CN104992013A - Mountain tunnel anti-seismic analysis method - Google Patents

Abstract

The invention discloses a mountain tunnel anti-seismic analysis method. For the aspect of cross section anti-seismic analysis of a tunnel, based on a stratal elastic shear deformation theory, horizontal stratum deformation, vertical stratum deformation and seismic self-weight inertial force of broken rock bodies at the top of the tunnel are considered at the same time, and related problems of tunnel cross section seismic resistance are studied; and for the aspect of longitudinal overall anti-seismic analysis of the tunnel, an elastic foundation beam is taken as a model, interaction of the tunnel and surrounding rocks is considered, a dynamic balance equation of a tunnel structure is created according to an anti-seismic dynamic theory and a deformation transfer theory by utilizing continuum mechanics, and a classic seismic deformation method is a particular case of the method. According to the method, the cross section anti-seismic analysis and the longitudinal overall anti-seismic analysis of the mountain tunnel are performed by adopting unified thought for the first time; the thought is novel; the method is feasible; and through example verification, the method has relatively good applicability for mountain tunnel primary design under the action of strong earthquake.

Description

A kind of method of mountain tunnel aseismic analysis

Technical field

The invention belongs to tunnel aseismic analysis technical field, particularly relate to a kind of method of mountain tunnel aseismic analysis.

Background technology

Along with the deep propelling of strategy to develop western regions, western China infrastructure construction will obtain development energetically, especially highway and railway transport development obtains great-leap-forward development, certainly will to build many tunnels like this, these areas are mostly in the area of highlight lines, ensure that the function of Tunnel Engineering when earthquake is normal, dark tool strategic importance.Especially subway earthquake and China in Japan's " slope god " earthquake " " in earthquake, the serious earthquake in 109 tunnels, makes the earthquake of people to underground works have understanding clearly in 5.12 Wenchuans.

Mountain tunnel Aseismic Analytical Method mostly adopts the finite element numerical analysis technology such as ANSYS to carry out, but the numerical simulation technology of advanced person is concerning more complicated project planner, and the time and expense all higher, and find a kind of simple, efficient and applicable Near covering, the primary design for Tunnel Engineering of Mountainous Region is necessary.

At present, mountain tunnel Practical Method of Designing is many, the Fu Jiyewafa, U.S. ST.John method etc. of such as USSR (Union of Soviet Socialist Republics), but these methods all do not consider the impact of top covering rockmass and tunnel structure deadweight, in fact, mountain tunnel, due to the limitation of current operating technique, certainly will produce massif loosening at tunnel vault, these loads will produce larger Earthquake Inertia Force Acting when earthquake, and it is unsafe for ignoring these loads to mountain tunnel.And current method have employed different thought and methods when analyzing mountain tunnel xsect aseismic analysis and longitudinal aseismic analysis, imperfect in system.

Summary of the invention

The object of the embodiment of the present invention is a kind of method providing mountain tunnel aseismic analysis, be intended to solve mountain tunnel under severe earthquake action, fairly simple method and program is utilized to carry out the primary design of mountain tunnel, for project planner provides necessary design parameter and the problem of data.

The embodiment of the present invention is achieved in that a kind of method of mountain tunnel aseismic analysis, and the method for this mountain tunnel aseismic analysis comprises:

Step one, determines the geometric parameter of mountain tunnel, determines and simplifies stratum basic parameter, determining the kinetic parameter of rock mass;

Step 2, according to geological exploration data and seismic strata deformable statistical data, determines the deformation pattern on stratum and the level of stratum deformation and vertical deformation;

Step 3, mountain tunnel xsect aseismic analysis;

Step 4, mountain tunnel Horizontal vibration of piles (Horizontal Deformation pressure q _h); Mountain tunnel Vertical Vibration (comprises stratum vertical deformation pressure q _v1with loose ground Earthquake Inertia Force Acting q _v2); Utilize structural mechanics, determine the internal force of tunnel-liner;

Step 5, mountain tunnel is overall aseismic analysis longitudinally, sets up the governing equation determination displacement transfer coefficient ξ of the longitudinal overall aseismic analysis of mountain tunnel _wand ξ _a;

Step 6, determines the longitudinal earthquake stress in tunnel, considers the randomness of geological process and the uncertainty of action direction, determines the meridional stress combination of tunnel structure;

Step 7, when carrying out longitudinal aseismic analysis to mountain tunnel, according to the concrete condition of mountain tunnel, carries out analytical calculation.

Further, in step one, determine that the geometric parameter of mountain tunnel comprises: h ₁-edpth of tunnel (m), h ₂-tunnel-liner overall height (m), the total span (m) in B-tunnel, the average thickness (m) of δ-tunnel-liner, R ₀the equivalent redius (m) in-tunnel, E _sthe elastic modulus (Gpa) of-tunnel-liner, μ _sthe Poisson ratio of-tunnel-liner;

Determine that stratum basic parameter and simplification comprise: γ=∑ γ _ih _i/ H, μ _d=0.45, v _s=H/ ∑ (h _i/ v _si), G _d=γ v _s ²/ g, E _d=2 (1-μ _d) G _d, the thickness (m) of H-top layer ground, E-soil-structure interactions elastic modulus; The Poisson ratio of μ-soil;

Determine that the kinetic parameter of rock mass comprises: K _h-top layer Foundation Design horizontal seismic coefficient, K _v-top layer Foundation Design vertical seismic action coefficient; a _v-stratum maximum vertical acceleration (m/s), T-stratum natural period, V _s-elastic shear velocity of wave, S _vthe velocity response spectrum of-vibrations reference field, K _a-horizontal resiliency foundation coefficient, K _w-vertical flat elastic foundation coefficient.

