Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated, poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.

AN ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL DIFFRACTION OF PLANE P-WAVES BY A HEMISPHERICAL ALLUVIAL VALLEY WITH SATURATED SOIL DEPOSITS

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot＇s dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot＇s dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

DYNAMIC ANALYSIS OF PIPELINES LAID THROUGH ALLUVIAL VALLEY

This paper describes the dynamic characteristics of pipelines laid through alluvial valleys. We assume that the alluvial valley has a semi-cylindrical cross-section. The ground motion of alluvial valley under harmonic seismic SH waves is carried out, and the pipeline-soil dynamic interaction is taken into account. Though simple, the model may qualitatively explain the earthquake damages of pipelines laid through an alluvial river valley.

Seismic responses of a hemispherical alluvial valley to SV waves: a three-dimensional analytical approximation

Abstract An analytical solution to the three-dimen-sional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expan-sion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot＇s dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn： （1） there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; （2） the nor-malized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; （3） with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

Surface Motion of Alluvial Valley in Layered Half-Space for Incident Plane P-Waves

The indirect boundary element method (IBEM) is used to study the surface motion of an alluvial valley in layered half-space for incident plane P-waves based on Wolf’s theory. Firstly, the free field response can be solved by the direct stiffness method, and the scattering wave response is calculated by Green’s functions of distributed loads acting on inclined lines in a layered half-space. The method is verified by comparing its results with literature and numerical analyses are performed by taking the amplification of incident plane P-waves by an alluvial valley in one soil layer resting on bedrock as an example. The results show that there exist distinct differences between the wave amplification by an alluvial valley embedded in layered half-space and that in homogeneous half-space and there is interaction between the valley and the soil layer. The amplitudes are relatively large when incident frequencies are close to the soil layer’s resonant frequencies.

Dynamic response of an alluvial valley consists of three types of soil

Dynamic response of an alluvial valley consisting of three different types of soil was studied.In the twodimensional model,the alluvial valley was assumed to have half-cylindrical shape.The alluvial valley contained three different types of soil with different shapes.The valley was surrounded by a half-space.All of the soil types and the half-space were assumed to be isotropic,homogeneous and linear elastic.The half-space was excited by simple harmonic SH-waves radiated from a strike-slip fault.The fault was assumed to have circular-arc shape in the mathematical model.The governing equations were solved by using wave function expansion method where boundary conditions were relatively simple.In the regions where boundary conditions were more complex,finite difference method was employed.Consequently,the wave propagation problem was solved semi-analytically.The obtained numerical results showed that surface displacement amplitudes are significantly affected by the material properties of the different soil types of the alluvial valley.It was also observed that the shapes of the soil types in the alluvial valley played a considerable role in surface displacements.

Scattering of Rayleigh waves by a shallow circular alluvial valley: High-frequency solution

A high-frequency analytical solution for scattering of Rayleigh waves by a shallow circular alluvial valley was derived using wave function expansion method, and the solution was utilized to analyze the effects of incident frequency, width of the valley, and depth of the valley, etc, on the wave scattering. Numerical results showed that, because of the alluvial valley, the distribution of surface displacement at the side where wave arrives becomes relatively complicated, but the displacement amplitude is not large; the distribution of the surface displacement at far side is relatively simple, but the displacement amplitude is relatively large, and in most cases the amplitude is larger than that at the alluvium.

Weighted residual method for diffraction of plane P-waves in a 2-D elastic half-spaceⅢ:on an almost circular arbitrary-shaped alluvial valley

Scattering and diffraction of elastic in-plane P- and SV-waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong motion seismologists for over forty years. The case of out-of- plane SH-waves on the same elastic canyon that is semicircular in shape on the half-space surface is the first such problem that was solved by analytic closed-form solutions over forty years ago by Trifunac. The corresponding case of in-plane P- and SV- waves on the same circular canyon is a much more complicated problem because the in-plane P- and SV- scattered waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by Lee and Liu. This paper uses their technique of defining these stress-free scattered waves, which Brandow and Lee previously used to solve the problem of the scattering and diffraction of these in-plane waves on an almost-circular surface canyon that is arbitrary in shape, to the study of the scattering and diffraction of these in-plane waves on an almost circular arbitrary-shaped alluvial valley.

