers due to its simplicity combined with inherent relevance for practical scenarios. We here derive analytical estimates for both the fundamental frequency and the amplitude of the first resonant mode of such systems by applying an intuitive argument based on resonance of single-degree-of-freedom systems. Our estimates do not presuppose a continuous velocity distribution, and can be used for fast assessment of site response in seismic hazard assessment and engineering design. On the basis of the said estimates of fundamental frequency and amplitude, we next propose a novel definition of “equivalent homogeneous shear modulus” of the inhomogeneous deposit, and we show that the response of the fundamental mode is controlled primarily by the properties of the layers contiguous to the bedrock. We finally discuss the validity of our argument, and evaluate the accuracy of our results by comparison with analytical and numerical solutions

From Stiffness to Strength: Formulation and Validation of a Hybrid Hyperbolic Nonlinear Soil Model for Site‐Response Analyses

Nonlinear site‐response analyses are becoming an increasingly important component of simulated ground motions for engineering applications. For regional‐scale problems for which geotechnical data are sparse, the challenge lies in computing site response using a very small number of input parameters. We developed a nonlinear soil model that, using only the shear‐wave velocity profile, captures both the low‐strain stiffness and large‐strain strength of soils and yields reliable predictions of soil response to weak and strong shaking. We here present the formulation of the model and an extensive validation study based on downhole array recordings, with peak ground acceleration (PGA) ranging from 0.01g to 0.9g. We also show that our model, referred to as hybrid hyperbolic (HH), outperforms existing nonlinear formulations and simplified site‐response analyses widely used in practice for ground motions that induce more than 0.04% of soil strain (roughly equivalent to PGA higher than 0.05g). In addition to site‐specific response predictions at sites with limited site characterization, the HH model can help improve site amplification factors of ground‐motion prediction equations (GMPEs) by complementing the empirical data with simulated site‐response analyses for very strong ground shaking, as well as physics‐based ground‐motion simulations, particularly for deeper sedimentary sites with low resonant frequencies

On the complexity of seismic waves trapped in non-flat geologic features

Most earthquake engineering and seismological models make the sweeping assumption that the world is flat. The ground surface topography, however, has been repeatedly shown to strongly affect the amplitude, frequency, duration and damage induced by earthquake shaking, effects mostly ignored in earthquake simulations and engineering design. In this talk, I will show a collection of examples that highlight the effects of topography on seismic ground shaking, and I will point out what these results suggest in the context of the current state-of-earthquake engineering practice. Examples will range from semi-analytical solutions of wave propagation in infinite wedge to three-dimensional numerical simulations of topography effects using digital elevation map-generated models and layered geologic features. I will conclude by demonstrating that ‘topography’ effects vary strongly with the stratigraphy and inelastic behavior of the underlying geologic materials, and thus cannot be accurately predicted by studying the effects of ground surface geometry alone

Geometrical Optics applied to 1D Site Response of Inhomogeneous Soil Deposits

The technique referred as Geometrical Optics entails considering the wave propagation in a heterogeneous medium as if it happened with infinitely small wavelength. This classic simplification allows to obtain useful approximate analytical results in cases where complete description of the waveform behavior is virtually unattainable, hence its wide use in Physics. This approximation is also commonly termed Ray Theory, and it has already been thoroughly applied in Seismology. This text presents an application of Geometrical Optics to 1D Site Response (1DSR): it is used herein to, first, explain and elucidate the generality of some previous observations and results; second, to partially settle an open question in 1DSR, namely “what are the equivalent homogeneous properties that yield the same response, in terms of natural frequencies and resonance amplitude, for a certain inhomogeneous site?”, provided few assumptions

International Benchmark on Numerical Simulations for 1D, Nonlinear Site Response (PRENOLIN): Verification Phase Based on Canonical Cases

PREdiction of NOn‐LINear soil behavior (PRENOLIN) is an international benchmark aiming to test multiple numerical simulation codes that are capable of predicting nonlinear seismic site response with various constitutive models. One of the objectives of this project is the assessment of the uncertainties associated with nonlinear simulation of 1D site effects. A first verification phase (i.e., comparison between numerical codes on simple idealistic cases) will be followed by a validation phase, comparing the predictions of such numerical estimations with actual strong‐motion recordings obtained at well‐known sites. The benchmark presently involves 21 teams and 23 different computational codes. We present here the main results of the verification phase dealing with simple cases. Three different idealized soil profiles were tested over a wide range of shear strains with different input motions and different boundary conditions at the sediment/bedrock interface. A first iteration focusing on the elastic and viscoelastic cases was proved to be useful to ensure a common understanding and to identify numerical issues before pursuing the nonlinear modeling. Besides minor mistakes in the implementation of input parameters and output units, the initial discrepancies between the numerical results can be attributed to (1) different understanding of the expression “input motion” in different communities, and (2) different implementations of material damping and possible numerical energy dissipation. The second round of computations thus allowed a convergence of all teams to the Haskell–Thomson analytical solution in elastic and viscoelastic cases. For nonlinear computations, we investigate the epistemic uncertainties related only to wave propagation modeling using different nonlinear constitutive models. Such epistemic uncertainties are shown to increase with the strain level and to reach values around 0.2 (log_(10) scale) for a peak ground acceleration of 5  m/s^2 at the base of the soil column, which may be reduced by almost 50% when the various constitutive models used the same shear strength and damping implementation