Scaling Analysis for the Liquefaction Phenomena Induced by Water Waves

2016 ◽  
Author(s):  
E. Arcos ◽  
E. Bautista ◽  
F. Méndez
Keyword(s):  
Governing Equation ◽  
Analytical Solutions ◽  
Water Waves ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Scaling Analysis ◽  
Governing Equations ◽  
Order Of Magnitude ◽  
Characteristic Scales

In this work an scaling analysis of the liquefaction phenomena is presented. The characteristic scales are obtained by balancing term by term of the well known partial dynamics governing equations (approximation U – P). The order of magnitude of the horizontal displacement are very smaller compared with the vertical displacement and therefore the governing equation are only a function of the dependent vertical variables. The U – P approximation is reduced and presented in its dimensionless version. This scaling analysis can be used to obtain analytical solutions of the liquefaction phenomena under the action of the water waves.

scholarly journals Variational formulations of steady rotational equatorial waves

2020 ◽  
Vol 10 (1) ◽  
pp. 534-547
Author(s):  
Jifeng Chu ◽  
Joachim Escher
Keyword(s):  
Linear Stability ◽  
Stream Function ◽  
Water Waves ◽  
Variational Formulation ◽  
Energy Functional ◽  
Equatorial Waves ◽  
Second Variation ◽  
Governing Equations ◽  
The Second Variation ◽  
Variational Formulations

Abstract When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

scholarly journals Influence of rigidity of retainers on dynamic behavior of implant-supported removable partial dentures

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Toshifumi Nogawa ◽  
Masayasu Saito ◽  
Naomichi Murashima ◽  
Yoshiyuki Takayama ◽  
Atsuro Yokoyama
Keyword(s):  
Dynamic Behavior ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Denture Base ◽  
Second Molar ◽  
Mechanical Simulation ◽  
Computed Tomography Images ◽  
Significant Difference ◽  
Abutment Teeth ◽  
Distal Extension

Abstract Background Implant-supported removable partial dentures (ISRPDs) are an effective treatment for partially edentulous patients. ISRPDs improve patients’ satisfaction and oral function to a greater extent than RPDs by improving denture stability and enhancing support. However, the effect of a type of direct retainer on displacement of the abutment teeth and dentures in ISRPDs remains unclear. Therefore, we made a resin mandibular model of unilateral mandibular distal-extension partial edentulism for mechanical simulation and compared the dynamic behavior of the abutment teeth and the denture base among different tooth-borne retainers with various rigidities for RPDs and ISRPDs. Methods A resin mandibular model for mechanical simulation that had unilateral mandibular distal-extension edentulism and was missing the first molar, second molar, first premolar, and second premolar, and a denture fabricated from the patient’s computed tomography images were used. Three types of direct retainers with different connecting rigidities were evaluated. The vertical displacement of the denture base and buccal and lingual sides and the mesial displacement of the abutment teeth were measured. Results Regardless of the rigidity of the direct retainers and loading positions, the displacement of the denture bases in the ISRPDs was significantly smaller than that in the RPDs (P < 0.001). There was no significant difference in vertical displacement of the denture bases among direct retainers with various connecting rigidities in the ISRPDs. Conversely, horizontal displacement of the abutment teeth in both the RPDs and ISRPDs tended to be larger with the cone crown telescope, which has high rigidity, than with the cast cingulum rest and wire clasp, which have much lower rigidities. Conclusion Our results suggested that cast cingulum rest and wire clasps as direct retainers are appropriate ISRPDs to minimize denture movement and suppress displacement of the remaining teeth in patients with unilateral mandibular distal-extension partial edentulism.

scholarly journals Mechanical Property Analysis of Circular Polymer Membrane under Uniform Pressure

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Sang Jianbing ◽  
Li Xiang ◽  
Xing Sufang ◽  
Wang Wenjia
Keyword(s):  
Mechanical Property ◽  
Polymer Material ◽  
Vertical Displacement ◽  
Polymer Membrane ◽  
Constitutive Parameter ◽  
Deformation Analysis ◽  
Strengthening Effect ◽  
Uniform Pressure ◽  
Governing Equations ◽  
Property Analysis

Mechanical property analysis of circular hyperelastic polymer membrane under uniform pressure has been researched in this work. The polymer membrane material is assumed to be homogeneous and isotropic and incompressibility of materials has been considered. Based on the modified stain energy function from Gao and nonmomental theory of axial symmetry thin shell, finite deformation analysis of polymer membrane under uniform pressure has been proposed in current configuration and governing equations of polymer membrane have been achieved. By utilizing the boundary condition, theoretical results of governing equations have been obtained and vertical displacement distribution and stress distribution have been achieved. The results show that the constitutive parameternhas a strengthening effect on the polymer material and the constitutive parameterαplays a controlling role for the second strain invariantI2, which also has a strengthening effect on the polymer material. This research has revealed the deformational mechanism of polymer membrane and provided reference for the design of polymer membrane.

