Three‐dimensional models of reservoir sediment and effects on the seismic response of arch dams

Abstract

SUMMARYThe important e ects of bottom sediments on the seismic response of arch dams are studied in this paper. To do so, a three-dimensional boundary element model is used. It includes the water reservoir as a compressible uid, the dam and unbounded foundation rock as viscoelastic solids, and the bottom sediment as a two-phase poroelastic domain with dynamic behaviour described by Biot's equations. Dynamic interaction among all those regions, local topography and travelling wave e ects are taken into account. The results obtained show the important in uence of sediment compressibility and permeability on the seismic response. The former is associated with a general change of the system response whereas the permeability has a signiÿcant in uence on damping at resonance peaks. The analysis is carried out in the frequency domain considering time harmonic excitation due to P and S plane waves. The timedomain results obtained by using the Fourier transform for a given earthquake accelerogram are also shown. The possibility of using simpliÿed models to represent the bottom sediment e ects is discussed in the paper. Two alternative models for porous sediment are tested. Simpliÿed models are shown to be able to reproduce the e ects of porous sediments except for very high permeability values.

Influence of reservoir geometry and conditions on the seismic response of arch dams

“…[11]), or it can be modeled as a porous elastic saturated material whose skeleton has taken on some type of elastic capacity (the sediment can transmit shear waves). This study follows earlier research [4,6,18,19,20,11] and assumes that the dynamic behavior of sediment is similar to that of the porous elastic saturated or quasi-saturated material in accordance with the Biot formulation [21]. All of these studies conclude that compressibility plays a role in how bottom sediments can significantly modify global dynamic behavior, especially in the case of partially saturated sediments.…”

“…Specifically, upstream reservoir geometry, reservoir level and degree of saturation of bottom sediments are investigated. A Boundary Element model developed by the authors is used which allows a direct and coupled analysis of all of the involved regions: dam, foundation rock, reservoir water and bottom sediments [20]. Dam and foundation rock are modeled as viscoelastic solids, water as an inviscid compressible fluid and bottom sediment as a poroelastic material according to a Biot model.…”

“…The Morrow Point dam (located in Black Canyon National Park, Gunnison River, Colorado, USA) has been chosen for the analysis proposed in this paper since it is well known from previous works ( [2], [5], [9], [10], [20], [23]). The model assumes that the dam and foundation rock are linear, isotropic, viscoelastic materials with internal damping according to hysteretic damping model, being the latter a boundless domain when compared to the dam dimensions.…”

“…The pressure-wave velocity of reservoir water is assumed to be c w = 1438 m/s and density ρ w = 1000 kg/m3. Bottom sediment is a two-phase porous material and has the same properties used by Bougacha & Tassoulas [6] and Domínguez, Gallego, & Japón [18] in their twodimensional studies of seismic response of gravity dams and adopted by Maeso, Aznárez, & Domínguez [20] in their three dimensional studies of arch dams: porosity φ = 0.6, shear modulus of the solid skeleton µ s = 7.7037 MPa, Poisson's ratio ν s = 0.35, internal damping factor ξ s = 0.05, solid particles density ρ s = 2640 kg/m3, pore water density ρ w =1000 kg/m 3 , added density ρ a = 0, bulk modulus of the fully saturated pore fluid f K = 2.0736x10 9 N/m 2 , dissipation constant b = 3.5316x10 6 Ns/m 4 (corresponding to a hydraulic conductivity κ = 10 -3 m/s). The bulk modulus, when sediment is partially saturated, has been calculated by using the following equation presented by Verruijt [22]:…”

“…To address it, a numerical model based on the Boundary Element Method is used. This model is described by the authors in previous studies, such as in [11] or [20]. All the regions of the dam-reservoir-sedimentfoundation system are represented by boundary integral equations discretized into boundary elements, taking into account their specific characteristics and the interaction between them by using existing compatibility and equilibrium relationships on the variables defined for each domain in the nodes of the contact surfaces.…”