CN105041331B - A kind of tunnel portal section anti-seismic fortified length computational methods - Google Patents
A kind of tunnel portal section anti-seismic fortified length computational methods Download PDFInfo
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Abstract
The invention discloses a kind of tunnel portal section anti-seismic fortified length computational methods, including：A, ground beam element is analyzed；B, introducing tunnel lateral direction deformation coefficientη 1 And Axial distortion parameterη 2 , obtain revised seismic wave shape displacement equation；C, it is calculated the Poisson ratioη 1 And Axial distortion parameterη 2 ；D, according to step B and step C, obtain corresponding maximum stress in bend equation and maximum axial stress equation；E, obtain revised maximum stress in bend equation and revised maximum axial stress equation；F, the parameters numerical value for determining the revised maximum stress in bend equation and the revised maximum axial stress equation；G, according to the parameters numerical computations tunnel maximum anti-seismic fortified length.The present invention proposes clear and definite solution to the length of setting up defences of tunnel portal section, improves the integrity degree and degree of accuracy of the length computation of setting up defences of the tunnel portal section of prior art.
Description
Technical field
The present invention relates to tunnel seismic resistance field, and in particular to a kind of tunnel portal section anti-seismic fortified length computational methods.
Background technology
Relevant tunnel earthquake damage characteristics research originates in the beginning of this century, and Chinese scholars pass through field investigation, to tunnel-liner
Structural damage degree and earthquake reason have carried out preliminary study.Such as W.L.Wang etc. (W.L.Wanga, T.T.Wangb, f,
J.J.Sua.Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi
Earthquake.Tunnelling and Underground Space Technology, 2011,16：133-150.) basis
57 mountain tunnel extent of damages in Chi Chi earthquake, take the lead in impaired tunnel to be divided into without destruction, light damage and severe
Destruction Three Estate, and the reason for give tunnel lining structure earthquake and may relate to.Domestic scholars it is lucky with prosperous grade (Ji Suiwang,
Tang Yongjian, Hu Degui etc. Sichuan Province Wenchuan earthquake disaster area arterial highway Typical Seismic Damage feature analysiss. rock mechanics and engineering
Report, 2009,28 (6) 2009：1250-1261) according to seimic disaster census statistics, Earthquake Inertia Force Acting and wall rock destabilization are thought in research
Effect is two main causes for causing tunnel structure earthquake.And Gao Bo etc. (Gao Bo, Wang Zhengzheng, Yuan Song. Wenchuan earthquake highway tunnel
Road earthquake enlightenment. Southwest Jiaotong University's journal, 2013,44 (3)：337-343) think, mountain tunnel earthquake mostly is face ripple, horizontal stroke
Caused by ripple, foundation failure and shoulder bed effects.
Tunnel portal section is used as antidetonation weak part, when Aseismic Design is carried out to earthquake territory tunnel, tunnel portal location
Tunnel-liner typically should give reinforcement, but on earth how long tunnel portal section lining cutting sets up defences length, and structural seismic can be only achieved
Optimum, is the problem of Tunnel Engineering circle general concern.Such as《Code for sesmic design of railway engineering》(GB 50111-2006) is also right
Tunnel portal section anti-seismic fortified length is made that regulation：Length of setting up defences can be determined according to landform, geology and fortification intensity, not
Less than 2.5 times of structural holes across the length of setting up defences is mainly according to some macroscopical seimic disaster census determining.Dull sequence etc. (Zhu Zhangan, it is high
Ripple, dull thread. meizoseismal area tunnel portal section shaking table model research. modern tunneling technique, 2009,45 (1)：48-52) from
The wave equation of the elastic fluid semi-infinite half-space sets out, the equation of motion under the R wave of foundation, has obtained tunnel under R wave
Displacement equation, and then derive the stratum peak displacement and stratum peak accelerator expression formula of structure.Consider on this basis
The impact that edpth of tunnel, formation condition and wavelength are set up defences to tunnel；Respectively in terms of formation curvature, earthquake intensity and displacement three
The value of length of setting up defences to hole is inquired into.As a result show：Portal Section buried depth is more than 150m, under 9 degree of geological processes, ground
Impact displacement of the layer to tunnel very little, it is not necessary to set up defences again；Portal Section anti-seismic fortified length is determined further according to anti-anti- buried depth；Should
The Portal Section anti-seismic fortified length that the existing Tunnel Design specification of the prolongation specifies.Geng Ping etc. (Li Lin, He Chuan, Geng Ping etc. shallow embedding is inclined