Further, in step 2, determine that the formula of the deformation pattern on stratum and the level of stratum deformation and vertical deformation is:

Further, in step 4, determine that the internal force of tunnel-liner is according to the mechanics of materials, tunnel cross sectional earthquake stress is:

$\begin{array}{cc}{\mathrm{\σ}}_{max}=\frac{M}{W}+\frac{N}{S}=\frac{6M}{{\mathrm{\δ}}^2}+\frac{N}{\mathrm{\δ}}& {\mathrm{\τ}}_{max}=\frac{3}{2}\frac{Q}{\mathrm{\δ}}\end{array}$

Further, in step 6, determine that the meridional stress combinatorial formula of tunnel structure is:

${\mathrm{\σ}}_p=\sqrt{{\mathrm{\σ}}_{amax}^2+{\mathrm{\σ}}_{wmax}^2}$

Further, in step 7, according to the concrete condition of mountain tunnel, the analytical calculation carried out comprises:

1. structure-the analysis of country rock interaction to lining cutting meridional stress; 2. edpth of tunnel is to the analysis of lining cutting meridional stress; 3. basement rock shearing wave input direction is analyzed lining cutting meridional stress; 4. overlying strata is analyzed lining cutting meridional stress eigenperiod; 5. tunnel foundation bedding value K _a=K _wanalysis to lining cutting stress when=β G, β change; 6. the analysis to lining cutting stress during elastic modulus of surrounding rocks change.

Further, the method for this mountain tunnel aseismic analysis for the implementation method that tunnel cross sectional aseismic analysis is concrete is:

The first step, according to geological exploration data and seismic strata deformable statistical data, determine the deformation pattern on stratum and stratum deformation level and vertical deformation:

$\left[\begin{array}{c}{u}_{h\max }\\ u_{v\max }\end{array}\right]=\frac{2}{{\mathrm{\π}}^2}{S}_v{\mathrm{TK}}_{H}cos\left(\frac{\mathrm{\π}z}{2H}\right)\left[\begin{array}{c}1\\ \frac{1}{2}\end{array}\right]$

In formula: S _vvelocity response spectrum (m/s) during-unit seismic coefficient;

The basic natural period (s) of T-top layer ground;

K _hdesign level seismic coefficient (earthquake degree) on the ground of-top layer;

Second step, mountain tunnel Horizontal vibration of piles:

$q_h=\frac{E}{(1+\mathrm{\μ})}\frac{S_v{\mathrm{TK}}_H}{{\mathrm{\π}}^2{h}_2}\{cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)-cos\[\frac{\mathrm{\π}(h_1+h_2)}{2H}\]\}$

3rd step, mountain tunnel Vertical Vibration:

A. stratum vertical deformation pressure:

$\begin{array}{c}{q}_{v1}={\mathrm{\δ}}_v{\mathrm{\ξ}}_w\\ =\frac{{\mathrm{\ξ}}_w}{{\mathrm{\π}}^2}{S}_v{\mathrm{TK}}_H\[cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)-cos\left(\frac{\mathrm{\π}(h_1+h_2)}{2H}\right)\]\end{array}$

B. utilize existing highway or Railway Design specification, top, hole loose ground pressure is:

$q_{v2}=m_0{a}_v=\frac{a_v}{g}{q}_0$

In formula: a _vfor stratum maximum vertical acceleration:

$\begin{array}{c}{q}_v=q_{v1}+q_{v2}\\ =\frac{{\mathrm{\ξ}}_w}{{\mathrm{\π}}^2}{S}_V{\mathrm{TK}}_H\[cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)-cos\left(\frac{\mathrm{\π}(h_1+h_2)}{2H}\right)\]+\frac{a_v}{g}{q}_0\end{array}$

4th step, under shearing wave effect, lining cutting xsect internal force calculates:

Highway and railway tunnel many employings curve wall-lining cutting of meizoseismal area, utilizes structural mechanics and mechanics of materials knowledge to obtain internal force and the cross section stresses of tunnel lining structure:

$M=\frac{1}{4}{q}_v{R}^{2}cos2\mathrm{\θ}-\frac{1}{2}{q}_h{R}^{2}sin2\mathrm{\θ}$

N＝q _vR sin ²θ+q _hR sin2θ ${\mathrm{\σ}}_{max}=\frac{M}{W}+\frac{N}{S}=\frac{6M}{{\mathrm{\δ}}^2}+\frac{N}{\mathrm{\δ}}$

Q＝-q _vR sinθcosθ-q _hR cos2θ

In formula: δ is the average thickness (m) of tunnel-liner;

5th step, utilizes reinforced concrete substantially theoretical, carries out the arrangement of reinforcement in tunnel-liner cross section.

Further, the method for this mountain tunnel aseismic analysis for the tunnel implementation method that longitudinally overall aseismic analysis is concrete is:

The first step, determines correlation parameter, sets up tunnel two dimensional motion equation under ground seismic wave function:

$\left\{\begin{array}{c}\mathrm{\ρ}A\frac{{\∂}^{2}v(x,t)}{\∂t^2}+K_w\[v(x,t)-g_w(x,t)\]+EI\frac{{\∂}^{4}v(x,t)}{\∂x^4}=0\\ \mathrm{\ρ}A\frac{{\∂}^{2}u(x,t)}{\∂t^2}+K_a\[u(x,t)-g_a(x,t)\]-EA\frac{{\∂}^{2}u(x,t)}{\∂x^2}=0\end{array}\right.$

E is the elastic modulus of beam, and I is beam section moment of inertia, and A is beam section area, K _wfor grade beam Poisson ratio, K _afor grade beam Axial distortion parameter, the transversal displacement that ν (x, t) is tunnel, the axial displacement that u (x, t) is tunnel, g _wthe transversal displacement that (x, t) is foundation soil, g _athe axial displacement that (x, t) is foundation soil;

Second step, introduces displacement transfer coefficient, the displacement transfer coefficient ξ of tunnel Earthquake Inertia Force Acting _wand ξ _afor:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_w=\frac{1}{1+\frac{EI}{K_w}{\left(\frac{2\mathrm{\π}\cos \mathrm{\φ}}{\mathrm{\λ}}\right)}^2-\mathrm{\β}\left(K_w\right)}\\ {\mathrm{\ξ}}_a=\frac{1}{1+\frac{\mathrm{EA}}{K_a}{\left(\frac{2\mathrm{\π}\cos \mathrm{\φ}}{\mathrm{\λ}}\right)}^2-\mathrm{\β}\left(K_a\right)}\end{array}\right.\mathrm{\β}\left(K\right)=\frac{{\mathrm{\ρA\ω}}^2}{K}$

