CN108333331A

CN108333331A - Small Data Sets shallow embedding tunnel overlying and side wall geotechnical stability evaluation method

Info

Publication number: CN108333331A
Application number: CN201810144469.0A
Authority: CN
Inventors: 马少坤; 李涛; 邵羽; 刘莹; 段智博
Original assignee: Guangxi University
Current assignee: Guangxi University
Priority date: 2018-02-12
Filing date: 2018-02-12
Publication date: 2018-07-27
Anticipated expiration: 2038-02-12
Also published as: CN108333331B

Abstract

A kind of Small Data Sets shallow embedding tunnel overlying and side wall geotechnical stability evaluation method, include the following steps：Overlying ground is layered, the side wall ground for simplifying shallow embedding tunnel is sliding block, the reinforcement effect for utilizing the concept of " angle of equivalent internal friction " to calculate soil nailing to overlying ground, the vertical stress of each layer top surface and bottom surface is calculated using stepping type, calculate vertical force of the overlying ground to side wall ground, the stability that side wall ground sliding block is checked using limiting equilibrium formula, with the overall stability of the judgement of stability Small Data Sets of side wall ground sliding block.The present invention evaluates the stability of Small Data Sets using Strength Reduction Method and method of random sampling, not only allow for reinforcement effect of the side wall ground to the effect of Small Data Sets monolithic stability and soil nailing to overlying ground, and it calculates simpler, the ease for use in engineering is greatly improved while ensureing accurate, technical guarantee is provided for urgent Small Data Sets ground of reinforcing.

Description

Small Data Sets shallow embedding tunnel overlying and side wall geotechnical stability evaluation method

Technical field

The present invention relates to a kind of evaluation method of geotechnical stability, especially a kind of Small Data Sets shallow embedding tunnel overlying and Side wall geotechnical stability evaluation method.

Background technology

The mined out range of Small Data Sets is relatively narrow, mining depth is shallower, and based on the digging of tunnel and branch tunnel is excavated on both sides, point Cloth is irregular or in latticed, and single-layer or multi-layer overlapping interlocks, and does not support mostly or interim simple support, earth's surface be also easy to produce compared with Big crack, step and pitfall, seriously threatens the safety of the built or proposed construction of structures of earth's surface.For with ensureing Small Data Sets The safety of the proposed construction of structures of table needs to carry out estimation of stability to Small Data Sets, subsequently to take measures in guarantee The safety of portion's structure.For solution of emergent event, need promptly to reinforce Small Data Sets ground in certain emergency works, then very It is necessary to a kind of quick and easy easy and accurate Small Data Sets method for estimating stability of application.

Encircle theoretical, Terzaghi K.Rock Defects and Loads on Tunnel Support according to Tai Shaji [M].Massachusetts:Harvard Univ., 1946, there is the inclined fracture face since bottom surface in shallow embedded tunnel, tilt The plane of fracture becomes the through ground of the vertical plane of fracture after reaching hole heights of roofs.Tai Shaji provides hanging down for arbitrary point in Mass Near The Top of Underground Cavity rock stratum The formula of vertical compression power.It is not supported mostly due to Small Data Sets tunnel or simple support, overlying ground acts on tunnel and push up temporarily The pressure in portion is mainly undertaken by side wall ground.Tai Shaji arches theory is not enough to the stabilization of evaluation Small Data Sets in this case Property, this is because the theory does not analyze the stability of the side wall ground without support tunnel.Moreover, when using overlying strata on Soil-nailed When native, to evaluate the stability of reinforced Small Data Sets, Tai Shaji arches are theoretical just more helpless.

On the basis of Chinese patent application 201710727470.1 discloses the plane of fracture set by Tai Shaji arch theories It is proposed a kind of numerical method of evaluation Small Data Sets stability.The numerical method analysis stability of side wall ground, and examine The reinforcement effect of soil nailing is considered.Ground on the plane of fracture is reduced to several anti-shearing member units by the numerical method, will be broken Soil nailing on broken face is reduced to several spring units, and the ground on the inside of the plane of fracture is reduced to several sliding blocks, and overlying ground is slided Interface between block and side wall ground sliding block is reduced to anti-shearing member unit, the interface letter between each sliding block of overlying ground Turn to chain.The stiffness matrix of each unit is carried out coordinate conversion by the numerical method, is then integrated into the overall stiffness square of system Battle array.By the overall stiffness equation of solving system, the stress of each unit is obtained.By stress to each unit and criterion of strength into Row relatively evaluates Small Data Sets stability.This method realizes that rock-soil material is non-linear using iteration.Although this method checks The precision of Small Data Sets stability is higher, but excessively complicated calculating reduces the ease for use in engineering.

Invention content

The technical problem to be solved in the present invention is to provide a kind of Small Data Sets shallow embedding tunnel overlying and side wall ground is steady Qualitative evaluating method, it can be considered that the effect of Soil-nailed and shallow embedding tunnel side wall ground, and it is big while ensureing accurate Width improves the ease for use in engineering.

To solve the above-mentioned problems, the present invention proposes a kind of Small Data Sets shallow embedding tunnel overlying and side wall geotechnical stability Evaluation method, along tunnel, axis direction takes unit width Small Data Sets to be analyzed, and small kiln shallow embedding tunnel (1) is reduced to square There is inclined fracture face DE and JK since shallow embedding tunnel (1) bottom surface in shape, the side wall ground of setting shallow embedding tunnel (1), tilt Become vertical plane of fracture EF and KL after plane of fracture DE and JK arrival shallow embedding shallow embedding tunnel (1) overhead height to go directly ground (2), when shallow When burying tunnel (1) and being not added with support completely, friction in inclined fracture face DE and the average equivalent that the angle of JK and horizontal plane is ground AngleUsing the average equivalent internal friction angle of depth at D points and E points or J points and K pointsBetween the two vertical Tai Shaji planes of fracture Away from half b, ground coefficient of static earth pressure k₀, jth layer soil angle of equivalent internal frictionCalculation formula, evaluate small kiln and adopt The stability of dead zone, Small Data Sets shallow embedding tunnel overlying and side wall geotechnical stability evaluation method, including without basement process feelings The analytic method of the Small Data Sets Stability Assessment of condition, have Soil-nailed situation Small Data Sets estimation of stability analytic method, The method of random sampling of the Strength Reduction Method and Small Data Sets stability of Small Data Sets stability.

The analytic method of the Small Data Sets estimation of stability of the no basement process situation, includes the following steps：

A, pass through the vertical shortest distance H at the top of field investigation acquisition ground (2) to shallow embedding tunnel (1), shallow embedding tunnel (1) Most wide size B in the horizontal direction, shallow embedding tunnel (1) vertical direction most wide size h." ground " refers to this parsing mould The ground (2) of type refers to the foundation pit bottom surface for being less than 0.5m corresponding to ground surface or depth in Practical Project.

