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 PDFInfo
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 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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 239000011159 matrix material Substances 0.000 claims description 16
 239000002689 soil Substances 0.000 claims description 8
 238000006073 displacement reaction Methods 0.000 claims description 6
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 235000013399 edible fruits Nutrition 0.000 claims 1
 230000000704 physical effect Effects 0.000 abstract description 2
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 G—PHYSICS
 G01—MEASURING; TESTING
 G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
 G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00  G01N31/00
 G01N33/24—Earth materials

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06F—ELECTRIC DIGITAL DATA PROCESSING
 G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
 G06F17/10—Complex mathematical operations
 G06F17/18—Complex 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 burieddepth 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
Technical field
The invention belongs to rocksoil 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 elasticperfectly 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 selfvibration 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 multigroup 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 DruckerPrager 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 selfvibration 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 a_{t+Δt}Formula 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 a_{t}、WithIt 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 burieddepth 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 elasticperfectly plastic material, definitely
Sill characterisitic parameter (elasticity modulus, density, damping ratio, Poisson's ratio, cohesive strength, angle of friction).Using DruckerPrager
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 selfvibration 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 t_{t+Δt}Formula 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 a_{t}、WithCalculate 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 multigroup 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 DruckerPrager yield criterion:
Calculate yield stress σ_{y}=79.25Kpa.The equation of motion is established, then undamped model analysis, calculates selfvibration
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=6.0623lnX30.606) when offset distance is 0
Power 79.25Kpa substitutes into equation, and obtaining critical burieddepth is 4.10 meters；Show that 1 meter of hole diameter, offset distance are 3 meters using same method
When regression equation y=9.6886lnX44.97, by yield stress 79.25Kpa substitute into equation, obtain critical burieddepth be 2.61
Rice.Neutrality buried depth can be fitted with center away from change curve according to above data (multigroup data can also be calculated)
(its equation is y=0.1658x^{2}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)
 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 elasticperfectly 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 selfvibration 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 multigroup 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.
 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 DruckerPrager yield criterion:Calculate bending in the model Take stressWherein c is the cohesive strength of soil,For the angle of friction of soil.
 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 selfvibration 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.
 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 a_{t+Δt}Formula passes through the equation of motion of time t+ Δ tAnd 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 a_{t}、WithTo calculate equivalent stress, Change the load period again, finds out the least favorable load period, obtain maximum equivalent.
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Cited By (1)
Publication number  Priority date  Publication date  Assignee  Title 

CN111778959A (en) *  20200528  20201016  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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Cited By (2)
Publication number  Priority date  Publication date  Assignee  Title 

CN111778959A (en) *  20200528  20201016  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) *  20200528  20211130  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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