The angle of the axis in Φ-incident direction and tunnel;

3rd step, the longitudinal earthquake stress analysis of mountain tunnel:

$\left\{\begin{array}{c}{\mathrm{\σ}}_{amax}=\frac{{\mathrm{ES}}_{v}T\{cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)+cos\[\frac{\mathrm{\π}(h_1+h_2)}{2H}\]\}sin2\mathrm{\φ}}{{\mathrm{\πv}}_{s}T+\frac{4{\mathrm{\π}}^{4}E(R_0^2-R_1^2){\cos }^2\mathrm{\φ}}{K_a{v}_{s}T}-\mathrm{\α}\left(K_a\right)v_s\mathrm{\η}}\\ {\mathrm{\σ}}_{wmax}=\frac{4{\mathrm{ES}}_v\{\cos \left(\frac{{\mathrm{\πh}}_1}{2H}\right)+\cos \[\frac{\mathrm{\π}(h_1+h_2)}{2H}\]\}{\cos }^3\mathrm{\φ}.R_0}{v_s^{2}T+\frac{4{\mathrm{\π}}^{5}E(R_0^4-R_1^4){\cos }^4\mathrm{\φ}}{K_w{v}_s^2{T}^3}-\mathrm{\α}\left(K_w\right)v_s^2\mathrm{\η}}\end{array}\right.$

$\begin{array}{cc}\mathrm{\α}\left(K\right)=\frac{4{\mathrm{\π}}^3{\mathrm{\γ}}_c(R_0^2-R_1^2)}{{\mathrm{KgT}}_1}& \mathrm{\η}=\frac{T}{T_1}\end{array}$

V _sfor shear wave velocity (m/s), T is the predominant period (s) in place; The thickness of basement rock superstratum is H, h ₁for edpth of tunnel (m); h ₂for tunnel-liner overall height (m);

4th step, under shearing wave effect, the longitudinal internal force of lining cutting calculates:

Now the meridional stress of tunnel structure is combined as:

${\mathrm{\σ}}_p=\sqrt{{\mathrm{\σ}}_{amax}^2+{\mathrm{\σ}}_{w\max }^2}$

5th step, tunnel longitudinal seismic response is analyzed:

When carrying out longitudinal aseismic analysis to mountain tunnel, according to the concrete condition of mountain tunnel, carry out following analytical calculation: the 1. structure-analysis of country rock interaction to lining cutting meridional stress; 2. edpth of tunnel is to the analysis of lining cutting meridional stress; 3. basement rock shearing wave input direction is analyzed lining cutting meridional stress; 4. overlying strata is analyzed lining cutting meridional stress eigenperiod; 5. tunnel foundation bedding value K _a=K _wanalysis to lining cutting stress when=β G, β change; 6. the analysis to lining cutting stress during elastic modulus of surrounding rocks change.

The method of mountain tunnel aseismic analysis provided by the invention, unified thought is adopted to analyze mountain tunnel xsect aseismic analysis and longitudinal overall aseismic analysis first, thinking is novel, method is feasible, pass through case verification, for the mountain tunnel primary design under severe earthquake action, there is good applicability.

The present invention need not by complicated mathematical modeling or numerical analysis techniques, only need to obtain geological mapping data more accurately in the geotechnical engineering investigation stage, the antidetonation proximate analysis of mountain tunnel under severe earthquake action can be carried out by the present invention, comparative analysis is optimized to various responsive parameter, obtains corresponding analysis of data and design parameter; Obtain the application of relevant design unit, repercussion is better, has liberated the previous work amount of Tunnel Engineering designer greatly, provides necessary parameter for carrying out detailed design.

The embodiment of the present invention, compares ANSYS modeling numerical method and the self programming result of calculation of the present invention, obtains some technological merit following:

(1) mountain tunnel aseismic analysis utilizes the numerical analysis methods such as ANSYS modeling, modeling is complicated, the modeling time is probably at about 24h, and utilize the self-editing calculation procedure of the present invention, as long as geotechnical investigation data is known, the great previous work amount having liberated Tunnel Engineering designer, counting yield very fast (about 1h);

(2) xsect aseismic analysis angle, the counting yield of the inventive method is not only high, and its result of calculation and engineering present situation completely the same.Application the present invention obtains larger lining cutting moment of flexure, and axle power is taken second place; And obtaining larger axle power by Finite Element Method, moment of flexure is taken second place.And engineering experience is known, mountain tunnel is under severe earthquake action, and liner structure bears the detrusion on stratum completely, and the variation of larger shape occurs liner structure, thus producing larger bending and shearing, calculating conclusion of the present invention is consistent with the time of day of mountain tunnel; Know according to application example of the present invention, bending and shearing within the scope of tunnel vault 45 degree is all larger, be the main region that hole ejects existing drawing crack seam and shear failure, arch springing position is also the place that maximal bending moment occurs, these conclusions are also consistent with the present situation of mountain tunnel eaerthquake damage.Illustrate that the present invention not only saves time, liberation human resources greatly, and calculated mass is also higher.

(3) from mountain tunnel longitudinally overall aseismic analysis, method provided by the invention can carry out comprehensive comparative analysis in above-mentioned various aspects, carries out tunnel and optimizes aseismic analysis, not only convenient, counting yield is high, and its result is consistent with case history.And the numerical methods such as ANSYS not only longitudinal Holistic modeling difficulty, and be difficult to carry out above-mentioned analysis, so cross-sectional analysis is all carried out in the numerical analyses such as the ANSYS of current most of mountain tunnel, seldom there is the application example of longitudinal holistic approach.

Accompanying drawing explanation

Fig. 1 is the method flow diagram setting up tunnel cross sectional analyses of shake that the embodiment of the present invention provides;

Fig. 2 is the stratum deformation pattern diagram that the embodiment of the present invention provides;

Fig. 3 is the velocity response spectrum schematic diagram of the unit level seismic coefficient that the embodiment of the present invention provides;

Fig. 4 is the horizontal vibrating stress distribution schematic diagram that the embodiment of the present invention provides;

Fig. 5 is the distortion schematic diagram of tunnel-country rock system that the embodiment of the present invention provides;

Fig. 6 is the stressed schematic diagram of tunnel unit that the embodiment of the present invention provides.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

Below in conjunction with drawings and the specific embodiments, application principle of the present invention is further described.