For convenience of calculating, practical small kiln tunnel is reduced to rectangle, enables practical small kiln tunnel most wide ruler in the horizontal direction Very little B is bottom edge and the top margin size in the shallow embedding tunnel (1) of rectangle, and the practical small kiln tunnel of order is in the most wide size h of vertical direction The side dimension in the shallow embedding tunnel (1) of rectangle.

B, the internal friction angle of ground is obtained by field sampling and laboratory testThe cohesion C of ground, the severe of ground γ.The angle of inclined fracture face DE and JK and horizontal plane are calculated according to formula (1)

In formula：For the internal friction angle of ground；C is the cohesion of ground；γ is the severe of ground.

C, k is calculated according to formula (2)₀,

D, b is calculated according to formula (3),

E, evenly load P is determined according to superstructure load₀.If superstructure load is un-uniformly distributed, needing will be non- Evenly load is equivalent to evenly load.The computational methods of equivalent uniform load refer to《Loading code for design of building structures》(GB 50009- 2012)。

F, it will be divided at the top of the ground on the inside of the Tai Shaji planes of fracture from Small Data Sets ground (2) to shallow embedding tunnel (1) If dried layer, shallow embedding tunnel (1) side wall is sliding block DEA and sliding block JKC.Set the angle of equivalent internal friction υ between each layer ground₀No Together, but the angle of equivalent internal friction υ of every layer of ground interior point₀It is equal.Every layer of thickness H is obtained at this time_j, wherein subscript j refers to J layers of ground.Take the vertical stress σ for the 1st layer of ground top surface for being close to Small Data Sets ground (2)_vt(j=1)=P₀。

G, it calculates the 1st layer of ground according to formula (4) and acts on the normal pressure σ on the vertical plane of fracture_Hj,

σ_Hj=k₀(σ_vt+0.5γH_j) (4)

H, shearing strength τ of the 1st layer of ground at the vertical plane of fracture is calculated according to formula (5)_fj,

I, the 1st layer of angle of equivalent internal friction is calculated according to formula (6)

J, the vertical stress σ of the 1st layer of ground bottom surface is calculated according to formula (7)_vb,

K, according to σ_vt(j+1)=σ_vb(j), the σ of lower layer of recursion_vt.Thus convolution (7), the top surface of any one layer of ground With the vertical stress of bottom surface all can recursion come out.

L, according to step g to the formula of step k, the σ that lower layer of recursion_Hj、τ_fj、σ_vb、σ_vt, so recycle to the last One layer, terminate recursion.

M, the vertical force F for acting on the top surfaces sliding block DEA is calculated according to formula (8)_nAE, work as F_nAE<F is taken when 0_nAE=0,

F_nAE=σ_vb(m)b (8)

In formula：M refers to last layer of ground, that is, is close to that layer of ground of shallow embedding tunnel (1) top surface；

N, the dead weight W of sliding block DEA is calculated_DEA.Take W_DEA=γ × A_DEA, A_DEAFor the cross-sectional area of sliding block DEA；

O, according to the stability of formula (9) checking computations sliding block DEA, the stability of sliding block DEA determines the whole steady of Small Data Sets It is qualitative.The limiting equilibrium formula of sliding block DEA is：

The molecule of formula (9) is skid resistance, and denominator is sliding force.When being more than 1 on the right of formula (9) equal sign, sliding block DEA stablizes； When being less than 1 on the right of equal sign, sliding block DEA unstabilitys；When being equal to 1 on the right of equal sign, sliding block DEA is in state of limit equilibrium.

Shape and the external force for setting Small Data Sets are symmetrical along shallow embedding tunnel (1) vertical central axes, then sliding block JKC Estimation of stability result it is identical as the estimation of stability result of sliding block DEA.

If p, sliding block DEA and sliding block JKC stablize, Small Data Sets monolithic stability is evaluated；Otherwise evaluation Small Data Sets It is whole unstable.

The analytic method of the Small Data Sets estimation of stability for having a Soil-nailed situation, includes the following steps：

C, k is calculated according to formula (2)₀,

D, b is calculated according to formula (3),

F, it will be divided at the top of the ground on the inside of the Tai Shaji planes of fracture from Small Data Sets ground (2) to shallow embedding tunnel (1) If dried layer, shallow embedding tunnel (1) side wall is sliding block DEA and sliding block JKC.Set the angle of equivalent internal friction between each layer groundNo Together, but the angle of equivalent internal friction of every layer of ground interior pointIt is equal.Every layer of thickness H is obtained at this time_j, wherein subscript j refers to Jth layer ground.Take the vertical stress σ for the 1st layer of ground top surface for being close to Small Data Sets ground (2)_vt(j=1)=P₀。

σ_Hj=k₀(σ_vt+0.5γH_j) (4)

H, for thering is the case where Soil-nailed, shearing strength of the jth layer ground at the plane of fracture to consist of two parts：The layer The intensity that shearing strength and soil nailing (3) at the plane of fracture of ground mean depth are contributed in Direction of fracture plane, setting soil nailing (3) exist The intensity of Direction of fracture plane contribution is generally evenly distributed in the vertical plane of fracture, and it is strong to obtain shearing resistance of the jth layer ground at the plane of fracture Spend τ_fjFor：

In formula：N be across the plane of fracture and be anchored at plane of fracture both ends ground soil nailing (3) quantity；σ_sIt is followed closely for soil nailing (3) The stress intensity of body；A_iFor the cross-sectional area of i-th soil nailing (3) rivet nut；α_iFor the angle of i-th soil nailing (3) and horizontal plane.

F_nAE=σ_vb(m)b (8)

The Strength Reduction Method of the evaluation Small Data Sets stability, includes the following steps：

A, by laboratory test, gather material and field investigation, the parameter of the factor of Small Data Sets stability, packet are obtained Include shallow embedding tunnel (1) most wide size B in the horizontal direction, the vertical shortest distance H at the top of ground (2) to shallow embedding tunnel (1), on Portion structure evenly load P₀, the severe γ of ground, shallow embedding tunnel (1) in the most wide size h of vertical direction, soil nailing (3) rivet nut Stress intensity sigma_s, i-th piece soil nailing (3) and horizontal plane angle α_i, soil nailing (3) shank diameter d_iOr cross-sectional area A_i, pass through rupture Face and the internal friction angle for being anchored at the quantity n of soil nailing (3) of plane of fracture both ends ground, groundThe cohesion C of ground.

B, under the premise of other parameters are constant, to the tangent function of the internal friction angle of groundWith cohesion C according to Following one of which rule is reduced：Only it is reducedOnly reduction C,Be reduced with C same parameters,With the folding of C Subtract coefficient it is proportional reduction,Coordinate to be reduced with C, other parameters remain unchanged, after taking adjustmentAfter the substitution of C Each step operation.

