scholarly journals An Equal-Strain Analytical Solution for the Radial Consolidation of Unsaturated Soils by Vertical Drains considering Drain Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Zhou ◽  
Zheng Chen ◽  
Xudong Wang
Keyword(s):  
Analytical Solution ◽  
Unsaturated Soils ◽  
Ground Surface ◽  
Matrix Analysis ◽  
Governing Equations ◽  
Vertical Drains ◽  
Ground Surface Settlement ◽  
Parametric Studies ◽  
Strain Model ◽  
Good Agreement

Developing an analytical solution for the consolidation of unsaturated soils remains a challenging task due to the complexity of coupled governing equations for air and water phases. This paper presents an equal-strain model for the radial consolidation of unsaturated soils by vertical drains, and the effect of drain resistance is also considered. Simplified governing equations are established, and an analytical solution to calculate the excess pore-air and pore-water pressures is derived by using the methods of matrix analysis and eigenfunction expansion. The average degrees of consolidation for air and water phases and the ground surface settlement are also given. The solutions of the equal-strain model are verified by comparing the proposed free-strain model with the equal-strain model, and reasonably good agreement is obtained. Moreover, parametric studies regarding the drain resistance effect are graphically presented.

Dynamic Response of Ground Surface Due to External Disturbance: Analytical Solution

2008 ◽  
Author(s):  
Hamid R. Hamidzadeh
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Wave Equations ◽  
External Disturbance ◽  
Ground Surface ◽  
Equation Of Motion ◽  
Elastic Half Space ◽  
Fourier Domain ◽  
Dynamics Analysis ◽  
Governing Equations

In this investigation the propagation of a harmonic disturbance on the surface of ground is considered. The medium is assumed to be a homogeneous and isotropic, continuous and infinite which can be modeled as an elastic half space medium. Implementing elasto-dynamics analysis, the governing equation of motion for the system is developed. The developed mathematical model formulates the displacement and stresses in the medium in terms of elastic dilatation and rotations and reduces the governing equations into three wave equations in terms of elastic dilatation and rotations. These equations are solved and boundary stresses are satisfied in Fourier domain and the displacement on the surface are provided in this domain.

scholarly journals A Generalized Analytical Model for Joule Heating of Segmented Wires

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Vivekananthan Balakrishnan ◽  
Toan Dinh ◽  
Hoang-Phuong Phan ◽  
Dzung Viet Dao ◽  
Nam-Trung Nguyen
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Joule Heating ◽  
Numerical Solutions ◽  
Analytical Data ◽  
Experimental Studies ◽  
Governing Equations ◽  
Steady State Temperature ◽  
The One ◽  
Good Agreement

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

Solute transport during unsteady, unsaturated soil water flow - the pulse input

Soil Research ◽  
1987 ◽  
Vol 25 (3) ◽  
pp. 223 ◽  
Author(s):  
WJ Bond
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Unsaturated Soils ◽  
Approximate Analytical Solution ◽  
Tritiated Water ◽  
Chloride Ion ◽  
Factors Affecting ◽  
Pulse Input ◽  
Structurally Stable ◽  
Good Agreement

A general approximate analytical solution was derived for the movement and dispersion of a solute pulse during unsteady flow of water in unsaturated soils. Two types of pulse were considered: that arising from a non-uniform distribution of solute initially in the soil, and that arising from a change in concentration of solute in the water supply. The movement of pulses of tritiated water and chloride ion was investigated experimentally for the specific case of constant flux horizontal infiltration of water into a strongly aggregated, structurally stable clay soil. Good agreement between the measured distributions of tritium and those predicted using the approximate solution confirmed the validity of the approximate solution. Agreement was much poorer for chloride. The approximate analytical solution was also used to examine factors affecting the shape of solute pulses. It was found that pulses may be asymmetric at short times, but that they rapidly become symmetric as time increases.

Experimental and Numerical Analysis of a Sandwich Beam With Tip Mass

2018 ◽  
Author(s):  
E. F. Joubaneh ◽  
O. R. Barry ◽  
D. C. D. Oguamanam
Keyword(s):  
Numerical Analysis ◽  
Sandwich Panel ◽  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Sandwich Beam ◽  
Design Parameters ◽  
Governing Equations ◽  
Parametric Studies ◽  
Tip Mass ◽  
Good Agreement

This paper presents experimental and numerical analyses of a vibrating sandwich beam with a tip mass. The mathematical formulation is based on higher order sandwich panel theory (HSAPT) and the governing equations of motion and boundary conditions are obtained using Hamilton’s principle. General Differential Quadrature (GDQ) is employed to solve the system governing equations of motion. Experiments are carried out to validate the proposed formulation and the results show very good agreement. Parametric studies are conducted to investigate the influence of key design parameters on the natural frequency and vibration response of the system.

scholarly journals Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2452
Author(s):  
Tian Qiao ◽  
Hussein Hoteit ◽  
Marwan Fahs
Keyword(s):  
Analytical Solution ◽  
Storage Site ◽  
Co2 Leakage ◽  
Transient Pressure ◽  
Flow Paths ◽  
Abandoned Wells ◽  
Diffusivity Equation ◽  
Carbon Dioxide Co2 ◽  
Good Agreement