The specific embodiment of the invention is: certain mountain tunnel, and stratum is more single, and its formation parameter, Analysis of Field Geotechnical Parameters and tunnel support parameter are in table 1.

Table 1 embodiment calculating parameter

As shown in Figure 1, the method for the mountain tunnel aseismic analysis of the embodiment of the present invention comprises the following steps:

S101: the geometric parameter determining mountain tunnel, determines stratum basic parameter and simplification, determines the kinetic parameter of rock mass;

S102: according to geological exploration data and seismic strata deformable statistical data, determines the deformation pattern on stratum and the level of stratum deformation and vertical deformation;

S103: mountain tunnel xsect aseismic analysis;

S104: mountain tunnel Horizontal vibration of piles (Horizontal Deformation pressure q _h); Mountain tunnel Vertical Vibration (comprises stratum vertical deformation pressure q _v1with loose ground Earthquake Inertia Force Acting q _v2); Utilize structural mechanics, determine the internal force of tunnel-liner;

S105: mountain tunnel is overall aseismic analysis longitudinally, sets up the governing equation determination displacement transfer coefficient ξ of the longitudinal overall aseismic analysis of mountain tunnel _wand ξ _a;

S106: determine the longitudinal earthquake stress in tunnel, consider the randomness of geological process and the uncertainty of action direction, determines the meridional stress combination of tunnel structure;

S107: when carrying out longitudinal aseismic analysis to mountain tunnel, according to the concrete condition of mountain tunnel, carries out analytical calculation.

In step S101, determine that the geometric parameter of mountain tunnel comprises: h ₁-edpth of tunnel (m), h ₂-tunnel-liner overall height (m), the total span (m) in B-tunnel, the average thickness (m) of δ-tunnel-liner, R ₀the equivalent redius (m) in-tunnel, E _sthe elastic modulus (Gpa) of-tunnel-liner, μ _sthe Poisson ratio of-tunnel-liner;

Determine that stratum basic parameter and simplification comprise: γ=∑ γ _ih _i/ H, μ _d=0.45, v _s=H/ ∑ (h _i/ v _si), G _d=γ v _s ²/ g, E _d=2 (1-μ _d) G _d, the thickness (m) of H-top layer ground, E-soil-structure interactions elastic modulus; The Poisson ratio of μ-soil;

Determine that the kinetic parameter of rock mass comprises: K _h-top layer Foundation Design horizontal seismic coefficient, K _v-top layer Foundation Design vertical seismic action coefficient; a _v-stratum maximum vertical acceleration (m/s), T-stratum natural period, V _s-elastic shear velocity of wave, S _vthe velocity response spectrum of-vibrations reference field, K _a-horizontal resiliency foundation coefficient, K _w-vertical flat elastic foundation coefficient.

In step s 102, determine that the formula of the deformation pattern on stratum and the level of stratum deformation and vertical deformation is:

$\left[\begin{array}{c}{u}_{h\max }\\ u_{v\max }\end{array}\right]=\frac{2}{{\mathrm{\π}}^2}{S}_v{\mathrm{TK}}_{H}cos\left(\frac{\mathrm{\π}z}{2H}\right)\left[\begin{array}{c}1\\ \frac{1}{2}\end{array}\right]$

In step S104, determine that the internal force of tunnel-liner is according to the mechanics of materials, tunnel cross sectional earthquake stress is:

$\begin{array}{cc}{\mathrm{\σ}}_{max}=\frac{M}{W}+\frac{N}{S}=\frac{6M}{{\mathrm{\δ}}^2}+\frac{N}{\mathrm{\δ}}& {\mathrm{\τ}}_{max}=\frac{3}{2}\frac{Q}{\mathrm{\δ}}\end{array}$

In step s 106, determine that the meridional stress combinatorial formula of tunnel structure is:

${\mathrm{\σ}}_p=\sqrt{{\mathrm{\σ}}_{amax}^2+{\mathrm{\σ}}_{wmax}^2}$

In step s 107, according to the concrete condition of mountain tunnel, the analytical calculation carried out comprises:

1. structure-the analysis of country rock interaction to lining cutting meridional stress;

2. edpth of tunnel is to the analysis of lining cutting meridional stress;

3. basement rock shearing wave input direction is analyzed lining cutting meridional stress;

4. overlying strata is analyzed lining cutting meridional stress eigenperiod;

5. tunnel foundation bedding value K _a=K _wanalysis to lining cutting stress when=β G, β change;

6. the analysis to lining cutting stress during elastic modulus of surrounding rocks change.

The method of the mountain tunnel aseismic analysis of the embodiment of the present invention mainly contains following two aspects:

1, for tunnel cross sectional aseismic analysis aspect, based on the elastic shear deformation theory of stratum, consider the earthquake deadweight inertial force of stratum horizontal distortion, stratum vertical deformation, tunnel top fragmented rock body first, the relevant issues of research tunnel cross sectional antidetonation simultaneously;

Concrete implementation method:

In order to set up the mathematical model of tunnel cross sectional analyses of shake and be convenient to obtain approximate calculation method, special proposition some supposition following:

1. the soil body is isotropic linear elasticity continuous medium;

2. edpth of tunnel is generally more than 5 times of tunnel radius, can think that tunnel is deep tunnel, meet Fig. 4 simplified condition;

3. stratum deformation linearly changes consideration from top to bottom, and tunnel detrusion can be similar to and replace with center, tunnel stratum deformation.

4. the impact that the difference of tunnel shape causes is confined to the local areas such as corner angle more, little on the differentiation Changing Pattern impact of generally sheaf space stress field.Therefore, to section configuration other shape underground structures non-circular, adopt the conversion form of " equivalent radius ", be not only conducive to the theoretical analysis of problem, and be easy to engineering site practical application.

