An explicit analytical solution for calculating horizontal stress changes and displacements around an excavated diaphragm wall panel

2003 ◽  
Vol 40 (4) ◽  
pp. 780-792 ◽  
Author(s):  
C WW Ng ◽  
G H Lei
Keyword(s):  
Analytical Solution ◽  
Uniaxial Stress ◽  
Horizontal Stress ◽  
Ease Of Use ◽  
Elastic Solution ◽  
Diaphragm Wall ◽  
Wall Panel ◽  
Principle Of Superposition ◽  
Explicit Analytical Solution ◽  
Stress Changes

A new, simple, and explicit analytical solution has been derived for calculating horizontal stress changes and displacements caused by the excavation for a diaphragm wall panel. The theoretical solution is obtained by applying the principle of superposition appropriately to model diaphragm wall construction using a basic elastic solution to the problem of an infinite horizontal plate with a rectangular opening subjected to a uniaxial stress at infinity. The basic elastic solution can be obtained by using the method of complex variables with a simplified conformal transformation function. Key parameters governing the magnitude of horizontal stress changes and displacements are identified. Computed results are given in a normalized form in terms of aspect ratio (length to width) of a diaphragm wall panel. Two extreme cases for diaphragm wall panels with dimensions 1 m × 1 m and 10 m × 1 m have been analysed to investigate the distributions of stress changes and deformations around the panels during the bentonite stage. By performing a parametric study, calculation charts have been developed for computing horizontal stress changes and displacements for practising engineers and researchers to carry out preliminary designs and for numerical modellers to verify their sophisticated predictions. The ease of use of the charts is illustrated by two examples, and the limitations of the derived solutions are discussed.Key words: diaphragm wall, elasticity, stress change, displacement, stress analysis, earth pressure.

scholarly journals Boundary problem on semi-direct for pseudoparabolic equation with a small parametr

2020 ◽  
pp. 29-41
Author(s):  
Б.С. Аблабеков ◽  
А.Т. Муканбетова
Keyword(s):  
Analytical Solution ◽  
Boundary Value Problem ◽  
Small Parameter ◽  
Boundary Problem ◽  
Unique Solvability ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Pseudoparabolic Equation ◽  
Explicit Analytical Solution ◽  
Initial Boundary Value

Данная статья посвящена построению классического решения краевой задачи на полупрямой для линейного псевдопараболического уравнения с малым параметром. Для построения явного решения используется метод преобразование Фурье. В работе исследуется вопрос об однозначной разрешимости начально-краевой задачи для псевдопараболического уравнения с малым параметром на полуоси. Получено явное аналитическое решение поставленной задачи. In this paper, we study the question of the unique solvability of the initial-boundary-value problem for a pseudoparabolic equation with a small parameter on the semi-axis. An explicit analytical solution to the problem is obtained.

ENTANGLEMENT DYNAMICS IN THE THREE-ATOM TAVIS-CUMMINGS MODEL

2009 ◽  
Vol 07 (05) ◽  
pp. 1001-1007 ◽  
Author(s):  
JIAN-SONG ZHANG ◽  
AI-XI CHEN
Keyword(s):  
Electromagnetic Field ◽  
Analytical Solution ◽  
Quantum System ◽  
Single Mode ◽  
Interaction Time ◽  
Entanglement Dynamics ◽  
Cavity Field ◽  
W States ◽  
Explicit Analytical Solution

We investigate the entanglement dynamics in a quantum system consisting of three two-level atoms resonantly coupled to a single mode electromagnetic field in a cavity. An explicit analytical solution of the system is obtained and the entanglement of the system is studied with the help of the concurrence and tangle. It is also shown that the W states could be generated if the interaction time of the two-level atoms and the cavity field is chosen appropriately.

A Semianalytical Model for Evaluating the Performance of a Refractured Vertical Well With an Orthogonal Refracture

SPE Journal ◽  
2019 ◽  
Vol 24 (02) ◽  
pp. 891-911 ◽  
Author(s):  
Bailu Teng ◽  
Huazhou Andy Li
Keyword(s):  
Production Rate ◽  
Horizontal Stress ◽  
Fracture Flow ◽  
Vertical Well ◽  
Flow Equations ◽  
Stress Reversal ◽  
Reservoir Flow ◽  
Proposed Model ◽  
Stress Changes ◽  
Initial Fracture