C, the angle of inclined fracture face DE and JK and horizontal plane are calculated according to formula (1)

D, k is calculated according to formula (2)₀,

E, b is calculated according to formula (3),

F, it will be divided at the top of the ground on the inside of the Tai Shaji planes of fracture from Small Data Sets ground (2) to shallow embedding tunnel (1) If dried layer, shallow embedding tunnel (1) side wall is sliding block DEA and sliding block JKC, obtains every layer of thickness H at this time_j, wherein subscript j refers to J layers of ground enable the vertical stress σ of the 1st layer of ground top surface_vt(j=1)=P₀。

σ_Hj=k₀(σ_vt+0.5γH_j) (4)

H, if no basement process the case where, calculates the 1st layer of shearing strength of the ground at the vertical plane of fracture according to formula (5) τ_fj,

If there is the case where Soil-nailed, τ is calculated according to formula (10)_fj, wherein from the design side of Soil-nailed obtain n, σ_s、A_i、α_i,

K, according to σ_vt(j+1)=σ_vb(j), the σ of lower layer of recursion_vt。

L, according to step g to the formula of step k, the σ that lower layer of recursion_Hj、τ_fj、υ_0j、σ_vb、σ_vt, so cycle is until most Later layer terminates recursion.

F_nAE=σ_vb(m)b (8)

In formula：M refers to last layer of ground, that is, is close to that layer of ground of shallow embedding tunnel (1) top surface.

N, the dead weight W of sliding block DEA is calculated_DEA, take W_DEA=γ × A_DEA, A_DEAFor the cross-sectional area of sliding block DEA.

O, according to the stability of formula (9) checking computations sliding block DEA, the stability of sliding block DEA determines the whole steady of Small Data Sets Qualitative, the limiting equilibrium formula of sliding block DEA is：

If p, sliding block DEA is not at state of limit equilibrium, returns to step b and continue to adjustWith C, again by all parameter generations Enter step c to step o, whether evaluation sliding block DEA is in state of limit equilibrium, so recycles flat in the limit until sliding block DEA Weighing apparatus state.

If q, sliding block DEA is in state of limit equilibrium, stops cycle, takeOr the reduction coefficient of C is mined out as small kiln The buckling safety factor in area.Strength Reduction Analysis calculates reduction coefficient according to formula (11).

R=X_r/X (11)

In formula：X is the parameter after reduction, after representing reductionOr C；X_rFor the parameter of original state ground, original state is represented GroundOr C；R is reduction coefficient.

R, evaluation Small Data Sets are stablized when buckling safety factor is higher than 1, and buckling safety factor is equal to or less than evaluate when 1 Small Data Sets are unstable, and buckling safety factor is higher, and Small Data Sets are more stable.

The method of random sampling of the evaluation Small Data Sets stability, includes the following steps：

A, by laboratory test, gather material, field investigation and mathematical statistics, the factor of Small Data Sets stability is obtained Statistical parameter and probability distribution, including shallow embedding tunnel (1) most wide size B in the horizontal direction, ground (2) to shallow embedding tunnel (1) vertical shortest distance H, superstructure evenly load P at the top of₀, the severe γ of ground, shallow embedding tunnel (1) in vertical direction Most wide size h, soil nailing (3) rivet nut stress intensity sigma_s, i-th piece soil nailing (3) and horizontal plane angle α_i, soil nailing (3) body of rod it is straight Diameter d_iOr cross-sectional area A_i, across the plane of fracture and be anchored at plane of fracture both ends ground soil nailing (3) design quantity n_d, pass through it is broken Broken face and be anchored at the construction substandard products quantity k of soil nailing (3) of plane of fracture both ends ground, the internal friction angle υ of ground, ground it is glutinous poly- Power C.Sampling generates corresponding random number according to the statistical parameter and probability distribution of each factor every time.When the random number of generation When less than 0, it is 0 to take random number.

Factor k obeys parameter M, N, n_dHypergeometric distribution, pass through the plane of fracture and be anchored at plane of fracture both ends ground at this time Soil nailing (3) design quantity be n_d, the defect rate of nail Construction is N/M.When sampling, according to parameter M, N, n_dHypergeometry point Cloth generates the random number of k.

B, the significant figure for the soil nailing (3) for passing through the plane of fracture and being anchored at plane of fracture both ends ground sampled every time measures n= n_d-k。

D, k is calculated according to formula (2)₀,

E, b is calculated according to formula (3),

σ_Hj=k0 (σ_vt+0.5γH_j) (4)

K, according to σ_vt(j+1)=σ_vb(j), the σ of lower layer of recursion_vt。

F_nAE=σ_vb(m)b (8)

The molecule of formula (9) is skid resistance, and denominator is sliding force, and when being more than 1 on the right of formula (9) equal sign, sliding block DEA stablizes； When being less than 1 on the right of equal sign, sliding block DEA unstabilitys；When being equal to 1 on the right of equal sign, sliding block DEA is in state of limit equilibrium.

P, the indicator function I to sample every time is calculated_F

In formula：X is the result sampled every time；F refers to sliding block DEA unstabilitys.

Q, circulation step a to step p, one cycle, that is, single sample, until reaching total frequency in sampling N_n.For safety Grade is the superstructure of level-one, N_nNot less than 235416 times；For the superstructure that safe class is two level, N_nIt is not less than 41945 times；For the superstructure that safe class is three-level, N_nNot less than 9596 times.

R, the estimated value of failure probability is calculated

In formula：J is jth time sampling；x_jFor the result of jth time sampling；N_fFor total Failure count.

S, whenLess than targeted failure probability [P_f] when evaluation Small Data Sets stablize；WhenMore than targeted failure probability [P_f] when evaluation Small Data Sets it is unstable.For the superstructure that safe class is level-one, [P_f] it is 0.000425；For peace Congruent grade is the superstructure of two level, [P_f] it is 0.002384；For the superstructure that safe class is three-level, [P_f] be 0.010421。

The present invention's has the prominent advantages that：

1, the case where not supporting for Small Data Sets tunnel or simply supporting temporarily mostly, it is contemplated that side wall ground is to small The reinforcement effect of the effect of kiln goaf monolithic stability and soil nailing to overlying ground.

2, the stability of Small Data Sets just can be evaluated using less calculating.Abandon the complexity meter to ground rigidity It calculates, the verification method of side wall geotechnical stability is proposed on the basis of limit equilibrium method；The concept of " angle of equivalent internal friction " is utilized, Soil nailing takes into account the reinforcement effect of overlying ground.This greatly improves easy-to-use in engineering while ensureing precision Property.Such as estimation of stability of the Small Data Sets without basement process only needs to substitute into parameter 9 analytic expressions of calculating, there is Soil-nailed The estimation of stability of Small Data Sets only needs to substitute into parameter 9 analytic expressions of calculating, the intensity folding of Small Data Sets estimation of stability Subtraction only needs to substitute into parameter simple cycle 9 analytic expressions of calculating, and the method for random sampling of Small Data Sets estimation of stability only needs generation Enter parameter simple cycle and calculates 9 analytic expressions.