Pressure Portal Section tunnel seismic response shaking table model research. Chinese Journal of Rock Mechanics and Engineering, 2011,30 (12)：2540-
2548) by taking span 6.4m, the railway tunnel of single line 140km/h as an example, using Numerical Model Analysis lining cutting physical mechanicses ginseng and
Impact of the factors such as number country rock rating conditions to tunnel portal section forces in lining change under geological process, Numerical results table
It is bright：Apart from Portal Section more than 3 times of Tunnels across rear, forces in lining change is obviously reduced；Shaketalle test result is also demonstrated that and takes tunnel
Road Portal Section be 3 times of Tunnels across set up defences length when, damping effect is notable.And peak etc. (peak, stone are kindly helped secure the success of, Yan Songhong. tunnel
The anti-seismic fortified length of road Portal Section. Chinese Highway journal, 2006,1, (3)：65-70), (Su Hui, Jia Liang, the Yan Songhong such as Su Hui
Deng. tunnel portal section Structural Seismic Response Analysis. water conservancy and architectural engineering journal, 2010,8 (2)：156-159) using viscous-bullet
Property Artificial Boundaries, with Newmark implicit time integration finite element unit methods, tunnel three-dimensional seismic inversion is analyzed to determine tunnel
Road hole anti-seismic fortified length；Result of study shows：The enclosing lithologies prevailing relationship of tunnel portal section tunnel and is provided fortification against earthquakes length
Degree, the enclosing lithologies of Portal Section are poorer, and tunnel anti-seismic fortified length value is longer；Tunnel-liner cross-sectional form and Portal Section week
The presence or absence for enclosing free face is little with the length value relation of setting up defences in tunnel.Zhou Depei (Zhou Depei. meizoseismal area tunnel portal
The dynamic trait research of section. earthquake engineering and Engineering Vibration, 1998,8 (1)：124-130) according to thatched hut tunnel on Nanning Kunming Railway and
The result of the test in No. 2 tunnels in Le Shan villages, have studied the damage -form and anti-seismic fortified length of meizoseismal area tunnel portal section.Li Yushu
Deng (Li Yushu, Li Tianbin. the numerical simulation study of high intensity Zone mountain tunnel hole damping problem. highway communication science and technology,
2009,26 (10)：100-104), arranged for tunnel shock-absorbing with the entrance section of tunnel of Dendrobium denneanum Kerr. level ground 2 on 318 line of national highway as reference prototypes
Apply, carry out the analysis and research of large vibration table physical experiments, result of study shows：Typically from away from 120～150cm of model hole
After (correspondence 48～60m of prototype), earthquake response gradually tends towards stability etc..
Tunnel is embedded in underground because of which, and longitudinal direction is changeable and is surrounded by country rock, and Aseismic Design is more complicated.How to ensure
Subterranean tunnel safely and reliably plays due function in Future Strong Earthquakes, is the urgent problem demanding prompt solution of Tunnel Engineering circle.
Chinese scholars are studied to underground tunnel portal section aseismic analysis, and its interpretation of result goes out tunnel portal section for antidetonation
Weakness zone, needs to carry out reinforcing and shock absorption process.Even if many achievements are achieved to the research that tunnel portal is provided fortification against earthquakes, but
The still no clear and definite conclusion of length of setting up defences of Portal Section.
The content of the invention
In order to solve these potential problems, it is an object of the invention to the above-mentioned deficiency in the presence of overcoming prior art,
A kind of tunnel portal section anti-seismic fortified length computational methods are provided.
In order to realize foregoing invention purpose, the technical solution used in the present invention is：
A kind of tunnel portal section anti-seismic fortified length computational methods, including：
A, ground beam element is analyzed, obtains the two dimensional motion differential equation in the tunnel under geological process；
B, introducing tunnel lateral direction deformation coefficient η1With Axial distortion parameter η2, obtain revised seismic wave shape displacement
Equation；
It is C, micro- according to the two dimensional motion in tunnel under the revised seismic wave shape displacement equation, the geological process
Divide equation, be calculated the Poisson ratio η1With Axial distortion parameter η2；
D, according to step B and step C, obtain corresponding maximum stress in bend equation and maximum axial stress equation；
E, the corresponding maximum stress in bend equation and the maximum axial stress equation are modified after, obtain
Revised maximum stress in bend equation and revised maximum axial stress equation；
F, determine each of the revised maximum stress in bend equation and the revised maximum axial stress equation
Individual parameter values；
G, according to the parameters numerical computations tunnel maximum anti-seismic fortified length.
