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Method for establishing unsaturated large-deformation consolidation analysis mathematical model based on fixed Lagrange coordinate system

A mathematical model and coordinate system technology, applied in the fields of sludge treatment, civil engineering, disaster prevention and mitigation engineering, water conservancy engineering, tailings treatment, can solve the problem of reducing the application value of program engineering, consuming large memory storage space, and computing time Unacceptable and other problems, to achieve the effect of high practical value and promotion value, wide application scope, excellent applicability and scalability

Active Publication Date: 2020-10-16
SICHUAN UNIV
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Problems solved by technology

Then, in the process of writing a program to solve the problem, it is necessary to continuously update the coordinate system and other related physical quantities. The program developed by this will consume a large amount of memory storage space during operation, thereby reducing the calculation efficiency. When the time domain of the analysis problem is too large , the calculation time will reach an unacceptable level, thus reducing the engineering application value of the program

Method used

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  • Method for establishing unsaturated large-deformation consolidation analysis mathematical model based on fixed Lagrange coordinate system
  • Method for establishing unsaturated large-deformation consolidation analysis mathematical model based on fixed Lagrange coordinate system
  • Method for establishing unsaturated large-deformation consolidation analysis mathematical model based on fixed Lagrange coordinate system

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Embodiment

[0037] like Figure 1 to Figure 4 As shown, this embodiment provides a method for establishing a mathematical model of unsaturated large deformation consolidation analysis based on a fixed Lagrangian coordinate system, which uses the finite element method to solve the problem, and its operation steps are as follows:

[0038] In the first step, based on Darcy's theorem and fluid continuity, the mass conservation equation of unsaturated seepage flow is established in the Euler coordinate system (ξ, t), namely:

[0039]

[0040] Among them, k is the permeability coefficient, h is the acting head (including position head ξ and pressure head u w ), e is the void ratio, S r is the saturation. Assuming that the pore pressure in the unsaturated area is atmospheric pressure, and the water pressure in the unsaturated area is negative, introduce suction s (saturated state, s≤0; unsaturated state, s>0), that is, 0-s=u w ,

[0041] Transform formula (1) into:

[0042]

[0043] T...

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Abstract

The invention discloses a method for establishing an unsaturated large-deformation consolidation analysis mathematical model based on a fixed Lagrange coordinate system, which comprises the followingsteps of establishing a mass conservation equation of unsaturated seepage under an Euler coordinate system; under an Euler coordinate system, establishing a force balance equation; mapping the position water head to a fixed Lagrange coordinate system, and establishing a relation equation of an initial void ratio and an instant void ratio of the loose granular material; obtaining an unsaturated seepage mass conservation equation and a force balance equation based on a fixed Lagrange coordinate system; introducing an unsaturated increment constitutive relation; solving the total differential ofthe instant void ratio, the saturation and the mass moisture content of the loose granular material by utilizing a Cramer method, and deriving in a Lagrange coordinate system; sorting to obtain an unsaturated seepage mass conservation equation and a force balance equation which take total stress and suction force as variables under a fixed Lagrange coordinate system; and under a fixed Lagrange coordinate system, obtaining an unsaturated large-deformation consolidation analysis mathematical model.

Description

technical field [0001] The invention relates to the technical fields of civil engineering, tailings treatment, sludge treatment, water conservancy engineering, and disaster prevention and mitigation engineering, in particular to a method for establishing an unsaturated large deformation consolidation analysis mathematical model based on a fixed Lagrangian coordinate system. Background technique [0002] Unsaturated loose granular materials widely exist in nature, and the soil involved in civil engineering construction is generally on the surface, so it is in an unsaturated state. The basic theory and related engineering application of unsaturated soil mechanics have been paid more and more attention by people. The theory of unsaturated soil consolidation is the most important thing in the research. At present, most of the consolidation theories and analysis and calculation methods assume that the soil deformation is small, which belongs to the category of small strain. This...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/23G06F30/28G06F113/08G06F119/14
CPCG06F30/23G06F30/28G06F2113/08G06F2119/14
Inventor 戚顺超陈宣全周家文杨兴国范刚鲁功达姚强
Owner SICHUAN UNIV
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