CN108052783A - A kind of unsaturated soil dynamic numerical calculation method based on adaptive step - Google Patents
A kind of unsaturated soil dynamic numerical calculation method based on adaptive step Download PDFInfo
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Abstract
The invention discloses a kind of unsaturated soil dynamic numerical calculation methods based on adaptive step, it solves the problems, such as computational accuracy in the prior art and efficiency cannot be unified well, time step is unable to adjust automatically, with can accurately assess calculation error and improve the efficiency of calculating, it saves and calculates the time, the effect of the deformation behaviour of unsaturated soil can accurately be described, technical solution is：Include the assessment of solid phase displacement error, pore water pressure error and hole barometric error, solid phase displacement error, pore water pressure error and hole barometric error in being analyzed by real-time evaluation, using combined error as the function of solid phase displacement error, pore water pressure error and hole barometric error, and the foundation for adjusting combined error as time step, accurate assessment calculates unsaturated soil power numerical error, and adjustment in real time calculates time step.
Description
Technical Field
The invention relates to the technical field of research on unsaturated soil mechanics, in particular to a method for calculating an unsaturated soil dynamic numerical value based on a self-adaptive step length.
Background
Research on unsaturated soil mechanics began in the last 30 th century, and unsaturated soil is characterized by consisting of three phases, namely a solid phase, a liquid phase and a gas phase, and simultaneously has matrix suction on a liquid-gas interface, and when calculating in-soil stress, the effective stress of the solid phase, the pore water pressure and the pore air pressure need to be calculated respectively.
In practical engineering, unsaturated soil is the majority, and for example, unsaturated soil is involved in foundation pit engineering, roadbed and pavement engineering and slope engineering. The research methods for unsaturated soil include theoretical analysis, experimental research and numerical analysis. And numerical analysis is favored by researchers as a third scientific research method.
The numerical analysis is divided into static calculation and dynamic calculation, in the finite element dynamic numerical calculation, the control equation needs to be dispersed in a space domain and a time domain at the same time, and the dispersion error is not negligible. The discrete error of the time domain is related to the time discrete method and the selection of the calculation time step, if an implicit solving method is adopted, higher precision can be obtained, but continuous iterative calculation is needed, and the defects of non-convergence and low efficiency are caused; the explicit solving method is adopted, the efficiency is high, but the influence of the selection of the calculation time step length on the accuracy of the calculation result is obvious.
In summary, the following problems still exist:
(1) in the explicit calculation, the calculation precision and efficiency cannot be well unified, the smaller the time step is, the higher the precision is, and meanwhile, the longer the calculation time is; when the time step length is larger, the calculation time is short, but the precision cannot be ensured;
(2) a calculation method capable of automatically adjusting the time step length is still lacked in the calculation of the unsaturated soil dynamic value.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the unsaturated soil dynamic numerical value calculation method based on the self-adaptive step length, which has the effects of accurately evaluating the calculation error, improving the calculation efficiency, saving the calculation time and accurately describing the deformation characteristics of unsaturated soil.
The invention adopts the following technical scheme:
a method for calculating unsaturated soil dynamic numerical values based on self-adaptive step length comprises the steps of evaluating solid phase displacement errors, pore water pressure errors and pore air pressure errors, calculating the solid phase displacement errors, the pore water pressure errors and the pore air pressure errors in numerical analysis in real time, taking mixed errors as functions of the solid phase displacement errors, the pore water pressure errors and the pore air pressure errors, taking the mixed errors as the basis of time step length adjustment, and accurately evaluating and calculating the calculated errors of the unsaturated soil dynamic numerical values.
Further, the method comprises the following steps:
setting control parameters which are respectively as follows: initial time step Δ t0Allowable value of mixing errorSolid phase displacement error adjustment coefficient lambdauAdjustment coefficient lambda of pore water pressure errorwAdjustment coefficient lambda of pore pressure erroraMinimum value f of step adjustment coefficientminAnd the maximum value f of the step-size adjustment coefficientmax；
Step (2) calculating the finite element numerical value in the current step;
step (3) solid phase displacement error evaluation, pore water pressure error evaluation and pore air pressure error evaluation are carried out;
calculating a mixing error and a time step length adjusting coefficient;
step (5) calculating a new time step and a new load item;
step (6) comparing the mixed error with the allowable error value;
if the mixing error is less than or equal to the error allowable value, continuing the next numerical calculation, and adopting a new time step; if the mixing error is larger than the error allowable value, returning to the current step for correction calculation, and adopting a new time step.