Further, the two dimensional motion differential equation is：
Wherein, elastic modelling quantity of the E for beam, the moment of inertias of the I for beam section, v (x, t) are tunnel lateral direction displacement, and u (x, t) is
The axial displacement in tunnel, ρ be beam density, s be beam cross-sectional area, klFor grade beam Poisson ratio, kaFor grade beam axial direction
Deformation coefficient, gl(x, t) is foundation soil lateral displacement, ga(x, t) is foundation soil axial displacement.
Further, the revised seismic wave shape displacement equation is：
Wherein, v (x, t) is tunnel lateral direction displacement, lateral displacements of the u (x, t) for foundation soil, and w is the circular frequency of seismic wave,
Wavelength of the λ ' for seismic wave, amplitudes of the A ' for seismic wave,For the axis angle in incident direction and the tunnel of seismic wave, when t is
Between, propagation displacements of the x for ripple.
Further, the Poisson ratio η1With Axial distortion parameter η2Respectively：
Wherein, E for beam elastic modelling quantity, I for beam section the moment of inertia, ρ be beam density, s be beam cross-sectional area, klFor
Grade beam Poisson ratio, kaFor grade beam linear deformation coefficient, wavelength of the λ ' for seismic wave, w are the circular frequency of seismic wave,For the axis angle of the incident direction and tunnel of seismic wave.
Further, the corresponding maximum stress in bend equation and maximum axial stress equation are respectively：
Wherein,
σlmaxFor maximum stress in bend, σamaxFor maximum axial stress, elastic modelling quantity of the E for beam, inertia of the I for beam section
Square, klFor grade beam Poisson ratio, kaFor grade beam Axial distortion parameter, ρ is beam density, and s is beam cross-sectional area, and H is
The distance of basement rock to ground surface, SvFor the value of velocity response spectrum, λ ' is the wavelength of seismic wave,For seismic wave incident direction with
The axis angle in tunnel, h be tunnel center buried depth, D for tunnel equivalent external diameter, VsFor the shear wave velocity of soil layer, TsFor soil layer
The natural period of oscillation, wherein, Ts=4H/Vs。
Further, the revised maximum stress in bend equation and revised maximum axial stress equation difference
For：
Wherein, σlmaxcorFor revised maximum stress in bend, σamaxcorFor revised maximum axial stress, E is beam
Elastic modelling quantity, distances of the H for basement rock to ground surface, SvFor the value of velocity response spectrum, λ ' is the wavelength of seismic wave,For seismic wave
Incident direction and tunnel axis angle, h is tunnel center buried depth, equivalent external diameters of the D for tunnel, VsFor the shearing wave of soil layer
Speed, TsFor the natural period of oscillation of soil layer, wherein, Ts=4H/Vs。
Further, the tunnel maximum anti-seismic fortified length computing formula is：
Wherein, ImaxFor tunnel maximum anti-seismic fortified length, [σ] is concrete flexural transverse stress feasible value, VsCutting for soil layer
Cut velocity of wave, TsFor the natural period of oscillation of soil layer, elastic modelling quantity of the E for beam, distances of the H for basement rock to ground surface, SvIt is anti-for speed
The value that should be composed, wavelength of the λ ' for seismic wave,For the axis angle in incident direction and the tunnel of seismic wave, h is buried for tunnel center
It is deep, equivalent external diameters of the D for tunnel.
Compared with prior art, beneficial effects of the present invention
A kind of tunnel portal section anti-seismic fortified length computational methods of the present invention, the length proposition of setting up defences to tunnel portal section
Clear and definite solution, improves the integrity degree and degree of accuracy of the length computation of setting up defences of the tunnel portal section of prior art.
Description of the drawings
Fig. 1 is a kind of tunnel portal section anti-seismic fortified length computational methods for being embodied as exemplifying of the present invention.