3, it is capable of the overall stability of quantitative assessment Small Data Sets, the Small Data Sets under different condition can be relatively more steady Qualitatively height is especially evaluated before whether the stability after Small Data Sets are reinforced relatively reinforces and is significantly improved.

Description of the drawings

Fig. 1 is the simplification figure of Small Data Sets shallow embedding roadway shape.

Fig. 2 is Small Data Sets overlying rock-reinforcing schematic diagram.

Fig. 3 is geotechnical stratified schematic diagram on the inside of the Tai Shaji planes of fracture.

Fig. 4 is the value of the limiting equilibrium formula right end of 1 sliding block DEA of embodiment.

Fig. 5 is the uniformly distributed upper load figure of analytic method and physical experiments in limiting condition.

Fig. 6 is the value of the limiting equilibrium formula right end of 2 sliding block DEA of embodiment.

Fig. 7 is the buckling safety factor figure of ground on the inside of the Small Data Sets Tai Shaji planes of fracture.

In figure label for：Shallow embedding tunnel 1, ground 2, soil nailing 3, concrete topping 4.

Specific implementation mode

Technical scheme of the present invention is further described below by way of specific embodiment.

Embodiment 1

The present embodiment for no basement process when Small Data Sets estimation of stability analytic method.Certain Small Data Sets shows Intention is shown in Fig. 2.

Along tunnel, axis direction takes unit width Small Data Sets to be analyzed.Earthing is viscosity on certain Small Data Sets Soil obtains each parameter by laboratory test and field investigation and is shown in Table 1.

Parameter of the table 1 without basement process situation Small Data Sets

1 parameter of table is substituted into following steps, wherein P₀Each of horizontal each evaluation 1 time, totally 3 evaluations.

Every 1 evaluation includes the following steps：

A, by the vertical shortest distance H at 1 top of field investigation acquisition ground 2 to shallow embedding tunnel, shallow embedding tunnel 1 in level The most wide size B in direction, shallow embedding tunnel 1 vertical direction most wide size h.

For convenience of calculating, practical small kiln tunnel is reduced to rectangle, enables practical small kiln tunnel most wide ruler in the horizontal direction Very little B is bottom edge and the top margin size in the shallow embedding tunnel 1 of rectangle, and the practical small kiln tunnel of order is square in the most wide size h of vertical direction The side dimension in the shallow embedding tunnel 1 of shape, as shown in Figure 1.

C, k is calculated according to formula (2)₀,

D, b is calculated according to formula (3),

F, according to the signal of Fig. 3, from Small Data Sets ground 2 to shallow embedding tunnel 1 by the ground on the inside of the Tai Shaji planes of fracture Top is divided into 10 layers, and 1 side wall of shallow embedding tunnel is sliding block DEA and sliding block JKC.Every layer of thickness H is obtained at this time_j, wherein subscript j Refer to jth layer ground.Enable the vertical stress σ of the 1st layer of ground top surface_vt=P₀。

σ_Hj=k₀(σ_vt+0.5γH_j) (4)

K, according to σ_vt(j+1)=σ_vb(j), the σ of lower layer of recursion_vt,

L, according to step g to the formula of step k, the σ that lower layer of recursion_Hj、τ_fj、σ_vb、σ_vt, so recycle to the last One layer, terminate recursion；

F_nAE=σ_vb(m)b (8)

In formula：M refers to last layer of ground, that is, is close to that layer of ground of 1 top surface of shallow embedding tunnel；

If p, sliding block DEA stablizes, Small Data Sets monolithic stability is evaluated；Otherwise evaluation Small Data Sets are whole unstable It is fixed.

The evaluation result of embodiment 1：

It obtains the value on the right side of formula (9) equal sign and sees Fig. 4.CR in Fig. 4 refers to the limiting condition value on the right side of formula (9) equal sign.Work Condition 1 refers in P₀Level 1 under conditions of each experiment calculation obtain the value on the right side of formula (9) equal sign, the curve of operating mode 1 is higher than at this time The curve of CR, evaluation result are Small Data Sets monolithic stability.Operating mode 2 refers in P₀Level 2 under conditions of each experiment calculation The value on the right side of formula (9) equal sign is obtained, the curve of operating mode 2 is almost overlapped with CR curves at this time, and sliding block DEA is in limiting equilibrium shape State, evaluation result are that Small Data Sets are integrally unstable.Operating mode 3 refers in P₀Level 3 under conditions of each experiment calculation obtain Value on the right side of formula (9) equal sign, for the curve of operating mode 3 less than CR curves, evaluation result is that Small Data Sets are integrally unstable at this time.

The verification test of embodiment 1：

The implementation case is verified using physical experiments.Influence the principal element that Small Data Sets are stablized：1. dimensioning Degree：Size l；2. physical and mechanical parameter：The internal friction angle of ground density p, the cohesive strength C of soil, soilTop evenly load P₀, again Power acceleration g.Parameter l, ρ, C,P₀, g the likelihood ratio be respectively C_l、C_ρ、C_C、C_P0、C_g.Enable C_l=10, C_ρ=1, C_g=1, Then C is obtained according to correspondence theorem_C=10,C_P0=10.That is l, C, P of model₀It is the 1/10 of prototype analog value.

Corresponding physical experiments, the P in table are arranged according to the parameter of table 1₀Except.Gradually increase in test P₀Directly It is destroyed to physical model, the point that record displacement-load curve mutates, the corresponding P of the point₀For limiting condition when P₀, see figure 5.P when " operating mode 1 " refers to the analytic method limiting condition of no basement process in figure₀, i.e. the P of table 1₀Level 2 data；" operating mode 2 " P when referring to the physical experiments limiting condition of no basement process₀。

From figure 5 it can be seen that the curve of operating mode 1 and the curve of operating mode 2 are closer to, physical experiments and without basement process when, are small P of the analytic method of the estimation of stability in kiln goaf in limiting condition₀Between error it is little.Show the present invention without ground at The analytic method of the estimation of stability of Small Data Sets is effective in force when reason.

Embodiment 2

The present embodiment is the analytic method of the estimation of stability of Small Data Sets when having Soil-nailed.Certain Small Data Sets shows Intention is shown in Fig. 2.

Along tunnel, axis direction takes unit width Small Data Sets to be analyzed.Earthing is viscosity on certain Small Data Sets Soil obtains each parameter by laboratory test, gather material and field investigation and is shown in Table 2.Factor d in table_iFor 3 shank diameter of soil nailing.

Table 2 has the parameter of Soil-nailed situation Small Data Sets

2 parameter of table is substituted into each step of embodiment 2, wherein P₀Each of horizontal each evaluation 1 time, totally 3 evaluations.

