CN108959189A - A method of it calculating Canal in Loess Area roadbed and underlies dark cave marginal stability - Google Patents

A method of it calculating Canal in Loess Area roadbed and underlies dark cave marginal stability Download PDF

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Publication number
CN108959189A
CN108959189A CN201810580883.6A CN201810580883A CN108959189A CN 108959189 A CN108959189 A CN 108959189A CN 201810580883 A CN201810580883 A CN 201810580883A CN 108959189 A CN108959189 A CN 108959189A
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loess
calculating
depth
dark cave
canal
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邓亚虹
吴伟
李喜安
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Changan University
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Changan University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/24Earth materials
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/18Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis

Abstract

Underlie the method for dark cave marginal stability the invention discloses a kind of calculating Canal in Loess Area roadbed, the present invention establishes computation model according to the physical property of Loess hidden holes hole diameter first, calculates its yield stress;Establish kinetic equation, the circular frequency of the vibration shape takes model analysis as a result, maximum equivalent under the conditions of calculating dynamic load;Change buried depth and carry out numerical value calculating, obtains the relationship of maximum equivalent and stable groundwater depth, the yield stress in model is brought into, obtain the stable groundwater depth in dark cave in model clay;Successively change center away from calculating stable groundwater depth, its result is carried out numerical fitting, the Canal in Loess Area roadbed is obtained and underlies dark cave stability distinguishing curve.Present invention incorporates the integralities of the flexibility of numerical analysis and analytic solutions, successional advantage, hole diameter, center are carried out away from bivariate critical buried-depth regression forecasting to Loess hidden holes stability under dynamic load, with faster speed and preferable accuracy, it is easy to spread, the requirement of concrete engineering can be met very well.