Fig. 2 is the present invention to cell schematics of the length for dx are taken out on grade beam.
Fig. 3 is the shearing wave of the present invention along tunnel axis Directional Decomposition schematic diagram.
The vertical displacement on stratum and horizontal displacement distribution schematic diagram when Fig. 4 is a kind of earthquake of the present invention.
Fig. 5 is velocity response spectrum of the horizontal seismic coefficient of present invention when being 1.
Fig. 6 is influence curve figure of the layered halfspace angle of the present invention to tunnel-liner buckling and axial stress.
Fig. 7 is influence curve figure of the edpth of tunnel of the present invention to tunnel-liner buckling and axial stress.
Fig. 8 is influence curve figure of the shear wave velocity of the present invention to tunnel-liner buckling and axial stress.
Fig. 9 is seismic wave of the invention edpth of tunnel and longitudinal stress graph of relation in 15 ° of angle of incidence.
Figure 10 is seismic wave of the invention edpth of tunnel and longitudinal stress graph of relation in 45 ° of angle of incidence.
Figure 11 is seismic wave of the invention edpth of tunnel and longitudinal stress graph of relation in 60 ° of angle of incidence.
Figure 12 is that the tunnel stress curve and tunnel of the present invention are set up defences regional relation curve chart.
Specific embodiment
With reference to specific embodiment, the present invention is described in further detail.But this should not be interpreted as the present invention
The scope of above-mentioned theme is only limitted to below example, and all technologies realized based on present invention belong to the model of the present invention
Enclose.
It is a kind of tunnel portal section anti-seismic fortified length calculating side for being embodied as exemplifying of the present invention shown in Fig. 1
Method, including：
A, ground beam element is analyzed, obtains the two dimensional motion differential equation in the tunnel under geological process；
B, introducing tunnel lateral direction deformation coefficient η1With Axial distortion parameter η2, obtain revised seismic wave shape displacement
Equation；
It is C, micro- according to the two dimensional motion in tunnel under the revised seismic wave shape displacement equation, the geological process
Divide equation, be calculated the Poisson ratio η1With Axial distortion parameter η2；
D, according to step B and step C, obtain corresponding maximum stress in bend equation and maximum axial stress equation；
E, the corresponding maximum stress in bend equation and the maximum axial stress equation are modified after, obtain
Revised maximum stress in bend equation and revised maximum axial stress equation；
F, determine each of the revised maximum stress in bend equation and the revised maximum axial stress equation
Individual parameter values；
G, according to the parameters numerical computations tunnel maximum anti-seismic fortified length.
Further, the two dimensional motion differential equation is：
Wherein, elastic modelling quantity of the E for beam, the moment of inertias of the I for beam section, v (x, t) are tunnel lateral direction displacement, and u (x, t) is
The axial displacement in tunnel, ρ be beam density, s be beam cross-sectional area, klFor grade beam Poisson ratio, kaFor grade beam axial direction
Deformation coefficient, gl(x, t) is foundation soil lateral displacement, ga(x, t) is foundation soil axial displacement.
A kind of tunnel portal section anti-seismic fortified length computational methods of the present invention, according to grinding to tunnel structure dynamic trait
Study carefully, the stress and deformation that go out to send by tunnel differential equation of motion analysis tunnel are beneficial to the simplification of model, make the letter of analysis process
Dan Hua, so as to improve the accuracy of tunnel portal section anti-seismic fortified length calculating.
Further, the revised seismic wave shape displacement equation is：
Wherein, v (x, t) is tunnel lateral direction displacement, lateral displacements of the u (x, t) for foundation soil, and w is the circular frequency of seismic wave,
Wavelength of the λ ' for seismic wave, amplitudes of the A ' for seismic wave,For the axis angle in incident direction and the tunnel of seismic wave, when t is
Between, propagation displacements of the x for ripple.
Further, the Poisson ratio η1With Axial distortion parameter η2Respectively：
Wherein, E for beam elastic modelling quantity, I for beam section the moment of inertia, ρ be beam density, s be beam cross-sectional area, klFor
Grade beam Poisson ratio, kaFor grade beam linear deformation coefficient, wavelength of the λ ' for seismic wave, w are the circular frequency of seismic wave,For the axis angle of the incident direction and tunnel of seismic wave.