Further, in the step (3), the relative error of the pore pressure error is expressed as:
wherein, ηa(t + deltat) is the relative error in pore pressure,is the maximum value of the pore pressure.
Further, the pore pressure error ea(t + Δ t) is expressed as:
wherein,a second order resolution of pore pressure at time t + deltat,is a first order accuracy solution of the pore pressure at time t + Δ t.
Further, the mixing error is expressed as:
wherein, ηmixIn order to mix the errors, the error rate of the mixing,in order to obtain a solid-phase displacement error,in order to determine the pore water pressure error,is the pore pressure error.
Further, in the step (5), the new time step is represented as:
Δtnew＝f·Δtold
wherein, Δ tnewFor the adjusted new step size, Δ toldF is the step length adjusting coefficient before adjusting.
Further, in the step (5), the adjustment formula of the load term is as follows:
wherein,is the load value of the (m + 1) th sub-step in the nth step,is the load value of the mth sub-step in the nth step, an+1Is the load value of step n +1, anIs the load value of step n, Δ tmaxIs the time step between the nth step and the (n + 1) th step.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method is characterized by comprising a solid phase, a liquid phase and a gas phase based on the characteristics of unsaturated soil, evaluating a solid phase displacement error, a pore water pressure error and a pore air pressure error, and obtaining a time domain discrete error calculated by an unsaturated soil three-phase medium dynamic numerical value through mixed error evaluation, so that the deformation characteristic of the unsaturated soil can be accurately described;
(2) the invention provides a time step correction formula, obtains a new time step, realizes the real-time adjustment of a load item, corresponds to the time step, and can realize the return correction and the recalculation if the mixed error is greater than the error allowable value, thereby achieving the purpose of improving the calculation precision.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As introduced in the background art, the prior art has the defects that the calculation accuracy and efficiency cannot be unified well, and the time step cannot be adjusted automatically, and in order to solve the technical problems, the application provides a method for calculating the unsaturated soil dynamic value based on the adaptive step.
In an exemplary embodiment of the present application, as shown in fig. 1, a method for calculating an unsaturated soil dynamic numerical value based on an adaptive step size is provided, which includes evaluating a solid phase displacement error, a pore water pressure error and a pore air pressure error, calculating the solid phase displacement error, the pore water pressure error and the pore air pressure error in a numerical analysis in real time, taking a mixed error as a function of the solid phase displacement error, the pore water pressure error and the pore air pressure error, and taking the mixed error as a basis for adjusting a time step size, and accurately evaluating and calculating the unsaturated soil dynamic numerical error.
The method comprises the following specific steps:
firstly, setting control parameters:
defining an initial time step Δ t0Allowable value of mixing errorSolid phase displacement error adjustment coefficient lambdauAdjustment coefficient lambda of pore water pressure errorwAdjustment coefficient lambda of pore pressure erroraMinimum value f of step adjustment coefficientminAnd the maximum value f of the step-size adjustment coefficientmax(ii) a And carrying out finite element numerical calculation on the current step.
Secondly, solid phase displacement error assessment, pore water pressure error assessment and pore air pressure error assessment:
and (3) evaluating the solid phase displacement error according to a Newmark- β time domain discrete formula to obtain an acceleration error formula:
in the formula (1), the reaction mixture is,for acceleration error, Δ t is the calculation time step,is the acceleration value at the time t,is the acceleration at the moment t + deltat, and tau is an arbitrary value between t-t + deltat.
Integrating the acceleration error formula to obtain a speed error formula:
in the formula (2) areA speed error.
Integrating the speed error formula to obtain a solid phase displacement error formula:
in the formula (3), the displacement error of the e (t + Δ t) solid phase is shown.
Thereby obtaining a relative error formula of solid phase displacement:
η in formula (4)u(t + Δ t) is the relative error in solid phase displacement,the maximum value of the solid phase shift.
The pore water pressure error is evaluated as the difference value of the center difference decomposition and the backward difference decomposition, and is a truncation error; pore water pressure error is expressed as:
in the formula (5) ew(t + Δ t) is the pore water pressure error,the rate of change of pore water pressure at time t,the rate of change of pore pressure at time t + Δ t.
The relative error in pore water pressure error is expressed as:
in formula (6), ηw(t + deltat) is the relative error in pore water pressure,is the maximum value of pore water pressure.
The pore pressure error was evaluated as:
e in formula (7)a(t + Δ t) is the pore pressure error,a second order resolution of pore pressure at time t + deltat,is a first order accuracy solution of the pore pressure at time t + Δ t.
The relative error in pore pressure is expressed as:
in formula (8), ηa(t + deltat) is the relative error in pore pressure,is the maximum value of the pore pressure.
