Evaluation of vertical effective stress and pile lateral capacities considering scour-hole dimensions

2019 ◽  
Vol 56 (1) ◽  
pp. 135-143 ◽  
Author(s):  
Cheng Lin ◽  
Randall Wu
Keyword(s):  
Effective Stress ◽  
Slope Angle ◽  
Closed Form Solution ◽  
Form Solution ◽  
Lateral Capacity ◽  
Wide Range ◽  
Scour Hole ◽  
Vertical Effective Stress ◽  
Scour Hole Dimensions ◽  
Hole Dimensions

Determination of vertical effective stress along piles is an essential part of calculation of both pile axial and lateral capacities under scour conditions. However, the current design manuals including those from the US Federal Highway Administration (FHWA) and American Petroleum Institute (API) recommend different methods for calculating vertical effective stress. Moreover, they are effective only for restricted scour-hole dimensions. This study presents an improved closed-form solution that allows estimation of the vertical effective stress for a wide range of scour-hole dimensions including scour depth, width, and slope angle. Using the improved analytical solution for stress, API p–y curves for sand were modified to compute pile lateral capacity at different scour-hole conditions. Based on a series of parametric analyses for laterally loaded piles in sand, errors of calculation using the existing methods were quantified and a simplified method was proposed for practical applications. Effects of different scour-hole dimensions on both vertical effective stress and pile lateral capacity were also discussed.

scholarly journals Analysis of Lateral Dynamic Response of Caisson Foundation in Layered Clayey Soils considering Scour-Hole Dimensions

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Wenbo Tu ◽  
Xiaoqiang Gu ◽  
Xianfeng Ma ◽  
Dawei Huang
Keyword(s):  
Dynamic Response ◽  
Resonant Frequency ◽  
Slope Angle ◽  
Scour Depth ◽  
Long Term Effect ◽  
Scour Hole ◽  
Scour Hole Dimensions ◽  
Hole Dimensions ◽  
Hole Effect

As a cross-sea or river deep-water foundation, it is clear that the caisson foundation will be subjected to significant lateral dynamic loads due to winds or waves and suffer from scouring under its long-term effect. In order to obtain the scour effect on the dynamic response of the foundation, an analytical model describing the scour-hole effect in terms of scour depth, scour width, and slope angle was constructed. Combined with the nonlinear Winkler theory, a method for the dynamic response of the caisson foundation considering the scour-hole dimensions was proposed. Comparisons against the results from the dynamic FEM demonstrate the reliability of this method. The effects of the scour width, slope angle, and scour depth on the dynamic response of the caisson were discussed. The results show that the scour depth affects the dynamic displacement and resonant frequency of the foundation most, whereas the scour width does less and the slope angle does the least; the dynamic response of caisson can be approximated as the case of the slope angle 5° and the scour width 5B when the slope angle is less than 5° and the scour width is greater than 5B, respectively; the effects of scour width and slope angle on the dynamic response of caisson have the similar change pattern in the displacement and resonant frequency when the scour depth is different. However, the effect of amplitude on dynamic response shows a nonlinear increase trend when the scour depth is relatively large.

The attachment length in orificed hollow cathodes

2021 ◽  
Author(s):  
Christopher Wordingham ◽  
Pierre-Yves Taunay ◽  
Edgar Choueiri
Keyword(s):  
Electron Temperature ◽  
Plasma Density ◽  
Hollow Cathode ◽  
Computational Models ◽  
Closed Form Solution ◽  
Form Solution ◽  
Decay Length ◽  
Plasma Density Profile ◽  
Wide Range ◽  
Approximate Boundary Condition

Abstract A first-principles approach to obtain the attachment length within a hollow cathode with a constrictive orifice, and its scaling with internal cathode pressure, is developed. This parameter, defined herein as the plasma density decay length scale upstream of (away from) the cathode orifice, is critical because it controls the utilization of the hollow cathode insert and influences cathode life. A two-dimensional framework is developed from the ambipolar diffusion equation for the insert-region plasma. A closed-form solution for the plasma density is obtained using standard partial differential equation techniques by applying an approximate boundary condition at the cathode orifice plane. This approach also yields the attachment length and electron temperature without reliance on measured plasma property data or complex computational models. The predicted plasma density profile is validated against measurements from the NSTAR discharge cathode, and calculated electron temperatures and attachment lengths agree with published values. Nondimensionalization of the governing equations reveals that the solution depends almost exclusively on the neutral pressure-diameter product in the insert plasma region. Evaluation of analytical results over a wide range of input parameters yields scaling relations for the variation of the attachment length and electron temperature with the pressure-diameter product. For the range of orifice-to-insert diameter ratio studied, the influence of orifice size is shown to be small except through its effect on insert pressure, and the attachment length is shown to be proportional to the insert inner radius, suggesting high-pressure cathodes should be constructed with larger-diameter inserts.

scholarly journals A Stochastic Analysis of Hard Disk Drives

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Field Cady ◽  
Yi Zhuang ◽  
Mor Harchol-Balter
Keyword(s):  
Stochastic Analysis ◽  
Hard Disk Drives ◽  
Closed Form Solution ◽  
Hard Disk ◽  
Form Solution ◽  
Access Time ◽  
Analytical Technique ◽  
Wide Range ◽  
Average Access Time ◽  
Memory Request

We provide a stochastic analysis of hard disk performance, including a closed form solution for the average access time of a memory request. The model we use covers a wide range of types and applications of disks, and in particular it captures modern innovations like zone bit recording. The derivation is based on an analytical technique we call “shuffling”, which greatly simplifies the analysis relative to previous work and provides a simple, easy-to-use formula for the average access time. Our analysis can predict performance of single disks for a wide range of disk types and workloads. Furthermore, it can predict the performance benefits of several optimizations, including short stroking and mirroring, which are common in disk arrays.

Analysis and Synthesis of Dynamic Response of a Flexibly Coupled Rotor Assembly

1997 ◽  
Author(s):  
Valdas Chaika
Keyword(s):  
Equations Of Motion ◽  
Excitation Frequency ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Response ◽  
Wide Range ◽  
Analysis And Synthesis ◽  
Coupling Parameters ◽  
Elastic Couplings ◽  
Rotor Assembly

Abstract Torsional vibration of two flexibly coupled reciprocating machines is investigated. The rotors of the machines are connected by elastic couplings of several types. The system is excited by a harmonic torque. The excitation frequency is proportional to the rotational speed which varies within a wide range. The motion of the system is described by nonlinear ordinary differential equations. These are linearized for the specific case of the rotor assembly design. Applying impedance functions, a closed-form solution of the equations of motion is derived. Three different cases of the system response are analyzed in the frequency domain. The passive vibration control of the rotor assembly using the centrifugal coupling is investigated. An analytical synthesis technique of the coupling parameters is devised.

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