A kind of tunnel portal section anti-seismic fortified length computational methods of the present invention, introduce tunnel lateral direction deformation coefficient η1And axle
To deformation coefficient η2To correct displacement when tunnel lateral direction vibration and axial vibration, according to the influence degree of different geological environments point
Not Shi Yong targetedly deformation coefficient, make result of calculation more they tend to reality, improve the accuracy of calculating.
Further, the corresponding maximum stress in bend equation and maximum axial stress equation are respectively：
Wherein,
σlmaxFor maximum stress in bend, σamaxFor maximum axial stress, elastic modelling quantity of the E for beam, inertia of the I for beam section
Square, klFor grade beam Poisson ratio, kaFor grade beam Axial distortion parameter, ρ is beam density, and s is beam cross-sectional area, and H is
The distance of basement rock to ground surface, SvFor the value of velocity response spectrum, λ ' is the wavelength of seismic wave,For seismic wave incident direction with
The axis angle in tunnel, h be tunnel center buried depth, D for tunnel equivalent external diameter, VsFor the shear wave velocity of soil layer, TsFor soil layer
The natural period of oscillation, wherein, Ts=4H/Vs。
The present invention a kind of tunnel portal section anti-seismic fortified length computational methods, using revised tunnel lateral direction vibration and
Displacement during axial vibration further increases the accuracy of calculating obtaining tunnel structure earthquake stress equation.
Further, the revised maximum stress in bend equation and revised maximum axial stress equation difference
For：
Wherein, σlmaxcorFor revised maximum stress in bend, σamaxcorFor revised maximum axial stress, E is beam
Elastic modelling quantity, distances of the H for basement rock to ground surface, SvFor the value of velocity response spectrum, λ ' is the wavelength of seismic wave,For seismic wave
Incident direction and tunnel axis angle, h is tunnel center buried depth, equivalent external diameters of the D for tunnel, VsFor the shearing wave of soil layer
Speed, TsFor the natural period of oscillation of soil layer, wherein, Ts=4H/Vs。
Further, the tunnel maximum anti-seismic fortified length computing formula is：
Wherein, ImaxFor tunnel maximum anti-seismic fortified length, [σ] is concrete flexural transverse stress feasible value, VsFor soil layer
Shear wave velocity, TsFor the natural period of oscillation of soil layer, elastic modelling quantity of the E for beam, distances of the H for basement rock to ground surface, SvFor speed
The value of response spectrum, wavelength of the λ ' for seismic wave,For the axis angle in incident direction and the tunnel of seismic wave, h is buried for tunnel center
It is deep, equivalent external diameters of the D for tunnel.
A kind of tunnel portal section anti-seismic fortified length computational methods of the present invention, by resisting to tunnel under ground seismic wave function
Shock stability carries out labor, has obtained the impact Changing Pattern of edpth of tunnel, shear wave velocity and angle of incidence to tunnel stress, resists
Shake set up defences length determination it is related to place tunnel many factors with practically seismic wave, by the analysis to these parameters, finally
Propose tunnel portal section anti-seismic fortified length formula.Instant invention overcomes prior art to earthquake protection length calculation method not
The shortcoming of the theoretical qualitative and quantitative analysis of energy, it is proposed that a kind of to have targetedly computational methods, improves anti-seismic fortified length meter
The accuracy of calculation, integrity degree.
Embodiment 1:
Shown in Fig. 2 be the present invention on grade beam take out length for dx cell schematics.To beam element by dynamic equilibrium
Condition can be obtained：
In formula：
Q is beam section shearing, and v (x, t) is tunnel lateral direction displacement, and ρ is beam density, and s is beam cross-sectional area, klFor ground
Beam Poisson ratio, gl(x, t) is foundation soil lateral displacement.
Can be obtained by moment equilibrium condition：
In formula：
Moments of flexure of the M for beam.