Thirdly, calculating a mixing error and a time step adjustment coefficient:
the mixing error as a function of solid phase displacement error, pore water pressure error and pore air pressure error is expressed as:
in formula (9), ηmixIn order to mix the errors, the error rate of the mixing,in order to obtain a solid-phase displacement error,the error of the pore water pressure is reduced,is the pore pressure error, λuIs an adjustment coefficient of solid phase displacement error, lambdawFor pore water pressure error adjustment coefficient, lambdaaThe pore pressure error adjustment coefficient is obtained.
By setting lambdau、λwAnd λaThe three adjusting coefficients can consider the proportion of displacement error, pore water pressure error and pore air pressure error in the mixing error. Can be properly adjusted for different working conditions, such as the working condition sensitive to pore water pressure, lambdawSuitably by taking a large value, λuAnd λaTaking a smaller value; for the operating mode in which the pore pressure is decisive, then λaTake a larger value, λuAnd λwTaking the smaller value.
Wherein the value ranges of the three parameters are that lambda is more than or equal to 0u≤1，0≤λw≤1，0≤λa≤1。
The adjustment factor for the time step is expressed as:
in the formula (10), f is a step adjustment coefficient,the allowable value of the mixing error.
Fourthly, calculating a new time step and a new load term:
the time step is limited, and the range is as follows:
fmin≤f≤fmax(11)
in the formula (11), fminFor the minimum value of the step-size adjustment coefficient, fmaxThe maximum value of the step size adjustment coefficient is obtained.
The new time step is represented as:
Δtnew＝f·Δtold(12)
in the formula (12), Δ tnewFor the adjusted new step size, Δ toldOld step size before adjustment.
The time step length and the load value are in one-to-one correspondence, after the time step length is adjusted, the load item needs to be adjusted correspondingly, and assuming that the load is linearly transformed, the load item is adjusted through the following formula:
in the formula (13), the reaction mixture is,is the load value of the (m + 1) th sub-step in the nth step,is the load value of the mth sub-step in the nth step, an+1Is the load value of step n +1, anIs the load value of step n, Δ tmaxIs the time step between the nth step and the (n + 1) th step.
Fifthly, comparing the size of the mixed error with the allowable error value; if the mixing error is less than or equal to the error allowable value, continuing the next calculation; and if the mixing error is larger than the error allowable value, returning to the previous step for correction calculation.
The whole calculation process is monitored in real time, and data such as solid phase displacement error, pore water pressure error, pore air pressure error, mixing error, step length adjustment coefficient, time step length and the like of each step are output.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (7)
1. A method for calculating unsaturated soil dynamic numerical values based on self-adaptive step length is characterized by comprising the steps of evaluating solid phase displacement errors, pore water pressure errors and pore air pressure errors, calculating the solid phase displacement errors, the pore water pressure errors and the pore air pressure errors in numerical analysis in real time, taking mixed errors as functions of the solid phase displacement errors, the pore water pressure errors and the pore air pressure errors, taking the mixed errors as the basis of time step length adjustment, and accurately evaluating and calculating the errors of the unsaturated soil dynamic numerical value calculation.
2. The method for calculating the unsaturated soil dynamic value based on the adaptive step size according to claim 1, characterized by comprising the following steps of:
setting control parameters which are respectively as follows: initial time step Δ t0Allowable value of mixing errorSolid phase displacement error adjustment coefficient lambdauAdjustment coefficient lambda of pore water pressure errorwAdjustment coefficient lambda of pore pressure erroraMinimum value f of step adjustment coefficientminAnd the maximum value f of the step-size adjustment coefficientmax；
Step (2) calculating the finite element numerical value in the current step;
step (3) solid phase displacement error evaluation, pore water pressure error evaluation and pore air pressure error evaluation are carried out;
calculating a mixing error and a time step length adjusting coefficient;
step (5) calculating a new time step and a new load item;
step (6) comparing the mixed error with the allowable error value;
if the mixing error is less than or equal to the error allowable value, continuing the next numerical calculation, and adopting a new time step; if the mixing error is larger than the error allowable value, returning to the current step for correction calculation, and adopting a new time step.
3. The method for calculating the unsaturated soil dynamic value based on the adaptive step size according to claim 2, wherein in the step (3), the relative error of the pore air pressure error is represented as:
<mrow> <msup> <mi>&eta;</mi> <mi>a</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mi>&Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mfrac> <mrow> <msup> <mi>e</mi> <mi>a</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mi>&Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <msubsup> <mi>p</mi> <mrow> <mi>t</mi> <mo>+</mo> <mi>&Delta;</mi> <mi>t</mi> </mrow> <mrow> <mi>a</mi> <mo>,</mo> <mi>max</mi> </mrow> </msubsup> </mfrac> <mo>|</mo> </mrow>
wherein, ηa(t + deltat) is the relative error in pore pressure,is the maximum value of the pore pressure.