Every 1 evaluation includes the following steps：

Each step of embodiment 2, in addition to step h calculates τ according to formula (10)_fj, remaining step is same as Example 1.Wherein, N, σ are obtained from the design side of Soil-nailed_s、A_i、α_i。

In formula：N be across the plane of fracture and be anchored at plane of fracture both ends ground soil nailing 3 quantity；σ_sFor 3 rivet nut of soil nailing Stress intensity；A_iFor the cross-sectional area of i-th 3 rivet nut of soil nailing；α_iFor the angle of i-th soil nailing 3 and horizontal plane.

The evaluation result of embodiment 2：

It obtains the value on the right side of formula (9) equal sign and sees Fig. 6.CR in Fig. 6 refers to the limiting condition value on the right side of formula (9) equal sign.Work Condition 1 refers in P₀Level 1 under conditions of each experiment calculation obtain the value on the right side of formula (9) equal sign, at this time operating mode 1 in addition to experiment 3, Experiment 7, experiment 12, experiment 18, experiment 24, test 27 value outside, remaining experiment value be higher than CR curve, evaluation result be except Experiment 3, experiment 7, experiment 12, experiment 18, experiment 24, outside experiment 27, the Small Data Sets monolithic stability of remaining experiment.Operating mode 2 refer in P₀Level 2 under conditions of each experiment calculation obtain the value on the right side of formula (9) equal sign, the curve Yu CR of operating mode 2 are bent at this time Line almost overlaps, and sliding block DEA is in state of limit equilibrium, and evaluation result is that Small Data Sets are integrally unstable.Operating mode 3 refer to P₀Level 3 under conditions of each experiment calculation obtain the value on the right side of formula (9) equal sign, at this time the curve of operating mode 3 be less than CR curves, comment Valence result is that Small Data Sets are integrally unstable.

The verification test of embodiment 2：

The implementation case is verified using physical experiments.The principal element that Small Data Sets are stablized is influenced, in embodiment 1 Case on the basis of increase：The yield strength σ of soil nailing 3_s.Parameter σ_sLikelihood ratio C_σs=10, the likelihood ratio of remaining parameter with The case of embodiment 1 is identical.

Corresponding physical experiments, the P in table are arranged according to the parameter of table 2₀Except.Gradually increase in test P₀Directly It is destroyed to physical model, the point that record displacement-load curve mutates, the corresponding P of the point₀For limiting condition when P₀, see figure 5.P when " operating mode 1 " refers to the analytic method limiting condition for having Soil-nailed in Fig. 5₀, i.e. the P of table 2₀Level 2 data；" work P when condition 3 " refers to the physical experiments limiting condition for having Soil-nailed₀。

As can be seen from Figure 5, the curve of operating mode 1 and the curve of operating mode 3 are closer to, and physical experiments and while having a Soil-nailed are small P of the analytic method of the estimation of stability in kiln goaf in limiting condition₀Between error it is little.Show that the present invention's has soil nailing to add Gu when Small Data Sets the analytic method of estimation of stability be effective in force.

Embodiment 3

The present embodiment is the concrete case for the Strength Reduction Method for evaluating Small Data Sets stability.Certain Small Data Sets shows Intention is shown in Fig. 2.

Along tunnel, axis direction takes unit width Small Data Sets to be analyzed.Earthing is viscosity on certain Small Data Sets Soil, laboratory test measure undisturbed soil υ=33.000, undisturbed soil C=43.987kPa.It is arranged using " orthogonal experimental design method " small The evaluation of the Strength Reduction Method of kiln goaf stability.The factor level of Small Data Sets stability is shown in Table 3, table 4.

Factor level of the table 3 without basement process situation Small Data Sets stability

Table 4 has the factor level of Soil-nailed situation Small Data Sets stability

The orthogonal arrage that no basement process situation uses is L₂₇(3⁵), that is, 5 factors are arranged, it is each because being known as 3 kinds of levels, altogether Make the orthogonal arrage of 27 experiments；There is the orthogonal arrage that Soil-nailed situation uses for L₂₇(3⁹), that is, arrange 9 factors, each factor There are 3 kinds of levels, makees the orthogonal arrage of 27 experiments altogether.The Strength Reduction Method of evaluation Small Data Sets stability is carried out according to orthogonal arrage 54 orthogonal tests, i.e. each case carry out 27 experiments, totally 2 kinds of situations.By the parameter combination orthogonal arrage L of table 3₂₇(3⁵), table 4 Parameter combination orthogonal arrage L₂₇(3⁹), during substitution following steps are rapid, evaluate the stability of Small Data Sets.

Include the following steps：

A, to the tangent function of the internal friction angle of groundWith cohesion C coordination reduction is carried out according to formula (14).Formula (14) it is the native in structural change of certain Small Data SetsThe functional relation showed with C, the formula is by laboratory test It measuresIt is fitted to obtain with C.Work as C<When 0, C=0 is taken.Other parameters remain unchanged.

If all parameters are substituted into the step a to step p of embodiment 1 by the case where b, belonging to without basement process, sliding block is evaluated Whether DEA is in state of limit equilibrium；If category has the case where Soil-nailed, the step a that all parameters are substituted into embodiment 2 is extremely walked Whether rapid p, evaluation sliding block DEA are in state of limit equilibrium.

If c, sliding block DEA is not at state of limit equilibrium, returns to step a and continue to adjustWith C, then presses step b evaluations and slide Whether block DEA is in state of limit equilibrium, so recycles until sliding block DEA is in state of limit equilibrium.

If d, sliding block DEA is in state of limit equilibrium, stops calculating, takeOr the reduction coefficient of C is mined out as small kiln The buckling safety factor in area.Strength Reduction Analysis calculates reduction coefficient according to formula (11).

R=X_r/X (11)

E, evaluation Small Data Sets are stablized when buckling safety factor is higher than 1, and buckling safety factor is equal to or less than evaluate when 1 Small Data Sets are unstable.Buckling safety factor is higher, and Small Data Sets are more stable.

The evaluation result of embodiment 3：

The buckling safety factor of ground is shown in Fig. 7 on the inside of the Small Data Sets Tai Shaji planes of fracture.The operating mode 1 of Fig. 7 is no ground The buckling safety factor that the Strength Reduction Method of the evaluation Small Data Sets stability of disposition obtains, operating mode 2 are to have soil nailing to add Gu the buckling safety factor that the Strength Reduction Method of the evaluation Small Data Sets stability of situation obtains.The result shows that for no ground Disposition only tests 13, experiment 14, experiment 15, tests 16, experiment 17, experiment 18, experiment 22, experiment 23, tests 24 Small Data Sets are stablized, and the Small Data Sets of remaining experiment are unstable；For having the case where Soil-nailed, the small kiln of all experiments Stablize in goaf.The curve of operating mode 2 is far above the curve of operating mode 1, shows that Soil-nailed significantly improves the stabilization of Small Data Sets Property.