The first step, according to geological exploration data and seismic strata deformable statistical data, determines deformation pattern (as shown in Figure 2) and stratum deformation (level and the vertical deformation) amount on stratum, as shown in Figure 3:

$\left[\begin{array}{c}{u}_{h\max }\\ u_{v\max }\end{array}\right]=\frac{2}{{\mathrm{\π}}^2}{S}_v{\mathrm{TK}}_{H}cos\left(\frac{\mathrm{\π}z}{2H}\right)\left[\begin{array}{c}1\\ \frac{1}{2}\end{array}\right]$

In formula: S _vvelocity response spectrum (m/s) during-unit seismic coefficient;

The basic natural period (s) of T-top layer ground;

K _hdesign level seismic coefficient (earthquake degree) on the ground of-top layer;

Second step, as shown in Figure 4, horizontal vibrating stress distribution, mountain tunnel Horizontal vibration of piles:

$q_h=\frac{E}{(1+\mathrm{\μ})}\frac{S_v{\mathrm{TK}}_H}{{\mathrm{\π}}^2{h}_2}\{cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)-cos\[\frac{\mathrm{\π}(h_1+h_2)}{2H}\]\}$

3rd step, mountain tunnel Vertical Vibration:

A. stratum vertical deformation pressure:

$\begin{array}{c}{q}_{v1}={\mathrm{\δ}}_v{\mathrm{\ξ}}_w\\ =\frac{{\mathrm{\ξ}}_w}{{\mathrm{\π}}^2}{S}_v{\mathrm{TK}}_H\[cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)-cos\left(\frac{\mathrm{\π}(h_1+h_2)}{2H}\right)\]\end{array}$

B. utilize existing highway or Railway Design specification, top, hole loose ground pressure is:

$q_{v2}=m_0{a}_v=\frac{a_v}{g}{q}_0$

In formula: a _vfor stratum maximum vertical acceleration:

$\begin{array}{c}{q}_v=q_{v1}+q_{v2}\\ =\frac{{\mathrm{\ξ}}_w}{{\mathrm{\π}}^2}{S}_V{\mathrm{TK}}_H\[cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)-cos\left(\frac{\mathrm{\π}(h_1+h_2)}{2H}\right)\]+\frac{a_v}{g}{q}_0\end{array}$

4th step, under shearing wave effect, lining cutting xsect internal force calculates:

Highway and railway tunnel many employings curve wall-lining cutting of meizoseismal area, know according to assumed condition, the thought that the version of this lining cutting can apply " equivalent radius " is converted into an equivalent circular liner to carry out the Quintic system seismic response analysis in tunnel, utilizes structural mechanics and mechanics of materials knowledge to obtain internal force and the cross section stresses of tunnel lining structure:

$M=\frac{1}{4}{q}_v{R}^{2}cos2\mathrm{\θ}-\frac{1}{2}{q}_h{R}^2\sin 2\mathrm{\θ}$

N＝q _vR sin ²θ+q _hR sin2θ ${\mathrm{\σ}}_{max}+\frac{M}{W}+\frac{N}{S}=\frac{6M}{{\mathrm{\δ}}^2}+\frac{N}{\mathrm{\δ}}$

Q＝-q _vR sinθcosθ-q _hR cos2θ

In formula: δ is the average thickness (m) of tunnel-liner;

5th step, utilizes reinforced concrete substantially theoretical, carries out the arrangement of reinforcement in tunnel-liner cross section.

For the said process of mountain tunnel xsect aseismic analysis design, key calculates tunnel level and vertical deformation pressure and vertical seismic action inertial force, application MATLAB programming technique, and above-mentioned thought can realize by following program:

%%%%%%%%%%%%%%%%%%%% tunnel cross sectional earthquake load analysis subroutine

2, for longitudinally overall aseismic analysis aspect, tunnel, take beam on elastic foundation as model, consider the interaction of tunnel and country rock, utilize continuum mechanics, according to anti-knock power theory, displacement transfer theory, set up tunnel structure power balance equation, this equation considers the deadweight inertial force in tunnel theoretically.As can be seen from this equation, classical reaction deflection method is the special case of the method.Tunnel meridional stress under the eigenperiod (soft or hard degree) on the thickness of comparative analysis tunnel in the size of the input direction of basement rock seismic event, earthquake shearing velocity of wave, overlying strata, stratum, the elastic stiffness coefficient impact on stratum and the Changing Pattern of strain, the change contrasting each factor, on the impact of tunnel meridional stress, finds rational parameter value scope.

Concrete implementation method:

In order to set up the mathematical model of tunnel cross sectional analyses of shake and be convenient to obtain approximate calculation method, special proposition some supposition following:

1. the soil body is isotropic linear elasticity continuous medium;

2. tunnel is considered as beam on elastic foundation, namely between tunnel with country rock for spring is connected;

3. exist between tunnel and country rock and interact, consider the relative displacement between tunnel and country rock.Tunnel produces distortion under geological process, and its distortion comprises axial deformation and transversely deforming.

4. do not consider the randomness of seismic event, time-frequency characteristic and the reflection in soil layer and scattering, seismic event is regarded as the simple harmonic wave of single-frequency.

The first step, as Fig. 5 and Fig. 6, if E is the elastic modulus of beam, I is beam section moment of inertia, and A is beam section area, K _wfor grade beam Poisson ratio, K _afor grade beam Axial distortion parameter, the transversal displacement that ν (x, t) is tunnel, the axial displacement that u (x, t) is tunnel, g _wthe transversal displacement that (x, t) is foundation soil, g _athe axial displacement that (x, t) is foundation soil; Tunnel two dimensional motion equation under ground seismic wave function:

$\left\{\begin{array}{c}\mathrm{\ρ}A\frac{{\∂}^{2}v(x,t)}{\∂t^2}+K_w\[v(x,t)-g_w(x,t)\]+EI\frac{{\∂}^{4}v(x,t)}{\∂x^4}=0\\ \mathrm{\ρ}A\frac{{\∂}^{2}u(x,t)}{\∂t^2}+K_a\[u(x,t)-g_a(x,t)\]-EA\frac{{\∂}^{2}u(x,t)}{\∂x^2}=0\end{array}\right.$

