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

Phase-space iterative solvers

I introduce a new iterative method to solve problems in small-strain non-linear elasticity. The method is inspired by recent work in data-driven computational mechanics, which reformulated the classic boundary value problem of continuum mechanics using the concept of "phase space". The latter is an abstract metric space, whose coordinates are indexed by strains and stress components, where each possible state of the discretized body corresponds to a point. Since the phase space is associated to the discretized body, it is finite dimensional. Two subsets are then defined: an affine space termed "physically-admissible set" made up by those points that satisfy equilibrium and a "materially-admissible set" containing points that satisfy the constitutive law. Solving the boundary-value problem amounts to finding the intersection between these two subdomains. In the linear-elastic setting, this can be achieved through the solution of a set of linear equations; when material non-linearity enters the picture, such is not the case anymore and iterative solution approaches are necessary. Our iterative method consists on projecting points alternatively from one set to the other, until convergence. The method is similar in spirit to the "method of alternative projections" and to the "method of projections onto convex sets", for which there is a solid mathematical foundation that furnishes conditions for existence and uniqueness of solutions, upon which we rely to uphold our new method's performance. We present two examples to illustrate the applicability of the method, and to showcase its strengths when compared to the classic Newton-Raphson method, the usual tool of choice in non-linear continuum mechanics.Comment: 22 pages, 7 tables, 6 figure

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

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

Linear one-dimensional site response analysis in the presence of stiffness-less free surface for certain power-law heterogeneities

We revisit previous results in small-strain One-dimensional Site Response Analysis of heterogeneous soil deposits. Specifically, we focus on sites whose shear modulus distribution is described by means of a power law that yields zero stiffness at the free surface. First, we show that in some cases (which we characterize in detail) considerations of energy finitude should prevail over considerations of vanishing tractions at the free-surface, as these may pose acuter constrains. We re-evaluate previous contributions in light of this result. Second, we analyze the previously-reported occurrence of “energy accumulation in upper layers”, providing a physical explanation for it. In passing, we supply estimates of the natural frequencies, and compare these with our previous results

Linear one-dimensional site response analysis in the presence of stiffness-less free surface for certain power-law heterogeneities

We revisit previous results in small-strain One-dimensional Site Response Analysis of heterogeneous soil deposits. Specifically, we focus on sites whose shear modulus distribution is described by means of a power law that yields zero stiffness at the free surface. First, we show that in some cases (which we characterize in detail) considerations of energy finitude should prevail over considerations of vanishing tractions at the free-surface, as these may pose acuter constrains. We re-evaluate previous contributions in light of this result. Second, we analyze the previously-reported occurrence of “energy accumulation in upper layers”, providing a physical explanation for it. In passing, we supply estimates of the natural frequencies, and compare these with our previous results

“El Turismo Rural como Modelo de Desarrollo Turístico y sus efectos ambientales en la Fundación María Cavalleri, Municipio de Matagalpa, Departamento de Matagalpa, durante el II Semestre 2009”

Se investigó el Turismo Rural como Modelo de Desarrollo Turístico y sus efectos ambientales en la Finca Agroecológica “Fundación María Cavalleri”, municipio de Matagalpa, departamento de Matagalpa, durante el II Semestre 2009. Con el propósito de analizar los efectos ambientales que genera el Turismo Rural en dicha finca. Las principales temáticas abordadas en esta investigación son: El Turismo Rural como Modelo de Desarrollo Turístico, Actividades de Turismo Rural en la Fundación María Cavalleri y Efectos que genera el Turismo Rural en el Medio Ambiente. Este estudio se realizó a través de entrevistas dirigidas a trabajadores de la Fundación María Cavalleri, giras de campo a la finca para la complementación y constatación de la información. Los aspectos más relevantes del estudio reflejan que El Turismo Rural se aplica como modelo de desarrollo turístico a rasgos generales en la Finca Agroecológica Fundación María Cavalleri, ya que se desarrolla en el medio rural debido a las condiciones físicas y geográficas de la misma. Por otro lado queda en manifiesto que el Turismo Rural crea conciencia turística en sus gestores y beneficiarios, así mismo innova en nuevas técnicas de producción sostenibles y, contribuye al rescate y conservación del Medio Ambient