Description

A method of it calculating Canal in Loess Area roadbed and underlies dark cave marginal stability
Technical field
The invention belongs to rock-soil mechanics technical fields, and in particular to a kind of roadbed dark cave of underliing in calculating Canal in Loess Area is critical steady Qualitative method.
Background technique
In the mass transportation engineering construction of Loess Area of Northwest China, roadbed underlies Geological Hazard brought by Loess hidden holes It can not be ignored.Due to the soil property particularity of loess and the concealment that dark acupuncture point sets of underliing, the unstability time it is sudden, caused Disaster not only break up road structure, more threat traffic safety.It is steady to roadbed it is therefore desirable to study the roadbed Loess hidden holes that underlie Qualitatively influence.If being unable to accurate quantitative analysis according to traditional calculation method and calculating Loess hidden holes of the different centers away from, hole diameter Marginal stability, and overall model calculating is many and diverse, effectively cannot carry out program realization to it, seriously affect the effect of calculating Rate does not meet the requirement of current engineering calculation.
Summary of the invention
Underlie dark cave neutrality the purpose of the present invention is to overcome the above shortcomings and to provide a kind of calculating Canal in Loess Area roadbed Property method, such method has faster speed and preferable precision, and easy to spread, can meet concrete engineering very well It is required that.
In order to achieve the above object, the present invention the following steps are included:
The dark cave of required hole diameter is embedded in loess foundation by step 1, it is assumed that and loess foundation is elastic-perfectly plastic material, Computation model is established according to the elasticity modulus of loess foundation, density, damping ratio, Poisson's ratio, cohesive strength and angle of friction, and is calculated The yield stress of the model;
Step 2 carries out undamped model analysis to computation model, and calculates the self-vibration circular frequency of mode, in conjunction with mode point Analysis calculates Rayleigh damping coefficient as a result, establish the equation of motion;
Step 3 solves the equation of motion, changes the progress power transient analysis of load period, finds out the least favorable load period, Obtain maximum equivalent;
Step 4 changes the dark cave depth of burying, repeats step 2 to step 3, carries out regression analysis to calculated result, intend Equivalent stress is with depth change curve under hole diameter needed for closing out;
Step 5, the equivalent stress that the yield stress substitution step 4 that step 1 obtains is obtained is with depth change curve In, obtain the dark cave hole top neutrality buried depth of required hole diameter;
Step 6 changes dark cave with a distance from road axis, repeats step 2 to step 5, obtains multi-group data, intend Curve of the hole diameter lower critical buried depth with center away from variation, i.e. stability distinguishing curve needed for closing out;
Step 7, in neutrality buried depth with center away from center needed for being substituted into change curve away from it is critical steady that you can get it Buried depth is determined, to judge whether Loess hidden holes are stable.
In step 1, using Drucker-Prager yield criterion:It calculates in the model Yield stressWherein c is the cohesive strength of soil,For the angle of friction of soil.
In step 2, calculating Rayleigh damping coefficient, the specific method is as follows:
Establish the equation of motion:
It is respectively node acceleration vector, node speed vector sum modal displacement, M, C, K and Q with a (t) It (t) is respectively the load vector of mass matrix, damping matrix, stiffness matrix and node, using consistent Mass Matrix, to calculating mould Type carries out undamped model analysis, calculates the self-vibration circular frequency of mode, in conjunction with modal analysis result, calculates Rayleigh damping system Number.Reyleigh' damping matrix C=α M+ β K, wherein α be Tuned mass damper coefficient, β stiffness and damping coefficient,
Wherein, ξ is mode damping ratio, and ω is circular frequency;
To reduce the influence that high order mode is artificially filtered out, i and j correspondence take 1 and 6 to be calculated;
In step 3, the method for solving of maximum equivalent is as follows:
The equation of motion is solved using Newmark implicit integration algorithm:
Assuming that:
The displacement of wherein δ=1/2, α=1/4, time t+ Δ t solve at+ΔtFormula passes through the equation of motion of time t+ Δ t
And it solves;
It is solved first from formula 5:
Then formula 4 is carried it into, then is brought into formula 1 together, to obtain atWithIt is equivalent to calculate Stress.Change the load period again, finds out the least favorable load period, obtain maximum equivalent.
Compared with prior art, the present invention establishes model according to the physical property of loess foundation first, in limited numerical value On the basis of analyzing result, available hole diameter, center can calculate the loessland away from bivariate critical buried-depth regression forecasting Area, roadbed underlie a certain hole diameter, center away from dark cave it is whether stable.Present invention incorporates the spirits of numerical analysis processing challenge Integrality, the successional advantage of the advantage reconciliation analysis solution of activity, obtain one approximately using the method for limited numerical solution Continuous analytic formula, the method have faster speed and preferable precision, and easy to spread, can meet concrete engineering very well Requirement.
Detailed description of the invention