The implementation case is verified using the numerical simulation of Strength Reduction of FEM：

Finite element modeling and method for solving are：The unit that ground part uses is the ginseng such as 8 node serendipity of quadrangle Counting unit；The semo-infinite boundary of ground is 5 node serendipity mapped infinite elements；Soil nailing is using two-dimentional 2 node axle powers Bar unit.The numerical integration method on ground part and semo-infinite boundary is Gauss integration, and reduces point；Soil nailing is using essence Really integral.Using Gauss-Jordan elimination solving finite element equation group.The stiffness matrix of soil nailing unit is integrated into the whole of ground The corresponding position of body stiffness matrix is simulated and is bonded between ground and soil nailing.The constitutive relation of soil nailing unit is ideal elastic-plastic mould Type；The constitutive relation of ground unit and Infinite Element is Duncan-change model.The non-linear of rock-soil material is realized with Euler buckling method Constitutive model, while Euler's drift is weakened using mid-point additive method.The yield criterion of soil nailing is maximum normal stress criterion；Ground It include mole-coulomb criterion in Duncan-change model.For no basement process situation, analytical procedure is：A. it establishes and initially answers Power, b. shallow embeddings roadway excavation, c. apply upper load；For thering is Soil-nailed situation, analytical procedure to be：A. it establishes and initially answers Power, b. shallow embeddings roadway excavation, c. arrangements soil nailing, d. apply upper load.

Strength Reduction Method with Small Data Sets estimation of stability equally uses " orthogonal experimental design method " to arrange numerical value imitative Very.Used parameter is identical as the Strength Reduction Method of Small Data Sets estimation of stability.It is mutated with displacement-load curve Criterion as finite element limiting condition.

The stabilization of ground on the inside of the Small Data Sets Tai Shaji planes of fracture that the numerical simulation of Strength Reduction of FEM obtains Safety coefficient is shown in Fig. 7.The buckling safety factor that the operating mode 3 of Fig. 7 obtains for the Strength Reduction of FEM of no basement process situation, Operating mode 4 is the buckling safety factor for having the Strength Reduction of FEM of Soil-nailed situation to obtain.From fig.7, it can be seen that the song of operating mode 1 Line and the curve of operating mode 3 are closer to, and the curve and the curve of operating mode 4 of operating mode 2 are closer to, Strength Reduction of FEM numerical simulation The buckling safety factor error obtained with the Strength Reduction Method of Small Data Sets estimation of stability is little.

Embodiment 4

The present embodiment is the concrete case of the method for random sampling of Small Data Sets estimation of stability.Certain Small Data Sets shows Intention is shown in Fig. 2.

Along tunnel, axis direction takes unit width Small Data Sets to be analyzed.Earthing is viscosity on certain Small Data Sets Soil.Pass through laboratory test, gather material, field investigation and mathematical statistics, the statistical parameter of the factor of Small Data Sets stability It is shown in Table 5, table 6 with probability distribution.When sampling, according to table 5, the statistical parameter of table 6 and probability distribution generate it is corresponding because The random number of element.K in table 6 refer to across the plane of fracture and be anchored at plane of fracture both ends ground soil nailing 3 construction substandard products quantity, this When across the plane of fracture and be anchored at plane of fracture both ends ground soil nailing 3 design quantity be n_dIt is 14, the defect rate of nail Construction It is 1/1000, then the event of " number of defective product k contained by 14 soil nailings " obeys parameter M=1000, N=1, n_d=14 hypergeometry point Cloth, when sampling, according to parameter M=1000, N=1, n_d=14 hypergeometric distribution generates the random number of k.Generate random number method side Method refers to the document in relation to sampling techniques.

The statistical parameter and probability distribution of factor of the table 5 without basement process situation Small Data Sets stability

Table 6 has the statistical parameter and probability distribution of the factor of Soil-nailed situation Small Data Sets stability

By the parameter of table 5, table 6 substitute into following steps it is rapid in, evaluate the stability of Small Data Sets.

Include the following steps：

A, the random number for the corresponding factor sampled every time is generated according to the statistical parameter and probability distribution of table 5 and table 6. When the random number of generation is less than 0, it is 0 to take random number.

B, the significant figure for the soil nailing 3 for passing through the plane of fracture and being anchored at plane of fracture both ends ground sampled every time measures n=n_d- k。

C, the cohesive strength C for the soil sampled every time is calculated according to formula (14).Formula (14) is the soil of certain Small Data Sets in structure When property changesThe functional relation showed with C, what which was measured by laboratory testIt is fitted to obtain with C.Work as C<When 0, Take C=0.

If the case where d, belonging to without basement process, the random number and n and C that table 5 and table 6 are generated substitute into the step a of embodiment 1 To step p, evaluate the sliding block DEA that samples every time whether unstability；If belong to have the case where Soil-nailed, by table 5 and table 6 generate with Machine number and n and C substitute into the step a to step p of embodiment 2, evaluate the sliding block DEA that samples every time whether unstability.

E, the indicator function I to sample every time is calculated_F

F, the step a to step e of the present embodiment, one cycle, that is, single sample, until reaching total frequency in sampling are recycled N_n=235416.

G, the estimated value of failure probability is calculated

H, whenLess than targeted failure probability [P_f] when evaluation Small Data Sets stablize；WhenMore than targeted failure probability [P_f] when evaluation Small Data Sets it is unstable.For the superstructure that safe class is level-one, [P_f] it is 0.000425；For peace Congruent grade is the superstructure of two level, [P_f] it is 0.002384；For the superstructure that safe class is three-level, [P_f] be 0.010421。

The evaluation result of embodiment 4：

For no basement process situation, the estimated value of the failure probability of ground is on the inside of the Small Data Sets Tai Shaji planes of fracture 0.007111, higher than the targeted failure probability [P that safe class is level-one, the superstructure of two level_f], for level-one, two level Small Data Sets are unstable for superstructure, but less than the targeted failure probability for the superstructure that safe class is three-level [P_f], Small Data Sets are stablized for the superstructure of three-level；For having Soil-nailed situation, Small Data Sets Tai Shaji The estimated value of the failure probability of ground is 0.000569 on the inside of the plane of fracture, higher than the target for the superstructure that safe class is level-one Failure probability [P_f], Small Data Sets are unstable for the superstructure of level-one, but are two level, three-level less than safe class Superstructure targeted failure probability [P_f], Small Data Sets are stablized for two level, the superstructure of three-level.

The implementation case is verified using the numerical simulation of stochastic finite element method：

Finite element modeling and method for solving are the same as embodiment 3.It is the same with the method for random sampling of Small Data Sets estimation of stability The random number for the corresponding factor sampled every time is generated according to the statistical parameter and probability distribution of table 5 and table 6.According to n=n_d- K calculates the effective quantity for the soil nailing 3 for passing through the plane of fracture and being anchored at plane of fracture both ends ground sampled every time.According to the present embodiment Step c formula (14) calculate sample every time soil cohesive strength C.The random number for the corresponding factor sampled according to each time is had It limits Meta Model and solves.It is mutated using displacement-load curve as the criterion of finite element limiting condition.According to the present embodiment The formula (12) of step e calculates the indicator function I to sample every time.Cyclic samples are until reaching total frequency in sampling N_n。N_nValue it is same The step f of the present embodiment.The estimated value of failure probability is calculated according to the formula (13) of the step g of the present embodiment

The result of stochastic finite element method numerical simulation is：For no basement process situation, Small Data Sets Tai Shaji ruptures The estimated value of the failure probability of ground is 0.007038 on the inside of face；For having Soil-nailed situation, Small Data Sets Tai Shaji broken The estimated value of the failure probability of ground is 0.000673 on the inside of broken face.Stochastic finite element method numerical simulation and Small Data Sets are stablized Property evaluation the obtained failure probability error of method of random sampling it is little.