Simplify above formula to obtain：
Formula (3.2) is substituted into formula (3.1) to obtain：
Can be obtained by elementary flexure theory：
In formula：
Elastic modelling quantity of the E for beam, the moment of inertias of the I for beam section,
Above formula is substituted into formula (3.3) to obtain：
It is assumed that tunnel bending stiffness does not change with x, therefore the equation of motion of tunnel lateral direction vibration is under ground seismic wave function：
In the same manner, theoretical according to earthquake motion, the infinitesimal for taking dx is analyzed and can obtain the equation of motion of axial vibration and be：
Further simplification can be obtained：
Simultaneous formula (3.7) and formula (3.9) are obtained the two dimensional motion differential equation in the tunnel under geological process：
In formula, elastic modelling quantity of the E for beam, the moment of inertias of the I for beam section, v (x, t) are tunnel lateral direction displacement, and u (x, t) is
The axial displacement in tunnel, ρ be beam density, s be beam cross-sectional area, klFor grade beam Poisson ratio, kaFor grade beam axial direction
Deformation coefficient, gl(x, t) is foundation soil lateral displacement, ga(x, t) is foundation soil axial displacement.
Discounting for Earthquake Inertia Force Acting, the two dimensional motion differential equation above can be write as：
It is from macroscopically research tunnel portal section anti-seismic fortified length, according to seismic wave theory, ground around tunnel
Motion of the body under geological process can regard monochromatic plane wave as, do not consider the randomness of seismic wave, time-frequency characteristic and reflection and
Scattering, its wavy shape displacement function can be written as：
In formula：
Circular frequency of the w for seismic wave, wavelength of the λ ' for seismic wave, amplitudes of the A ' for seismic wave, x ' they are shearing wave advance side
To coordinate.
It is shearing wave shown in Fig. 3 along tunnel axis Directional Decomposition schematic diagram.Hypothesis seismic wave be shearing wave, incident direction with
The axis in tunnel intoAngle, shearing wave are as shown in Figure 3 to the impact that tunnel axis direction is fluctuated.
Under shearing wave effect, the lateral displacement g that tunnel surrounding soil is producedl(x, t) and axial displacement ga(x, t) is respectively：
Wherein, v (x, t) is tunnel lateral direction displacement, lateral displacements of the u (x, t) for foundation soil, and w is the circular frequency of seismic wave,
Wavelength of the λ ' for seismic wave, amplitudes of the A ' for seismic wave,For the axis angle in incident direction and the tunnel of seismic wave, when t is
Between, propagation displacements of the x for ripple.
It is theoretical according to relative deformation, it is considered to which that tunnel is interacted with country rock, introduce tunnel lateral direction deformation coefficient η1And axial direction
Deformation coefficient η2, then tunnel lateral direction vibration and during axial vibration displacement be：
Formula (3.14) is substituted in formula (3.10), and considers tunnel Earthquake Inertia Force Acting, obtain tunnel lateral direction deformation coefficient η1
With Axial distortion parameter η2For：
Wherein, E for beam elastic modelling quantity, I for beam section the moment of inertia, ρ be beam density, s be beam cross-sectional area, klFor
Grade beam Poisson ratio, kaFor grade beam linear deformation coefficient, wavelength of the λ ' for seismic wave, w are the circular frequency of seismic wave,For the axis angle of the incident direction and tunnel of seismic wave.
Formula (3.15) is substituted into lateral displacement and the axial position for being obtained in formula (3.14) that the lower tunnel of shearing wave effect is produced
Shifting is respectively：
The axial strain that local derviation can obtain tunnel is asked to be to u (x, t)：
Ask second order local derviation to obtain curvature v (x, t) formula to be：
The bending strain that can be derived tunnel by elementary flexure theory is：
It is hereby achieved that the maximum bending strain in tunnel and maximum axial strain are：
Wherein, εlmaxFor the maximum bending strain in tunnel, εamaxMaximum axial for tunnel is strained, springforms of the E for beam
Amount, I for beam section the moment of inertia, ρ be beam density, s be beam cross-sectional area, klFor grade beam Poisson ratio, kaFor ground
Beam linear deformation coefficient, wavelength of the λ ' for seismic wave, amplitudes of the A ' for seismic wave, equivalent external diameters of the D for tunnel, w is seismic wave
Circular frequency,For the axis angle of the incident direction and tunnel of seismic wave.
The vertical displacement on stratum and horizontal displacement distribution schematic diagram when being a kind of earthquake shown in the present invention shown in Fig. 4.
In earthquake research, general only to consider effect of the lateral shear ripple to tunnel, this ripple not only delivers most of energy, and makes
Stratum produces horizontal sinusoid displacement as shown in Figure 4.