Fig. 1 is roadbed model figure;
Fig. 2 is maximum equivalent with hole top buried depth change curve;
Fig. 3 is for neutrality buried depth with center away from change curve;
Fig. 4 is the dark cave arrangement schematic diagram in embodiment.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
The present invention the following steps are included:
Step 1 establishes computation model, road structure such as Fig. 1, it is assumed that loess foundation is elastic-perfectly plastic material, definitely Sill characterisitic parameter (elasticity modulus, density, damping ratio, Poisson's ratio, cohesive strength, angle of friction).Using Drucker-Prager Yield criterion:Calculate the yield stress in the modelWherein c is the viscous of soil Poly- power,For the angle of friction of soil;
Step 2 establishes the equation of motion
It is respectively the displacement of the node acceleration vector, node speed vector sum node of system with a (t), M, C, K, Q (t) are respectively the load vector of the mass matrix of system, damping matrix, stiffness matrix and node, it is contemplated that consistant mass Matrix has many advantages, such as small memory, computational short cut, solves conveniently and result is reasonable, uses consistent Mass Matrix here.Secondly, right Computation model carries out undamped model analysis, calculates the self-vibration circular frequency of mode, in conjunction with modal analysis result, calculates Rayleigh resistance Buddhist nun's coefficient.Specifically: Reyleigh' damping matrix C=α M+ β K, wherein α is Tuned mass damper coefficient, and β stiffness and damping coefficient is to disobey Rely the constant in frequency,
Wherein, ξ is mode damping ratio, and ω is circular frequency;
To reduce the influence that is artificially filtered out of high order mode, when calculating, takes i, j correspondence to take 1,6 to be calculated.
Solution for the equation of motion, it is contemplated that the accuracy of its result uses Newmark implicit integration algorithm, tool here Body are as follows:
Assuming that:
Wherein δ=1/2, α=1/4, the displacement solutions a of time t+ Δ tt+ΔtFormula passes through the equation of motion of time t+ Δ t
And it solves.It is solved first from formula 5:
Then formula 4 is carried it into, then is brought into formula 1 together, to obtain atWithCalculate equivalent stress.
Step 3, for the stability of roadbed, maximum dynamic load determines whether it destroys, and therefore, changes The time dependent loading period carries out power transient analysis, finds out the least favorable load period, obtains maximum equivalent;
Step 4 changes the dark cave depth of burying, repeats step 2 to step 3, carries out regression analysis to calculated result, intend Equivalent stress is with depth change curve, such as Fig. 2 under hole diameter needed for closing out;
Step 5, the equivalent stress that the yield stress substitution step 4 that step 1 obtains is obtained is with depth change curve In, obtain the dark cave hole top neutrality buried depth of required hole diameter;
Step 6 changes dark cave with a distance from road axis, repeats step 2 to step 5, theoretically obtain two groups with Upper data can be carried out calculating, but for the accuracy of result, is fitted just generally obtaining multi-group data, obtains required hole Curve of the diameter lower critical buried depth with center away from variation, such as Fig. 3.Model whether actually stabilization here it is a certain hole diameter Loess hidden holes Line of demarcation is enclosed, is unstable when hole is withstood in curve, is then stable in extra curvature.
Embodiment:
Canal in Loess Area roadbed according to the present invention underlies the principle of dark cave marginal stability method, calculates a certain loess 1 meter of hole diameter under regional roadbed, center are away from 3 meters, the stability in 3.5 meters of buried depth dark caves.Ground loess material parameter is as shown in Table 1:
According to Drucker-Prager yield criterion:
Calculate yield stress σy=79.25Kpa.The equation of motion is established, then undamped model analysis, calculates self-vibration Circular frequency calculates Rayleigh damping coefficient in conjunction with modal analysis result;The equation of motion is solved using Newmark implicit integration algorithm, Calculate equivalent stress;Change the progress power transient analysis of load period, finds out the least favorable load period, calculate maximum equivalent Stress;Change buried depth (1 meter, 3 meters, 5 meters), repeat step, regression analysis is carried out to the above calculated result, fits 1 meter of hole diameter, Maximum equivalent answers surrender with depth change curve (its equation are as follows: y=6.0623lnX-30.606) when offset distance is 0 Power 79.25Kpa substitutes into equation, and obtaining critical buried-depth is 4.10 meters;Show that 1 meter of hole diameter, offset distance are 3 meters using same method When regression equation y=9.6886lnX-44.97, by yield stress 79.25Kpa substitute into equation, obtain critical buried-depth be 2.61 Rice.Neutrality buried depth can be fitted with center away from change curve according to above data (multi-group data can also be calculated) (its equation is y=0.1658x2-4.0977).Therefore, when hole diameter is 1 meter, by center away from curvilinear equation is brought into for 3 meters, y is obtained =-2.6055 meters, that is to say, that under the conditions of such the Loess hidden holes neutrality buried depth of (1 meter of hole diameter, 3 meters of centers away from) be - 2.6055 meters, result be greater than -3.5 meters of its buried depth, so the Loess hidden holes be it is stable, as shown in Figure 4.
The present invention also extend to other hole diameters, center away from roadbed underlie Loess hidden holes neutrality buried depth calculate, And precision with higher and rate.