The Cedar Mountain, Nevada, earthquake of December 20, 1932*

1934 ◽  
Vol 24 (4) ◽  
pp. 345-384 ◽  
Author(s):  
Vincent P. Gianella ◽  
Eugene Callaghan
Keyword(s):  
Sierra Nevada ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Relative Movement ◽  
East Side ◽  
Owens Valley ◽  
The West ◽  
Horizontal Movement ◽  
San Andreas

Summary The Cedar Mountain, Nevada, earthquake took place at about 10h 10m 04s p.m., December 20, 1932. It was preceded by a foreshock noted locally and followed by thousands of aftershocks, which were reported as still continuing in January 1934. No lives were lost and there was very little damage. The earthquake originated in southwest central Nevada, east of Mina. A belt of rifts or faults in echelon lies in the valley between Gabbs Valley Range and Pilot Mountains on the west and Cedar Mountain and Paradise Range on the east. The length of this belt is thirty-eight miles in a northwesterly direction, and the width ranges from four to nine miles. The rifts consist of zones of fissures which commonly reveal vertical displacement and in a number of places show horizontal displacement. The length of the rifts ranges from a few hundred feet to nearly four miles, and the width may be as much as 400 feet. The actual as well as indicated horizontal displacement is represented by a relative southward movement of the east side of each rift. The echelon pattern of the rifts within the rift area indicates that the relative movement of the adjoining mountain masses is the same. The direction of relative horizontal movement corresponds to that along the east front of the Sierra Nevada at Owens Valley and on the San Andreas rift.

Estimation and Scaling of the Near-Saturated Hydraulic Conductivity

1999 ◽  
Vol 30 (3) ◽  
pp. 177-190 ◽  
Author(s):  
Per Atle Olsen
Keyword(s):  
Hydraulic Conductivity ◽  
Saturated Hydraulic Conductivity ◽  
Scaling Analysis ◽  
Laboratory Measurements ◽  
Estimation Errors ◽  
Geometric Means ◽  
Top Soil ◽  
Structured Soils ◽  
Order Of Magnitude

The hydraulic conductivity in structured soils is known to increase drastically when approaching saturation. Tension infiltration allows in situ infiltration of water at predetermined matric potentials, thus allowing exploration of the hydraulic properties near saturation. In this study, the near saturated (ψ≥-0.15 m) hydraulic conductivity was estimated both in the top- and sub-soil of three Norwegian soils. A priory analysis of estimation errors due to measurement uncertainties was conducted. In order to facilitate the comparison between soils and depths, scaling analysis was applied. It was found that the increase in hydraulic conductivity with increasing matric potentials (increasing water content) was steeper in the sub-soil than in the top-soil. The estimated field saturated hydraulic conductivity was compared with laboratory measurements of the saturated hydraulic conductivity. The geometric means of the laboratory measurements was in the same order of magnitude as the field estimates. The variability of the field estimates of the hydraulic conductivity from one of the soils was also assessed. The variability of the field estimates was generally smaller than the laboratory measurements of the saturated hydraulic conductivity.

scholarly journals CONCERNING THE EXTRACTION OF A SLACK SOIL LAYER FROM COMPRESSIBLE THICKNESS OF FOUNDATION STRATUM OF FINITE WIDTH FOUNDATIONS

2019 ◽  
Vol 7 (4) ◽  
pp. 49-56
Author(s):  
Zaven Ter-Martirosyan ◽  
Armen Ter-martirosyan ◽  
Valery DEMYANENKO
Keyword(s):  
Analytical Solutions ◽  
Soft Soil ◽  
Soil Layer ◽  
Horizontal Displacement ◽  
Creep Model ◽  
Shear Stresses ◽  
Finite Width ◽  
Relative Depth ◽  
Weak Layer ◽  
Horizontal Displacements

The paper provides a quantitative assessment of the deflected mode of foundation stratum of finite width foundation, in the compressible thickness of which there is a slack clay soil layer. A number of criteria for assessing the possibility or impossibility of extruding a slack layer depending on its strength and rheological properties, as well as the relative thickness of the layer to its length (h/l) and the relative depth of the layer (h/d) have been given. Closed analytical solutions are given to determine the rate of Foundation precipitation depending on the rate of extrusion of the weak layer, including taking into account the damped and undamped creep. The analytical solutions in the article are supported by the graphical part made with the help of the Mathcad program. Plots of changes in shear stresses in the layer along the x axis at different distances from the axis and at different values 0, contours of horizontal displacement velocities in the weak layer at different distances from the x axis, plots of horizontal displacement velocities in the middle of the weak layer and plots of horizontal displacement velocities in the weak layer at different distances from the x axis are given. As a calculation model for describing the creep of a slack layer, rheological ones of the soil using power and hyperbolic functions and their modifications have been considered. In addition, most modern rheological models that take into account soil hardening during creep have been considered. Based on these models, the problem is solved by means analytical and numerical methods using the Mathcad PC and the PLAXIS PC according to the Soft Soil Creep model. The graphical part shows the isofields of horizontal displacements for 300 days and 600 days and the corresponding contours of horizontal displacements.