Second step, introduces displacement transfer coefficient, considers the displacement transfer coefficient ξ of tunnel Earthquake Inertia Force Acting _wand ξ _afor:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_w=\frac{1}{1+\frac{EI}{K_w}{\left(\frac{2\mathrm{\π}\cos \mathrm{\φ}}{\mathrm{\λ}}\right)}^2-\mathrm{\β}\left(K_w\right)}\\ {\mathrm{\ξ}}_a=\frac{1}{1+\frac{\mathrm{EA}}{K_a}{\left(\frac{2\mathrm{\π}\cos \mathrm{\φ}}{\mathrm{\λ}}\right)}^2-\mathrm{\β}\left(K_a\right)}\end{array}\right.\mathrm{\β}\left(K\right)=\frac{{\mathrm{\ρA\ω}}^2}{K}$

The angle of the axis in Φ-incident direction and tunnel;

3rd step, the longitudinal earthquake stress analysis of mountain tunnel:

$\left\{\begin{array}{c}{\mathrm{\σ}}_{amax}=\frac{{\mathrm{ES}}_{v}T\{cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)+cos\[\frac{\mathrm{\π}(h_1+h_2)}{2H}\]\}sin2\mathrm{\φ}}{{\mathrm{\πv}}_{s}T+\frac{4{\mathrm{\π}}^{4}E(R_0^2-R_1^2){\cos }^2\mathrm{\φ}}{K_a{v}_{s}T}-\mathrm{\α}\left(K_a\right)v_s\mathrm{\η}}\\ {\mathrm{\σ}}_{wmax}=\frac{4{\mathrm{ES}}_v\{\cos \left(\frac{{\mathrm{\πh}}_1}{2H}\right)+\cos \[\frac{\mathrm{\π}(h_1+h_2)}{2H}\]\}{\cos }^3\mathrm{\φ}.R_0}{v_s^{2}T+\frac{4{\mathrm{\π}}^{5}E(R_0^4-R_1^4){\cos }^4\mathrm{\φ}}{K_w{v}_s^2{T}^3}-\mathrm{\α}\left(K_w\right)v_s^2\mathrm{\η}}\end{array}\right.$

$\begin{array}{cc}\mathrm{\α}\left(K\right)=\frac{4{\mathrm{\π}}^3{\mathrm{\γ}}_c(R_0^2-R_1^2)}{{\mathrm{KgT}}_1}& \mathrm{\η}=\frac{T}{T_1}\end{array}$

V _sfor shear wave velocity (m/s), T is the predominant period (s) in place; The thickness of basement rock superstratum is H, h ₁for edpth of tunnel (m); h ₂for tunnel-liner overall height (m);

4th step, under shearing wave effect, the longitudinal internal force of lining cutting calculates:

Consider the randomness of geological process and the uncertainty of action direction, then now the meridional stress of tunnel structure is combined as:

${\mathrm{\σ}}_p=\sqrt{{\mathrm{\σ}}_{\mathrm{\α}max}^2+{\mathrm{\σ}}_{wmax}^2}$

5th step, tunnel longitudinal seismic response is analyzed:

When carrying out longitudinal aseismic analysis to mountain tunnel, according to the concrete condition of mountain tunnel, can following analytical calculation be carried out:

1. structure-the analysis of country rock interaction to lining cutting meridional stress;

2. edpth of tunnel is to the analysis of lining cutting meridional stress;

3. basement rock shearing wave input direction is analyzed lining cutting meridional stress;

4. overlying strata is analyzed lining cutting meridional stress eigenperiod;

5. tunnel foundation bedding value K _a=K _wanalysis to lining cutting stress when=β G, β change;

6. the analysis to lining cutting stress during elastic modulus of surrounding rocks change.

For the said process of the longitudinal seismic analysis of mountain tunnel, apply the above-mentioned algorithm of MATLAB programming realization, program design is as follows:

Xsect Aseismic Analytical Method and longitudinal overall Aseismic Analytical Method adopt unified thought to analyze by the present invention first, and thought is novel, and scheme is reasonable.

For tunnel cross sectional aseismic analysis aspect, based on the elastic shear deformation theory of stratum, consider the earthquake deadweight inertial force of stratum horizontal distortion, stratum vertical deformation, tunnel top fragmented rock body first, the relevant issues of research tunnel cross sectional antidetonation simultaneously;

For longitudinally overall aseismic analysis aspect, tunnel, take beam on elastic foundation as model, consider the interaction of tunnel and country rock, utilize continuum mechanics, according to anti-knock power theory, displacement transfer theory, set up tunnel structure power balance equation, this equation considers the deadweight inertial force in tunnel theoretically.Classical reaction deflection method is the special case of the method.The method can analyze the Changing Pattern of tunnel meridional stress under the elastic stiffness coefficient impact on thickness in the size of the input direction of basement rock seismic event, earthquake shearing velocity of wave, overlying strata, the eigenperiod (soft or hard degree) on stratum, stratum and strain, the change contrasting each factor, on the impact of tunnel meridional stress, finds rational parameter value scope.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (8)

1. a method for mountain tunnel aseismic analysis, is characterized in that, the method for this mountain tunnel aseismic analysis comprises:

Step one, determines the geometric parameter of mountain tunnel, determines and simplifies stratum basic parameter, determining the kinetic parameter of rock mass;

Step 2, according to geological exploration data and seismic strata deformable statistical data, determines the deformation pattern on stratum and the level of stratum deformation and vertical deformation;

Step 3, mountain tunnel xsect aseismic analysis;

Step 4, mountain tunnel Horizontal vibration of piles; Mountain tunnel Vertical Vibration; Utilize structural mechanics, determine the internal force of tunnel-liner;

Step 5, mountain tunnel is overall aseismic analysis longitudinally, sets up the governing equation determination displacement transfer coefficient ξ of the longitudinal overall aseismic analysis of mountain tunnel _wand ξ _a;

Step 6, determines the longitudinal earthquake stress in tunnel, considers the randomness of geological process and the uncertainty of action direction, and then determines the meridional stress combination of tunnel structure;

Step 7, when carrying out longitudinal aseismic analysis to mountain tunnel, according to the concrete condition of mountain tunnel, carries out analytical calculation.