Claims (4)

  1. A kind of method of dark cave marginal stability 1. calculating Canal in Loess Area roadbed underlies, which comprises the following steps:
    The dark cave of required hole diameter is embedded in loess foundation by step 1, it is assumed that and loess foundation is elastic-perfectly plastic material, according to Elasticity modulus, density, damping ratio, Poisson's ratio, cohesive strength and the angle of friction of loess foundation establish computation model, and calculate the mould The yield stress of type;
    Step 2 carries out undamped model analysis to computation model, and calculates the self-vibration circular frequency of mode, in conjunction with model analysis knot Fruit establishes the equation of motion, calculates Rayleigh damping coefficient;
    Step 3 solves the equation of motion, changes the progress power transient analysis of load period, finds out the least favorable load period, obtain Maximum equivalent;
    Step 4 changes the dark cave depth of burying, repeats step 2 to step 3, carries out regression analysis to calculated result, fit Equivalent stress is with depth change curve under required hole diameter;
    Step 5, the equivalent stress that the yield stress substitution step 4 that step 1 obtains is obtained are obtained in depth change curve Neutrality buried depth is pushed up in the dark cave hole of required hole diameter out;
    Step 6 changes dark cave with a distance from road axis, repeats step 2 to step 5, obtains multi-group data, fit Curve of the required hole diameter lower critical buried depth with center away from variation, i.e. stability distinguishing curve;
    Step 7, neutrality buried depth with center away from change curve substitute into needed for center away from you can get it, and neutrality is buried It is deep, to judge whether Loess hidden holes are stable.
  2. The method of dark cave marginal stability 2. a kind of calculating Canal in Loess Area roadbed according to claim 1 underlies, feature It is, in step 1, using Drucker-Prager yield criterion:Calculate bending in the model Take stressWherein c is the cohesive strength of soil,For the angle of friction of soil.
  3. The method of dark cave marginal stability 3. a kind of calculating Canal in Loess Area roadbed according to claim 1 underlies, feature It is, in step 2, calculating Rayleigh damping coefficient, the specific method is as follows:
    Establish the equation of motion:
    It is respectively node acceleration vector, node speed vector sum modal displacement with a (t), M, C, K and Q (t) are respectively Computation model is carried out using consistent Mass Matrix for the load vector of mass matrix, damping matrix, stiffness matrix and node Undamped model analysis calculates the self-vibration circular frequency of mode, and Reyleigh' damping matrix C=α M+ β K, wherein α is Tuned mass damper system Number, β stiffness and damping coefficient, in conjunction with modal analysis result,
    Wherein, ξ is mode damping ratio, and ω is circular frequency;
    To reduce the influence that high order mode is artificially filtered out, i, j take 1 and 6 two vibration shape to be calculated.
  4. The method of dark cave marginal stability 4. a kind of calculating Canal in Loess Area roadbed according to claim 3 underlies, feature It is, in step 3, the method for solving of maximum equivalent is as follows:
    The equation of motion is solved using Newmark implicit integration algorithm:
    Assuming that:
    The displacement of wherein δ=1/2, α=1/4, time t+ Δ t solve at+ΔtFormula passes through the equation of motion of time t+ Δ t
    And it solves;
    It is solved first from formula 5:
    Then formula 4 is carried it into, then is brought into formula 1 together, to obtain atWithTo calculate equivalent stress, Change the load period again, finds out the least favorable load period, obtain maximum equivalent.
CN201810580883.6A 2018-06-07 2018-06-07 A method of it calculating Canal in Loess Area roadbed and underlies dark cave marginal stability Pending CN108959189A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111778959A (en) * 2020-05-28 2020-10-16 榆林市天元路业有限公司 Construction method for treating loess collapse in tunnel site area by adopting cement stabilized soil

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111778959A (en) * 2020-05-28 2020-10-16 榆林市天元路业有限公司 Construction method for treating loess collapse in tunnel site area by adopting cement stabilized soil
CN111778959B (en) * 2020-05-28 2021-11-30 榆林市天元路业有限公司 Construction method for treating loess collapse in tunnel site area by adopting cement stabilized soil

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