scholarly journals Comparison of Dynamic Characteristics between Small and Super-Large Diameter Cross-River Twin Tunnels under Train Vibration

2021 ◽  
Vol 11 (16) ◽  
pp. 7577
Author(s):  
Lin Wu ◽  
Xiedong Zhang ◽  
Wei Wang ◽  
Xiancong Meng ◽  
Hong Guo
Keyword(s):  
Dynamic Characteristics ◽  
Large Diameter ◽  
Horizontal Displacement ◽  
Element Model ◽  
Vertical Displacement ◽  
Decisive Factor ◽  
Cross River ◽  
Static Responses ◽  
Train Vibration ◽  
Twin Tunnels

Train vibration from closely aligned adjacent tunnels could cause safety concerns, especially given the soaring size of the tunnel diameter. This paper established a two-dimensional discrete element model (DEM) of small (d = 6.2 m) and super-large (D = 15.2 m) diameter cross-river twin tunnels and discussed the dynamic characteristics of adjacent tunnels during the vibration of a train that runs through the tunnel at a speed of 120 km/h. Results in the D tunnel showed that the horizontal walls have the same horizontal displacement (DH) and the vertical walls have the same vertical displacement (DV). The stress state of the surroundings of the D tunnel is the decisive factor for DH, and the distance from the vibration point to the measurement point is the decisive factor for DV. Results in the comparison of the d and D tunnels showed that the D tunnel is more stable than the d tunnel with respect to two aspects: the time the tunnel reaches the equilibrium state and the vibration amplitude of the structure’s dynamic and static responses. The dynamic characteristic of the d and D tunnel is significantly different. This research is expected to guide the design and construction of large diameter twin tunnels.

scholarly journals The Gujarat, West India, earthquake (Jan 26th 2001). A geodynamic event in an intraplate compressional regime?

2001 ◽  
Vol 34 (4) ◽  
pp. 1405
Author(s):  
Γ. Δ. ΔΑΝΑΜΟΣ ◽  
Ε. Λ. ΛΕΚΚΑΣ ◽  
Σ. Γ. ΛΟΖΙΟΣ
Keyword(s):  
Large Scale ◽  
Lateral Displacement ◽  
Indian Subcontinent ◽  
Plate Boundary ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Lateral Spreading ◽  
Tectonic Deformation ◽  
Epicentral Area ◽  
Surface Ruptures

The Jan. 26, 2001, Ms=7.7 earthquake occurred in Gujarat region of W. India, which lies 200-400 Km away from the active plate boundary zone, between the Indian subcontinent and the Asian plate, along the India-Pakistan border and the Himalayan belt. An Ms=7.7±0.2 earthquake also occurred in the same region in 1819. A zone of co-seismic E-W surface ruptures, 30-40 Km long and 15-20 Km wide, observed near the epicentral area and seems to be associated with pre-existing reverse faults and thrust folds, which were partially reactivated during the recent earthquake. Except the reverse vertical displacement a significant right lateral displacement was also observed along these E-W surface ruptures. This Ms=7.7 seismic event has been also accompanied by a large scale flexural-slip folding, as the absence of significant co-seismic fault displacement and fault scarp shows. This type of compressional tectonic deformation is also confirmed by the focal mechanism of the earthquake and the seismo-tectonic "history" of the area. The NW-SE open cracks, also observed along the same zone, are associated with the right lateral horizontal displacement of the reactivated fault (or branch faults) and the development of local extensional stress field in the huge anticlinic hinges of the co-seismic flexural-slip folds. A large number of ground ruptures, failures and open cracks are also associated with extensive sand boils, liquefaction phenomena and lateral spreading.

Stress and Deformation Characteristics of Rock-Fill Dam with Asphalt Concrete Core Wall Founded on Deep Overburden

2013 ◽  
Vol 405-408 ◽  
pp. 428-433
Author(s):  
Fu Yong Chu ◽  
Jun Gao Zhu
Keyword(s):  
Yield Surface ◽  
Asphalt Concrete ◽  
Water Storage ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Surface Model ◽  
Concrete Core ◽  
Rock Fill ◽  
Stress And Deformation ◽  
Double Yield

Abstract: The stress and deformation of rock-fill dam with asphalt concrete core wall founded on deep overburden is calculated and analyzed by Duncan E-ν model and double-yield-surface model through three-dimensional finite element method. The stress and deformation of dams in water storage period is compared by the two models, the results show that the deformation distribution of dam core via two different models are coincide one another. The horizontal displacement and vertical displacement of rock-fill dam with asphalt concrete core wall by double-yield-surface model is smaller than which by Duncan E-ν model in the period of water storage. Furthermore, the horizontal displacement and vertical displacement by double-yield-surface model, which are close to the practical test data through the deformation via two models are in good agreement. The analysis of core-wall stress via double-yield-surface model is more reasonable than the Duncan E-ν model. The analysis result of resisting hydraulic fracturing of core dams by DuncanE-ν model is coincide which of core dams by double-yield-surface model.

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