Embodiments of the present invention are explained in detail above in conjunction with attached drawing, but the present invention is not limited to above-mentioned implementations Mode, one skilled in the relevant art within the scope of knowledge, can also make it a variety of simple variants, such as will Ground on the inside of the Tai Shaji planes of fracture is divided equally into arbitrary more than 1 layer from Small Data Sets ground 2 to 1 top of shallow embedding tunnel Integer layer；When for another example carrying out Strength Reduction Analysis, only it is reducedOnly reduction C,Be reduced with C same parameters,With C The proportional reduction of reduction coefficient.These simple variants all belong to the scope of protection of the present invention.

Claims

1. a kind of Small Data Sets shallow embedding tunnel overlying and side wall geotechnical stability evaluation method, along tunnel, axis direction takes unit Width Small Data Sets are analyzed, and small kiln shallow embedding tunnel (1) is reduced to rectangle, sets the side wall ground of shallow embedding tunnel (1) In the presence of the inclined fracture face DE and JK since shallow embedding tunnel (1) bottom surface, inclined fracture face DE and JK reach shallow embedding shallow embedding tunnel (1) become vertical plane of fracture EF and KL after overhead height to go directly ground (2), when shallow embedding tunnel (1) is not added with support completely, tilt The angle of plane of fracture DE and JK and horizontal plane is the average equivalent internal friction angle of groundUsing D points and E points or J points and K points Locate the average equivalent internal friction angle of depthThe half b of two vertical Tai Shaji ruptures interplanar distances, the earth pressure at rest system of ground Number k₀, jth layer soil angle of equivalent internal frictionCalculation formula, evaluate the stability of Small Data Sets, it is characterised in that：Without ground The analytic method of the Small Data Sets Stability Assessment of base disposition, includes the following steps：

A, obtain that vertical shortest distance H at the top of ground (2) to shallow embedding tunnel (1), shallow embedding tunnel (1) in water by field investigation Square to most wide size B, shallow embedding tunnel (1) vertical direction most wide size h,

" ground " refers to the ground (2) of this analytic modell analytical model, refers to being less than corresponding to ground surface or depth in Practical Project The foundation pit bottom surface of 0.5m,

For convenience of calculating, practical small kiln tunnel is reduced to rectangle, the practical small kiln tunnel most wide size B in the horizontal direction of order is The bottom edge in the shallow embedding tunnel (1) of rectangle and top margin size, the practical small kiln tunnel of order are rectangle in the most wide size h of vertical direction The side dimension in shallow embedding tunnel (1),

B, the internal friction angle of ground is obtained by field sampling and laboratory testThe cohesion C of ground, the severe γ of ground, are pressed Illuminated (1) calculates the angle of inclined fracture face DE and JK and horizontal plane

In formula：For the internal friction angle of ground；C is the cohesion of ground；γ is the severe of ground,

C, k is calculated according to formula (2)₀,

D, b is calculated according to formula (3),

E, evenly load P is determined according to superstructure load₀If superstructure load is un-uniformly distributed, need non-uniformly distributed lotus Load is equivalent to evenly load, and the computational methods of equivalent uniform load refer to《Loading code for design of building structures》(GB 50009-2012),

F, it will be divided at the top of the ground on the inside of the Tai Shaji planes of fracture from Small Data Sets ground (2) to shallow embedding tunnel (1) several Layer, shallow embedding tunnel (1) side wall are sliding block DEA and sliding block JKC, set the angle of equivalent internal friction between each layer groundDifference, but The angle of equivalent internal friction of every layer of ground interior pointIt is equal, every layer of thickness H is obtained at this time_j, wherein subscript j refers to jth layer Ground takes the vertical stress σ for the 1st layer of ground top surface for being close to Small Data Sets ground (2)_vt(j=1)=P₀,

σ_Hj=k₀(σ_vt+0.5γH_j) (4)

K, according to σ_vt(j+1)=σ_vb(j), the σ of lower layer of recursion_vt, thus convolution (7), the top surface and bottom of any one layer of ground The vertical stress in face all can recursion come out,

L, according to step g to the formula of step k, the σ that lower layer of recursion_Hj、τ_fj、σ_vb、σ_vt, such cycle to the last one Layer terminates recursion,

F_nAE=σ_vb(m)b (8)

N, the dead weight W of sliding block DEA is calculated_DEA, take W_DEA=γ × A_DEA, A_DEAFor the cross-sectional area of sliding block DEA；

O, according to the stability of formula (9) checking computations sliding block DEA, the stability of sliding block DEA determines the overall stability of Small Data Sets, The limiting equilibrium formula of sliding block DEA is：

The molecule of formula (9) is skid resistance, and denominator is sliding force, and when being more than 1 on the right of formula (9) equal sign, sliding block DEA stablizes；Equal sign When the right is less than 1, sliding block DEA unstabilitys；When being equal to 1 on the right of equal sign, sliding block DEA is in state of limit equilibrium,

Shape and the external force for setting Small Data Sets are symmetrical along shallow embedding tunnel (1) vertical central axes, then sliding block JKC's is steady Qualitative evaluation result is identical as the estimation of stability result of sliding block DEA,

If p, sliding block DEA and sliding block JKC stablize, Small Data Sets monolithic stability is evaluated；Otherwise evaluation Small Data Sets are whole It is unstable.