Geological carbon storage is an effective method capable of reducing carbon dioxide (CO2) emissions at significant scales. Subsurface reservoirs with sealing caprocks can provide long-term containment for the injected fluid. Nevertheless, CO2 leakage is a major concern. The presence of abandoned wells penetrating the reservoir caprock may cause leakage flow-paths for CO2 to the overburden. Assessment of time-varying leaky wells is a need. In this paper, we propose a new semi-analytical approach based on pressure-transient analysis to model the behavior of CO2 leakage and corresponding pressure distribution within the storage site and the overburden. Current methods assume instantaneous leakage of CO2 occurring with injection, which is not realistic. In this work, we employ the superposition in time and space to solve the diffusivity equation in 2D radial flow to approximate the transient pressure in the reservoirs. Fluid and rock compressibilities are taken into consideration, which allow calculating the breakthrough time and the leakage rate of CO2 to the overburden accurately. We use numerical simulations to verify the proposed time-dependent semi-analytical solution. The results show good agreement in both pressure and leakage rates. Sensitivity analysis is then conducted to assess different CO2 leakage scenarios to the overburden. The developed semi-analytical solution provides a new simple and practical approach to assess the potential of CO2 leakage outside the storage site. This approach is an alternative to numerical methods when detailed simulations are not feasible. Furthermore, the proposed solution can also be used to verify numerical codes, which often exhibit numerical artifacts.

Results of an Instrumented Static Loading Test and Its Application to Design Compilation of an International Survey

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Bengt Fellenius
Keyword(s):  
Prestressed Concrete ◽  
Static Loading ◽  
Ground Surface ◽  
Loading Test ◽  
Text Book ◽  
Ground Surface Settlement ◽  
Static Loading Test ◽  
Residual Force ◽  
Available Information ◽  
Piled Foundations

Results of a static loading test were used together with soil exploration records in a survey comprising analysis of the test records and estimating settlement of piled foundation to support a pipe rack. The test pile was a strain-gage instrumented, 400-mm diameter, precast, prestressed concrete pile driven into a clay and silt deposit to 25 m embedment. Two main issues were expected to be addressed by the survey participants: First, realization that the strain records were affected by presence of residual force in the pile and, second, calculation of the settlement of the piled foundation expected from the foundation load. A total of 52 submissions were received from 20 different countries. Only 12 of the submissions realized the presence of residual force. Most submissions reported a calculated settlement of the piled foundations ranging from 10 mm through 50 mm; however, 11 reported values between 60 and 200 mm. Surprisingly, only 20 submissions reported ground surface settlement close to the 200-mm value resulting from text-book analysis based on the available information. The subsequent construction of the piled foundations coincided with placing a fill across the site and lowering of the groundwater table, thus, causing a general subsidence.

Interaction Between Impeller and Volute of Pumps at Off-Design Conditions

1986 ◽  
Vol 108 (1) ◽  
pp. 12-18 ◽  
Author(s):  
J. A. Lorett ◽  
S. Gopalakrishnan
Keyword(s):  
Analytical Solution ◽  
Flow Behavior ◽  
Cyclic Variation ◽  
Test Results ◽  
Flow Parameters ◽  
Pump Output ◽  
Simplifying Assumptions ◽  
Radial Thrust ◽  
Relative Flow ◽  
Good Agreement

In a centrifugal pump of volute type, the respective characteristics of the impeller and the volute are such that at only one operating point can the flow parameters be constant along the length of the volute. At off-design conditions the mismatching of characteristics causes variations of velocity and pressure along the periphery of the impeller. This in turn forces cyclic variation of the flow in the impeller channels, introduces variations of the inlet incidence and contributes significantly to the direction and the magnitude of the radial thrust. Furthermore, below a certain pump output, a complete flow reversal occurs over a part of the impeller periphery, thus explaining the onset of recirculation. The paper describes the calculation approach used to derive this aspect of the flow behavior. Because of difficulties in obtaining a closed analytical solution, a step by step computation is employed. Beginning with arbitrarily chosen conditions at the volute tongue, the program computes the flow parameters for following segments, using the continuity and the momentum equations, until the exit from the last segment is reached. The inherent unsteadiness of the relative flow in the impeller is explicitly accounted for. Since the inflow and the velocity in the first segment depend upon the exit conditions of the last, the initial input must be modified, and the computation repeated, until the values are compatible with the exit conditions. In spite of several simplifying assumptions, the results of the calculations show very good agreement with published test results.

Analysis of Surface Subsidence Rule of the Shallow Subway Tunnel Construction

2013 ◽  
Vol 671-674 ◽  
pp. 1081-1086 ◽  
Author(s):  
Fei Fei Wang ◽  
Hui Ren Bai ◽  
Jing Jing Li
Keyword(s):  
Ground Surface ◽  
Calculation Model ◽  
Surface Subsidence ◽  
Surface Settlement ◽  
Tunnel Construction ◽  
Maximum Point ◽  
Subway Tunnel ◽  
Monitoring Frequency ◽  
Ground Surface Settlement ◽  
Value Range

In order to study the Dalian Metro section 202(Cujin Road station-Chunguang Street station, which is shallowly buried and covered with plain fill)’s ground surface settlement, the monitoring measuring station was built during the construction. After 3 months’ measuring by precision level,the data shows that the maximum point is in the center line of the tunnel of the upper part. The settlement is about 25.66-31.82mm. This paper put forward the concept of the distance span ratio β, β effective value range was - 4 <β< 4,Surface subsidence is closely related with β, Severe surface subsidence stage is -2 <β< 2, Occupy whole deformation is 67.5-77.6%,settlement rate about 0.84-0.93mm/d, so should strengthen the monitoring frequency, Suggest increases site tour. Field test results and the ground surface settlement calculation model winkle are identical with each other; the monitoring results have important guiding significance and reference for Dalian subway and the similar shallow depth excavation tunnel construction.

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