2. the method for mountain tunnel aseismic analysis as claimed in claim 1, is characterized in that, in step one, determine that the geometric parameter of mountain tunnel comprises: h ₁-edpth of tunnel (m), h ₂-tunnel-liner overall height (m), the total span (m) in B-tunnel, the average thickness (m) of δ-tunnel-liner, R ₀the equivalent redius (m) in-tunnel, E _sthe elastic modulus (Gpa) of-tunnel-liner, μ _sthe Poisson ratio of-tunnel-liner;

Determine and simplify stratum basic parameter to comprise: γ=∑ γ _ih _i/ H, μ _d=0.45, v _s=H/ ∑ (h _i/ v _si), G _d=γ v _s ²/ g, E _d=2 (1-μ _d) G _d, the thickness (m) of H-top layer ground, E-soil-structure interactions elastic modulus; The Poisson ratio of μ-soil;

Determine that the kinetic parameter of rock mass comprises: K _h-top layer Foundation Design horizontal seismic coefficient, K _v-top layer Foundation Design vertical seismic action coefficient; a _v-stratum maximum vertical acceleration (m/s ²), T-stratum natural period, V _s-elastic shear velocity of wave, S _vthe velocity response spectrum of-vibrations reference field, K _a-horizontal resiliency foundation coefficient, K _w-vertical flat elastic foundation coefficient.

3. the method for mountain tunnel aseismic analysis as claimed in claim 1, is characterized in that, in step 2, determine that the formula of the deformation pattern on stratum and the level of stratum deformation and vertical deformation is:

$\left[\begin{array}{c}{u}_{h\max }\\ u_{v\max }\end{array}\right]=\frac{2}{{\mathrm{\π}}^2}{S}_v{\mathrm{TK}}_H\cos \left(\frac{\mathrm{\π}z}{2H}\right)\left[\begin{array}{c}1\\ \frac{1}{2}\end{array}\right].$

4. the method for mountain tunnel aseismic analysis as claimed in claim 1, it is characterized in that, in step 4, determine that the internal force of tunnel-liner is according to the mechanics of materials, tunnel cross sectional earthquake stress is:

$\begin{array}{cc}{\mathrm{\σ}}_{\max }=\frac{M}{W}+\frac{N}{S}=\frac{6M}{{\mathrm{\δ}}^2}+\frac{N}{\mathrm{\δ}}& {\mathrm{\τ}}_{\max }=\frac{3}{2}\frac{Q}{\mathrm{\δ}}\end{array}.$

5. the method for mountain tunnel aseismic analysis as claimed in claim 1, is characterized in that, in step 6, determine that the meridional stress combinatorial formula of tunnel structure is:

${\mathrm{\σ}}_p=\sqrt{{\mathrm{\σ}}_{amax}^2+{\mathrm{\σ}}_{wmax}^2}.$

6. the method for mountain tunnel aseismic analysis as claimed in claim 1, it is characterized in that, in step 7, according to the concrete condition of mountain tunnel, the analytical calculation carried out comprises:

1. structure-the analysis of country rock interaction to lining cutting meridional stress;

2. edpth of tunnel is to the analysis of lining cutting meridional stress;

3. basement rock shearing wave input direction is analyzed lining cutting meridional stress;

4. overlying strata is analyzed lining cutting meridional stress eigenperiod;

5. tunnel foundation bedding value K _a=K _wanalysis to lining cutting stress when=β G, β change;

6. the analysis to lining cutting stress during elastic modulus of surrounding rocks change.

7. the method for mountain tunnel aseismic analysis as claimed in claim 1, it is characterized in that, the method for this mountain tunnel aseismic analysis for the implementation method that tunnel cross sectional aseismic analysis is concrete is:

The first step, according to geological exploration data and seismic strata deformable statistical data, determine the deformation pattern on stratum and stratum deformation level and vertical deformation:

$\left[\begin{array}{c}{u}_{h\max }\\ u_{v\max }\end{array}\right]=\frac{2}{{\mathrm{\π}}^2}{S}_v{\mathrm{TK}}_H\cos \left(\frac{\mathrm{\π}z}{2H}\right)\left[\begin{array}{c}1\\ \frac{1}{2}\end{array}\right];$

In formula: S _vvelocity response spectrum (m/s) during-unit seismic coefficient;

The basic natural period (s) of T-top layer ground;

K _hdesign level seismic coefficient (earthquake degree) on the ground of-top layer;

Second step, mountain tunnel Horizontal vibration of piles:

$q_h=\frac{E}{(1+\mathrm{\μ})}\frac{S_v{\mathrm{TK}}_H}{{\mathrm{\π}}^2{h}_2}\{cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)-cos\[\frac{\mathrm{\π}(h_1+h_2)}{2H}\]\};$

3rd step, mountain tunnel Vertical Vibration:

A. stratum vertical deformation pressure:

$\begin{array}{c}{q}_{v1}={\mathrm{\δ}}_v{\mathrm{\ξ}}_w\\ =\frac{{\mathrm{\ξ}}_w}{{\mathrm{\δ}}_v}{S}_v{\mathrm{TK}}_H\[\cos \left(\frac{{\mathrm{\πh}}_1}{2H}\right)-\cos \left(\frac{\mathrm{\π}(h_1+h_2)}{2H}\right)\]\end{array};$

B. utilize existing highway or Railway Design specification, top, hole loose ground pressure is:

$q_{v2}=m_0{a}_v=\frac{a_v}{g}{q}_0;$

In formula: a _vfor stratum maximum vertical acceleration:

$\begin{array}{c}{q}_v=q_{v1}+q_{v2}\\ =\frac{{\mathrm{\ξ}}_w}{{\mathrm{\π}}^2}{S}_v{\mathrm{TK}}_H\[cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)-cos\left(\frac{\mathrm{\π}(h_1+h_2)}{2H}\right)\]+\frac{a_v}{g}{q}_0\end{array};$

4th step, under shearing wave effect, lining cutting xsect internal force calculates:

Highway and railway tunnel many employings curve wall-lining cutting of meizoseismal area, according to waiting generation circle thought, and utilizes structural mechanics and mechanics of materials knowledge to obtain internal force and the cross section stresses of tunnel lining structure:

$M=\frac{1}{4}{q}_v{R}^{2}cos2\mathrm{\θ}-\frac{1}{2}{q}_h{R}^{2}sin2\mathrm{\θ}$

N＝q _vRsin ²θ+q _hRsin2θ ${\mathrm{\σ}}_{max}=\frac{M}{W}+\frac{N}{S}=\frac{6M}{{\mathrm{\δ}}^2}+\frac{N}{\mathrm{\δ}};$

Q＝-q _vRsinθcosθ-q _hRcos2θ ${\mathrm{\τ}}_{max}=\frac{3}{2}\frac{Q}{\mathrm{\δ}}$

In formula: δ is the average thickness (m) of tunnel-liner;

5th step, utilizes reinforced concrete substantially theoretical, carries out the arrangement of reinforcement in tunnel-liner cross section.

8. the method for mountain tunnel aseismic analysis as claimed in claim 1, is characterized in that, the method for this mountain tunnel aseismic analysis for the tunnel implementation method that longitudinally overall aseismic analysis is concrete is:

The first step, determine the two dimensional equation of longitudinal body vibration of mountain tunnel:

$\left\{\begin{array}{c}\mathrm{\ρ}A\frac{{\∂}^{2}v(x,t)}{\∂t^2}+K_w\[v(x,t)-g_w(x,t)\]+EI\frac{{\∂}^{4}v(x,t)}{\∂x^4}=0\\ \mathrm{\ρ}A\frac{{\∂}^{2}u(x,t)}{\∂t^2}+K_a\[u(x,t)-g_a(x,t)\]-EA\frac{{\∂}^{2}u(x,t)}{\∂x^2}=0\end{array}\right.,$ Correlation parameter implication is as follows:

E is the elastic modulus of beam, and I is beam section moment of inertia, and A is beam section area, K _wfor grade beam Poisson ratio, K _afor grade beam Axial distortion parameter, the transversal displacement that ν (x, t) is tunnel, the axial displacement that u (x, t) is tunnel, g _wthe transversal displacement that (x, t) is foundation soil, g _athe axial displacement that (x, t) is foundation soil;

Second step, introduces displacement transfer coefficient, the displacement transfer coefficient ξ of tunnel Earthquake Inertia Force Acting _wand ξ _afor:

$\{\begin{array}{c}{\mathrm{\ξ}}_w=\frac{1}{1+\frac{EI}{K_w}{\left(\frac{2\mathrm{\π}\cos \mathrm{\φ}}{\mathrm{\λ}}\right)}^4-\mathrm{\β}\left(K_w\right)}\\ {\mathrm{\ξ}}_a=\frac{1}{1+\frac{EA}{K_a}{\left(\frac{2\mathrm{\π}\cos \mathrm{\φ}}{\mathrm{\λ}}\right)}^2-\mathrm{\β}\left(K_a\right)}\end{array}\mathrm{\β}\left(K\right)=\frac{\mathrm{\ρA}{\mathrm{\ω}}^2}{K};$

The angle of the axis in Φ-incident direction and tunnel;

3rd step, the longitudinal earthquake stress analysis of mountain tunnel:

$\left\{\begin{array}{c}{\mathrm{\σ}}_{amax}=\frac{{\mathrm{ES}}_{v}T\{cos\left(\frac{{\mathrm{\πh}}_1}{2H}\right)+cos\[\frac{\mathrm{\π}(h+h_2)}{2H}\]\}sin2\mathrm{\φ}}{{\mathrm{\πv}}_{s}T+\frac{4{\mathrm{\π}}^{4}E(R_0^2-R_1^2){\cos }^2\mathrm{\φ}}{K_a{v}_{s}T}-\mathrm{\α}\left(K_a\right)v_s\mathrm{\η}}\\ {\mathrm{\σ}}_{wmax}=\frac{4{\mathrm{ES}}_v\{cos\left(\frac{\mathrm{\π}{h}_1}{2H}\right)+\cos \[\frac{\mathrm{\π}(h+h_2)}{2H}\]\}{\cos }^3\mathrm{\φ}.R_0}{v_s^{2}T+\frac{4{\mathrm{\π}}^{5}E(R_0^4-R_1^4){\cos }^4\mathrm{\φ}}{K_w{v}_s^2{T}^3}-\mathrm{\α}\left(K_w\right)v_s^2\mathrm{\η}}\end{array}\right.;$

$\begin{array}{cc}\mathrm{\α}\left(K\right)=\frac{4{\mathrm{\π}}^3{\mathrm{\γ}}_c(R_0^2-R_1^2)}{\mathrm{Kg}{T}_1}& \mathrm{\η}=\frac{T}{T_1}\end{array};$

V _sfor shear wave velocity (m/s), T is the predominant period (s) in place; The thickness of basement rock superstratum is H, h ₁for edpth of tunnel (m); h ₂for tunnel-liner overall height (m);

4th step, under shearing wave effect, the longitudinal internal force of lining cutting calculates:

Now the meridional stress of tunnel structure is combined as:

${\mathrm{\σ}}_p=\sqrt{{\mathrm{\σ}}_{\mathrm{\α}max}^2+{\mathrm{\σ}}_{wmax}^2};$

5th step, tunnel longitudinal seismic response is analyzed:

When carrying out longitudinal aseismic analysis to mountain tunnel, according to the concrete condition of mountain tunnel, carry out following analytical calculation: the 1. structure-analysis of country rock interaction to lining cutting meridional stress; 2. edpth of tunnel is to the analysis of lining cutting meridional stress; 3. basement rock shearing wave input direction is analyzed lining cutting meridional stress; 4. overlying strata is analyzed lining cutting meridional stress eigenperiod; 5. tunnel foundation bedding value K _a=K _wanalysis to lining cutting stress when=β G, β change; 6. the analysis to lining cutting stress during elastic modulus of surrounding rocks change.