Summary Production from a fractured vertical well will lead to a redistribution of the stress field in formations. If the induced stress changes are sufficiently large to overcome the effect of the initial horizontal-stress deviator, the direction of the minimum horizontal stress can be turned into the direction of the maximum horizontal stress within an elliptical region around the initial fracture, resulting in a stress-reversal region near the wellbore. In such cases, a refracturing treatment can create a refracture that propagates orthogonally to the initial fracture because of the stress reversal. As such, the high-pressure area of the formation can be stimulated by the refracture, and the productivity of the refractured well can be improved. In this work, we develop a semianalytical model to evaluate the performance of a refractured vertical well with an orthogonal refracture. To simulate the well performance throughout the entire production period, we divide the well production into three stages: the first stage, when the well is producing oil with the initial fracture; the second stage, when the well is shut down for the refracturing treatment; and the third stage, when the well is producing oil with both the initial fracture and the refracture. In addition, by discretizing the initial fracture and the refracture into small segments, the conductivity of the fractures can be taken into account, and the geometry of the fracture system can be captured. We use the Green-function method to analytically simulate the reservoir flow and use the finite-difference method to numerically simulate the fracture flow; therefore, a semianalytical model can be constructed by coupling the reservoir-flow equations with the fracture-flow equations. This proposed model is applied to different wellbore and reservoir conditions. The calculated results show that this proposed model is versatile because it can simulate various wellbore constraints, including the conditions of constant bottomhole pressure (BHP), varying BHP, constant production rate, and varying production rate. The permeability anisotropy of the reservoir system, as well as the nonuniform conductivity distribution along the fracture, can also be incorporated into this proposed model. In addition, we demonstrate that this proposed model can be used to simulate other types of refractured vertical wells with minor modifications.

Observed performance of a short diaphragm wall panel

Géotechnique ◽  
1999 ◽  
Vol 49 (5) ◽  
pp. 681-694 ◽  
Author(s):  
C. W. W. Ng ◽  
D. B. Rigby ◽  
G. H. Lei ◽  
S. W. L. Ng
Keyword(s):  
Diaphragm Wall ◽  
Wall Panel

ENTANGLEMENT DYNAMICS OF TWO TWO-MODE TWO-PHOTON JAYNES–CUMMINGS MODELS IN THE PRESENCE OF PHASE DECOHERENCE

2008 ◽  
Vol 22 (08) ◽  
pp. 561-568 ◽  
Author(s):  
JIAN-SONG ZHANG ◽  
JING-BO XU
Keyword(s):  
Analytical Solution ◽  
Finite Time ◽  
Entanglement Dynamics ◽  
Two Photon ◽  
Explicit Analytical Solution ◽  
Phase Decoherence ◽  
Entangled Atoms

We investigate the entanglement of two two-mode two-photon Jaynes–Cummings models in the presence of phase decoherence. We find an explicit analytical solution of the system and discuss the influence of the phase decoherenc on the entanglement dynamics. Our results shows that the entanglement of the two initially entangled atoms can remain zero for a finite time and revive later. However, if the phase decoherence is taken into accounted, the entanglement cannot revive completely.

Deformation characteristics of a 38 m deep excavation in soft clay

2011 ◽  
Vol 48 (12) ◽  
pp. 1817-1828 ◽  
Author(s):  
Guo B. Liu ◽  
Rebecca J. Jiang ◽  
Charles W.W. Ng ◽  
Y. Hong
Keyword(s):  
Soft Clay ◽  
Field Performance ◽  
Lateral Wall ◽  
Diaphragm Wall ◽  
Deep Excavation ◽  
Wall Panel ◽  
Soft Clays ◽  
Measured Ratio ◽  
Increasing Demand ◽  
Ground Settlements

To meet the increasing demand for underground space for economical development and infrastructural needs, more and more deep excavations have been constructed in Shanghai. In this paper, field performance of a 38 m deep multistrutted excavation in Shanghai soft clay is reported. The deep excavation was retained by a 65 m deep diaphragm wall. Inclinometers as well as settlement and heave markers were installed to monitor the performance of the deep excavation. This project provides an unusual opportunity to study the differential heaves of center columns and diaphragm walls during excavation. Because of the significant stress relief resulting from the 38 m deep excavation, maximum heaves of the center column and diaphragm wall panel were about 30 and 16 mm, respectively. The measured ratio δp/H (heave/final excavation depth) of column is less than 0.1% whereas the observed δp/H of the diaphragm wall panel is about 0.04%. The maximum distortion between the column and the diaphragm wall panel is smaller than 1/500, which is within the limit range proposed by Bjerrum in 1963. Owing to careful construction control, stiff strutting system, and compaction grouting, the measured lateral wall deflections and ground settlements at this site are generally smaller than other shallower excavations in soft clays in Shanghai, Singapore, and Taipei.

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