4. The method for calculating the unsaturated soil dynamic value based on the adaptive step size as claimed in claim 3, wherein the pore air pressure error ea(t + Δ t) is expressed as:
<mrow> <msup> <mi>e</mi> <mi>a</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mi>&Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>p</mi> <mrow> <mi>t</mi> <mo>+</mo> <mi>&Delta;</mi> <mi>t</mi> </mrow> <mrow> <mi>a</mi> <mn>2</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>p</mi> <mrow> <mi>t</mi> <mo>+</mo> <mi>&Delta;</mi> <mi>t</mi> </mrow> <mrow> <mi>a</mi> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
wherein,a second order resolution of pore pressure at time t + deltat,is a first order accuracy solution of the pore pressure at time t + Δ t.
5. The method for calculating the unsaturated soil dynamic value based on the adaptive step size according to claim 2, wherein the mixing error is expressed as:
<mrow> <msup> <mi>&eta;</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> </msup> <mo>=</mo> <msqrt> <mrow> <msub> <mi>&lambda;</mi> <mi>u</mi> </msub> <msup> <mrow> <mo>(</mo> <msup> <mover> <mi>&eta;</mi> <mo>&OverBar;</mo> </mover> <mi>u</mi> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>&lambda;</mi> <mi>w</mi> </msub> <msup> <mrow> <mo>(</mo> <msup> <mover> <mi>&eta;</mi> <mo>&OverBar;</mo> </mover> <mi>w</mi> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>&lambda;</mi> <mi>a</mi> </msub> <msup> <mrow> <mo>(</mo> <msup> <mover> <mi>&eta;</mi> <mo>&OverBar;</mo> </mover> <mi>a</mi> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>
wherein, ηmixIn order to mix the errors, the error rate of the mixing,in order to obtain a solid-phase displacement error,in order to determine the pore water pressure error,is the pore pressure error.
6. The method for calculating the unsaturated soil dynamic force value based on the adaptive step length as claimed in claim 2, wherein in the step (5), the new time step length is represented as:
Δtnew＝f·Δtold
wherein, Δ tnewFor the adjusted new step size, Δ toldF is the step length adjusting coefficient before adjusting.
7. The method for calculating the unsaturated soil dynamic value based on the adaptive step size according to claim 2, wherein in the step (5), the adjustment formula of the load term is as follows:
<mrow> <msubsup> <mi>a</mi> <mi>n</mi> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>a</mi> <mi>n</mi> <mi>m</mi> </msubsup> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&Delta;t</mi> <mrow> <mi>n</mi> <mi>e</mi> <mi>w</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>&Delta;t</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>a</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow>
wherein,is the load value of the (m + 1) th sub-step in the nth step,is the load value of the mth sub-step in the nth step, an+1Is the load value of step n +1, anIs the load value of step n, Δ tmaxIs the time step between the nth step and the (n + 1) th step.
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| CN114861134A (en) * | 2022-07-08 | 2022-08-05 | 四川大学 | Step length determination method for calculating water drop motion track and storage medium |
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| CN111209657B (en) * | 2019-12-30 | 2022-04-22 | 南京航空航天大学 | Solid deformation interface calculation method considering liquid surface tension |
| CN113927584A (en) * | 2021-10-19 | 2022-01-14 | 深圳市优必选科技股份有限公司 | Robot control method, device, computer readable storage medium and robot |
| CN113927584B (en) * | 2021-10-19 | 2023-04-21 | 深圳市优必选科技股份有限公司 | Robot control method and device, computer readable storage medium and robot |
| CN114861134A (en) * | 2022-07-08 | 2022-08-05 | 四川大学 | Step length determination method for calculating water drop motion track and storage medium |
| CN114861134B (en) * | 2022-07-08 | 2022-09-06 | 四川大学 | Step length determination method for calculating water drop motion track and storage medium |
| CN116680965A (en) * | 2023-08-04 | 2023-09-01 | 矿冶科技集团有限公司 | FDEM acceleration method based on self-adaptive time step excavation supporting simulation |
| CN116680965B (en) * | 2023-08-04 | 2023-09-29 | 矿冶科技集团有限公司 | FDEM acceleration method based on self-adaptive time step excavation supporting simulation |
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