Semi‐analytical solution for one‐dimensional consolidation of a two‐layered soil system with unsaturated and saturated conditions

2021 ◽  
Author(s):  
Linzhong Li ◽  
Aifang Qin ◽  
Lianghua Jiang
Keyword(s):  
Analytical Solution ◽  
Layered Soil ◽  
Soil System ◽  
One Dimensional

scholarly journals Analytical Solution for One-Dimensional Nonlinear Consolidation of Saturated Double-Layered Soil Subjected to Cyclic Loadings

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Pyol Kim ◽  
Chol-U Pak ◽  
Hakbom Myong
Keyword(s):  
Cyclic Loading ◽  
Analytical Solution ◽  
Soft Soil ◽  
Layered Soil ◽  
Time Dependent ◽  
Saturated Soils ◽  
One Dimensional ◽  
Special Cases ◽  
Nonlinear Consolidation ◽  
Good Agreement

Cyclic loading-induced consolidation behavior of soft soil is of great interest for the analysis of offshore and onshore structures. In this study, an analytical solution for one-dimensional (1D) nonlinear consolidation of saturated double-layered soil under various types of cyclic loadings such as trapezoidal cyclic loading, rectangular cyclic loading, and triangular cyclic loading was derived. The proposed solution was subsequently degenerated into solutions for special cases and compared to the existing solutions. The degenerate solutions show good agreement with the existing results, which proves that the proposed solutions are more general ones for 1D nonlinear consolidation of saturated soils under time-dependent loading. Finally, a comprehensive parametric study was conducted to investigate the influences of different layer parameters, drainage conditions, and loading parameters on nonlinear consolidation of saturated double-layered soil under cyclic loadings.

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

State-of-the-Art Techniques for Seismic Soil-Structure Interaction Analysis of Steel Gravity Structures

2014 ◽  
Author(s):  
Frederick Tajirian ◽  
Mansour Tabatabaie ◽  
Basilio Sumodobila ◽  
Stephen Paulson ◽  
Bill Davies
Keyword(s):  
Soil Structure ◽  
State Of The Art ◽  
Interaction Analysis ◽  
Layered Soil ◽  
Soil Structure Interaction ◽  
Soil System ◽  
Cyclonic Storm ◽  
Structure Interaction ◽  
Analysis Methods ◽  
Moderate Seismicity

The design of steel jacket fixed offshore structures in zones of moderate seismicity is typically governed by Metocean loads. In contrast the steel gravity structure (SGS) presented in this paper, is a heavy and stiff structure. The large mass results in foundation forces from seismic events that may exceed those created by extreme cyclonic storm events. When computing the earthquake response of such structures it is essential to account for soil-structure interaction (SSI) effects. Seismic SSI analysis of the SGS platform was performed using state-of-the-art SSI software, which analyzed a detailed three-dimensional model of the SGS supported on layered soil system. The results of this analysis were then compared with those using industry standard impedance methods whereby the layered soil is replaced by equivalent foundation springs (K) and damping (C). Differences in calculated results resulting from the different ways by which K and C are implemented in different software are presented. The base shear, overturning moment, critical member forces and maximum accelerations were compared for each of the analysis methods. SSI resulted in significant reduction in seismic demands. While it was possible to get reasonable alignment using the different standard industry analysis methods, this was only possible after calibrating the KC foundation model with software that rigorously implements SSI effects. Lessons learned and recommendations for the various methods of analysis are summarized in the paper.

Building Vertical Walls by Deposition of Molten Metal Droplets

2005 ◽  
Author(s):  
M. Fang ◽  
S. Chandra ◽  
C. B. Park
Keyword(s):  
Surface Layer ◽  
Analytical Solution ◽  
Substrate Temperature ◽  
Layer By Layer ◽  
Droplet Temperature ◽  
Droplet Generator ◽  
One Dimensional ◽  
Metallurgical Bonding ◽  
Experimental Parameters ◽  
Vertical Walls

Experiments were conducted to determine conditions under which good metallurgical bonding was achieved in vertical walls composed of multiple layers of droplets that were fabricated by depositing tin droplets layer by layer. Molten tin droplets (0.75 mm diameter) were deposited using a pneumatic droplet generator on an aluminum substrate. The primary parameters varied in experiments were those found to most affect bonding between droplets on different layers: droplet temperature (varied from 250°C to 325°C) and substrate temperature (varied from 100°C to 190°C). Considering the cooling rate of droplet is much faster than the deposition rate previous deposition layer cooled down too much that impinging droplets could only remelt a thin surface layer after impact. Assuming that remelting between impacting droplets and the previous deposition layer is a one-dimensional Stefan problem with phase change an analytical solution can be found and applied to predict the minimum droplet temperature and substrate temperature required for local remelting. It was experimentally confirmed that good bonding at the interface of two adjacent layers could be achieved when the experimental parameters were such that the model predicted remelting.

scholarly journals Simplified analytical solution for stress concentration ratio of piled embankments incorporating pile–soil interaction

2021 ◽  
Author(s):  
Qiang Luo ◽  
Ming Wei ◽  
Qingyuan Lu ◽  
Tengfei Wang
Keyword(s):  
Stress Concentration ◽  
Analytical Solution ◽  
High Speed ◽  
Concentration Ratio ◽  
Differential Settlement ◽  
Fundamental Parameter ◽  
Soil System ◽  
Rigid Pile ◽  
Stress Concentration Ratio ◽  
Piled Embankments

AbstractPiled embankments have been extensively used for high-speed rail over soft soils because of their effectiveness in minimizing differential settlement and shortening the construction period. Stress concentration ratio, defined as the ratio of vertical stress carried by pile heads (or pile caps if applicable) to that by adjacent soils, is a fundamental parameter in the design of piled embankments. In view of the complicated load transfer mechanism in the framework of embankment system, this paper presents a simplified analytical solution for the stress concentration ratio of rigid pile-supported embankments. In the derivation, the effects of cushion stiffness, pile–soil interaction, and pile penetration behavior are considered and examined. A modified linearly elastic-perfectly plastic model was used to analyze the mechanical response of a rigid pile–soil system. The analytical model was verified against field data and the results of numerical simulations from the literature. According to the proposed method, the skin friction distribution, pile–soil relative displacement, location of neural point, and differential settlement between the pile head (or cap) and adjacent soils can be determined. This work serves as a fast algorithm for initial and reasonable approximation of stress concentration ratio on the design aspects of piled embankments.

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