3-D Scattering of Obliquely Incident Plane P Waves by Alluvial Valley Embedded in Layered Half-Space

The indirect boundary element method(IBEM) was established to solve the problem of 3-D seismic responses of 2-D topographies,by calculating the free-field responses with the direct-stiffness method and simulating the scattering wave fields with the dynamic Green's functions of moving distributed loads.The proposed method yields accurate results,because the 3-D dynamic stiffness matrixes used are exact and the fictitious moving distributed loads can be acted directly on the interface between the alluvial valley and the layered half-space without singularity.The comparison with the published methods verifies the validity of the proposed method.And the numerical analyses are performed to give some beneficial conclusions.The study shows that 3-D scattering by an alluvial valley is essentially different from the 2-D case,and that the presence of soil layer affects not only the amplitude value of surface displacements but also the distribution of surface displacements.

Three-dimensional Scattering of Obliquely Incident Plane SH Waves by an Alluvial Valley in a Layered Half-space

The indirect boundary element method （IBEM） is used to study three-dimensional scattering of obliquely incident plane SH waves by an alluvial valley embedded in a layered half-space. The free-field response of the layered half-space is calculated by the direct stiffness method, and dynamic Green＇s functions of moving distributed loads acting on inclined lines in a layered half-space are calculated to simulate the scattering wave field. The presented method yields very accurate results since the three-dimensional dynamic stiffness matrix is exact and the moving distributed loads can act directly on the valley boundary without singularity. Numerical results and analyses are performed for amplification of obliquely incident plane SH waves around an alluvial valley in a uniform half-space and in single layer over half-space. The results show that the three-dimensional responses are distinctly different from the two-dimensional responses, and the displacement amplitudes around alluvial valleys in a uniform haft-space are obviously different from those in a layered half-space.

Hydrogeochemical Characterization of Aquifer Systems and Surface Water/Groundwater Relations in the Lower Senegal River Valley

This study assesses the chemical quality of water resources in the Lower Senegal River valley, based on 35 samples collected in November 2022. Major ion concentrations in surface water and groundwater were analyzed using classical geochemical interpretation diagrams (Piper, GIBBS, etc.) and multivariate geostatistical analyses, including hierarchical cluster analysis (HCA) and principal component analysis (PCA). The results revealed three types of facies: Ca-Mg-HCO3-type facies, characteristic of poorly mineralized waters such as surface waters and groundwater from dune formations and the alluvial plain close to the hydraulic axis;Na-Cl type facies associated with well waters located in the alluvial plain that tap Inchirian or Nouakchottian shallow reservoirs and Maastrichtian deep borehole waters;and mixed Ca-Cl and Na-HCO3 type facies observed in certain floodplain and dune reservoirs. The results showed a strong correlation between sodium, chlorides, bromides, and electrical conductivity, indicating a significant contribution of these ions to groundwater mineralization. The various sources of water mineralization include mixing processes between surface water or rainwater, or calcite or dolomite dissolution processes (for weakly mineralized waters), basic exchanges or inverse basic exchanges between the aquifer and the water table (for moderately mineralized waters), and evaporation processes, halite dissolution, and paleosalinity during periods of marine transgression and regression (for highly mineralized waters). The study also highlighted the high vulnerability of the alluvial aquifer to pollution from intensive irrigated agriculture, as significant quantities of sulfates and nitrates were measured in some samples. These results also highlight the importance of water quality management in the Lower Senegal Valley, particularly as concerns the protection of the alluvial aquifer against pollution from irrigated agriculture.