2. Small Data Sets shallow embedding according to claim 1 tunnel overlying and side wall geotechnical stability evaluation method, special Sign is：The analytic method for having the Small Data Sets estimation of stability of Soil-nailed situation, includes the following steps：

C, k is calculated according to formula (2)₀,

D, b is calculated according to formula (3),

E, evenly load P is determined according to superstructure load₀If superstructure load is un-uniformly distributed, need non-uniformly distributed lotus Load is equivalent to evenly load,

σ_Hj=k₀(σ_vt+0.5γH_j) (4)

H, for thering is the case where Soil-nailed, shearing strength of the jth layer ground at the plane of fracture to consist of two parts：This layer of ground The intensity that shearing strength and soil nailing (3) at the plane of fracture of mean depth are contributed in Direction of fracture plane, setting soil nailing (3) are rupturing The intensity of face direction contribution is generally evenly distributed in the vertical plane of fracture, obtains shearing strength τ of the jth layer ground at the plane of fracture_fj For：

In formula：N be across the plane of fracture and be anchored at plane of fracture both ends ground soil nailing (3) quantity；σ_sFor soil nailing (3) rivet nut Stress intensity；A_iFor the cross-sectional area of i-th soil nailing (3) rivet nut；α_iFor the angle of i-th soil nailing (3) and horizontal plane,

F_nAE=σ_vb(m)b (8)

3. Small Data Sets shallow embedding according to claim 1 tunnel overlying and side wall geotechnical stability evaluation method, special Sign is：The Strength Reduction Method for evaluating Small Data Sets stability, includes the following steps：

A, by laboratory test, gather material and field investigation, the parameter of the factor of Small Data Sets stability is obtained, including shallow Bury tunnel (1) most wide size B in the horizontal direction, the vertical shortest distance H at the top of ground (2) to shallow embedding tunnel (1), top knot Structure evenly load P₀, the severe γ of ground, shallow embedding tunnel (1) in the most wide size h of vertical direction, the stress of soil nailing (3) rivet nut Intensity σ_s, i-th piece soil nailing (3) and horizontal plane angle α_i, soil nailing (3) shank diameter d_iOr cross-sectional area A_i, pass through the plane of fracture and It is anchored at the quantity n of the soil nailing (3) of plane of fracture both ends ground, the internal friction angle of groundThe cohesion C of ground,

B, under the premise of other parameters are constant, to the tangent function of the internal friction angle of groundWith cohesion C according to as follows One of which rule is reduced：Only it is reducedOnly reduction C,Be reduced with C same parameters,With the reduction system of C The proportional reduction of number,Coordinate to be reduced with C, other parameters remain unchanged, after taking adjustmentWith it is each after the substitution of C The operation of step,

D, k is calculated according to formula (2)₀,

E, b is calculated according to formula (3),

F, it will be divided at the top of the ground on the inside of the Tai Shaji planes of fracture from Small Data Sets ground (2) to shallow embedding tunnel (1) several Layer, shallow embedding tunnel (1) side wall are sliding block DEA and sliding block JKC, obtain every layer of thickness H at this time_j, wherein subscript j refers to jth layer Ground enables the vertical stress σ of the 1st layer of ground top surface_vt(j=1)=P₀,

σ_Hj=k₀(σ_vt+0.5γH_j) (4)

H, if no basement process the case where, calculates shearing strength τ of the 1st layer of ground at the vertical plane of fracture according to formula (5)_fj,

If there is the case where Soil-nailed, τ is calculated according to formula (10)_fj, wherein obtain n, σ from the design side of Soil-nailed_s、A_i、 α_i,

K, according to σ_vt(j+1)=σ_vb(j), the σ of lower layer of recursion_vt,

F_nAE=σ_vb(m)b (8)

In formula：M refers to last layer of ground, that is, is close to that layer of ground of shallow embedding tunnel (1) top surface,

N, the dead weight W of sliding block DEA is calculated_DEA, take W_DEA=γ × A_DEA, A_DEAFor the cross-sectional area of sliding block DEA,

If p, sliding block DEA is not at state of limit equilibrium, returns to step b and continue to adjustWith C, all parameters is substituted into walk again Whether rapid c to step o, evaluation sliding block DEA are in state of limit equilibrium, so recycle until sliding block DEA is in limiting equilibrium shape State,

If q, sliding block DEA is in state of limit equilibrium, stops cycle, takeOr the reduction coefficient of C is as Small Data Sets Buckling safety factor, Strength Reduction Analysis calculate reduction coefficient according to formula (11),

R=X_r/X (11)

In formula：X is the parameter after reduction, after representing reductionOr C；X_rFor the parameter of original state ground, original state ground is represented 'sOr C；R is reduction coefficient,

R, evaluation Small Data Sets are stablized when buckling safety factor is higher than 1, and buckling safety factor is equal to or less than evaluate small kiln when 1 Goaf is unstable, and buckling safety factor is higher, and Small Data Sets are more stable.

4. Small Data Sets shallow embedding according to claim 1 tunnel overlying and side wall geotechnical stability evaluation method, special Sign is：The method of random sampling for evaluating Small Data Sets stability, includes the following steps：

A, by laboratory test, gather material, field investigation and mathematical statistics, the system of the factor of Small Data Sets stability is obtained Count parameter and probability distribution, including shallow embedding tunnel (1) most wide size B in the horizontal direction, ground (2) to shallow embedding tunnel (1) top Vertical shortest distance H, the superstructure evenly load P in portion₀, the severe γ of ground, shallow embedding tunnel (1) in the most wide of vertical direction The stress intensity sigma of size h, soil nailing (3) rivet nut_s, i-th piece soil nailing (3) and horizontal plane angle α_i, soil nailing (3) shank diameter d_iOr Cross-sectional area A_i, across the plane of fracture and be anchored at plane of fracture both ends ground soil nailing (3) design quantity n_d, pass through the plane of fracture and It is anchored at the construction substandard products quantity k of the soil nailing (3) of plane of fracture both ends ground, the internal friction angle of groundThe cohesion C of ground, often Secondary sampling generates corresponding random number according to the statistical parameter and probability distribution of each factor, when the random number of generation is less than 0 When, it is 0 to take random number,

Factor k obeys parameter M, N, n_dHypergeometric distribution, pass through the plane of fracture at this time and be anchored at the soil nailing of plane of fracture both ends ground (3) design quantity is n_d, the defect rate of nail Construction is N/M, when sampling, according to parameter M, N, n_dHypergeometric distribution generate k Random number,

B, the significant figure for the soil nailing (3) for passing through the plane of fracture and being anchored at plane of fracture both ends ground sampled every time measures n=n_d- k,

D, k is calculated according to formula (2)₀,

E, b is calculated according to formula (3),

σ_Hj=k₀(σ_vt+0.5γH_j) (4)

K, according to σ_vt(j+1)=σ_vb(j), the σ of lower layer of recursion_vt,

F_nAE=σ_vb(m)b (8)

P, the indicator function I to sample every time is calculated_F

In formula：X is the result sampled every time；F refers to sliding block DEA unstabilitys,

Q, circulation step a to step p, one cycle, that is, single sample, until reaching total frequency in sampling N_n, for safe class For the superstructure of level-one, N_nNot less than 235416 times；For the superstructure that safe class is two level, N_nNot less than 41945 It is secondary；For the superstructure that safe class is three-level, N_nNot less than 9596 times,

R, the estimated value of failure probability is calculated

In formula：J is jth time sampling；x_jFor the result of jth time sampling；N_fFor total Failure count,

S, whenLess than targeted failure probability [P_f] when evaluation Small Data Sets stablize；WhenMore than targeted failure probability [P_f] when Evaluation Small Data Sets are unstable, for the superstructure that safe class is level-one, [P_f] it is 0.000425；For safe class For the superstructure of two level, [P_f] it is 0.002384；For the superstructure that safe class is three-level, [P_f] it is 0.010421.