Assume that basement rock is fixed, the distance of basement rock to ground surface is H；TsFor the natural period of oscillation of soil layer, Ts=4H/Vs；Sv
For the value of velocity response spectrum；VsFor the shear wave velocity of soil layer.Then the amplitude of the soil vibration at any depth z of ground surface can
With approximate representation it is：
Then the stratum amplitude at tunnel approximately can be calculated with formula the following：
In formula：
H is tunnel center buried depth.
The wavelength X ' of seismic wave approximately can be calculated as follows：
In formula：
λ′1With λ '2The respectively shearing wavelength of soil layer and horizon d, λ '1=VsTs, λ '2=V0Ts；
V0For horizon d shear-wave velocity.
By maximum deflection and axial stress that formula (3.22) substitution formula (3.20) tries to achieve tunnel it is：
Can obtain during the moment of inertia and area of section are substituted into：
Wherein：
Severes of the γ for tunnel；
D and d is respectively the equivalent external diameter and equivalent internal diameter in tunnel；
G is acceleration of gravity；
T1For the vibration period of seismic wave.
If do not consider the impact of country rock deadweight inertia force, the maximum stress in bend and axial stress in tunnel are：
If disregarding country rock. when the interaction of structure affects, tunnel lateral direction deformation coefficient and Axial distortion parameter all take 1,
Then the tunnel structure Stress calculation formula under geological process is：
Wherein, σlmaxcorFor revised maximum stress in bend, σamaxcorFor revised maximum axial stress, E is beam
Elastic modelling quantity, distances of the H for basement rock to ground surface, SvFor the value of velocity response spectrum, λ ' is the wavelength of seismic wave,For seismic wave
Incident direction and tunnel axis angle, h is tunnel center buried depth, equivalent external diameters of the D for tunnel, VsFor the shearing wave of soil layer
Speed, TsFor the natural period of oscillation of soil layer, wherein, Ts=4H/Vs。
From formula (3.27), the incident direction of the maximum axial stress in tunnel and maximum stress in bend and seismic wave,
The factors such as edpth of tunnel, Shear wave velocity of foundation ground, tunnel across footpath are relevant.
Further, by factors such as the incident direction to seismic wave, edpth of tunnel, Shear wave velocity of foundation ground, tunnel across footpaths
Analysis, the parameters being related in obtaining the method for the present invention, so as to effectively be calculated.
The lower stratum deformation of shearing wave effect is extremely complex, in order to multilayer formation is converted into single stratum by convenience of calculation.This
Suitable earthquake vibration datum level must be selected outward.General, datum level is not less than below ground 25m, ties nor less than underground
10m below structure, concrete engineering will determine earthquake coverage according to actual.
Natural period is calculated according to the shear wave velocity in structure place.The natural period eigenvalue of multi-layered Soils is TG=4 ∑s
hi/Vsi；Due to stratum strain when stratum strain occurs more than earthquake during exploration, T is typically takens=1.25TG。
Shear wave velocity should be extracted from exploration report, it is contemplated that survey condition is different from earthquake physical condition, by exploration report
Accuse 2/3 employing of numerical value.Vibration datum level velocity response spectrum is Sv=KhVh(3.28) in formula：
Kh--- design level seismic coefficient, according to earthquake specification value, it is considered to when buried depth and revised place, Kh=
CgCuKh0The respectively revised coefficient in place and the revised coefficient of buried depth；
Vh--- the velocity response spectrum of unit level seismic coefficient, the speed that Fig. 5 is shown when horizontal seismic coefficient is 1 are anti-
Ying Pu, when being calculated, can determine according to Fig. 5.
The value of elastic foundation coefficient is not only relevant with planform size, formation condition and buried depth, and applies with tunnel
Work method is relevant.With regard to klAnd kaDetermination can be calculated using program of finite element, it would however also be possible to employ Japan《Chemical industry
Equipment antidetonation criterion》Simplified approach, i.e.,：
kl=ka=3Gs (3.29)
In formula：
GsFor the modulus of shearing on foundation soil.
Affecting laws of the tunnel stress in tunnel longitudinal direction are analyzed for convenience, so as to provide for the set up defences determination of length of tunnel
Foundation, two class land seismic dynamic peak accelerators are 0.1g；The Ground motion response spectrum signature cycle is 0.4s, i.e. Tg=0.4s, Ts=
1.25 × 0.4=0.5s, can obtain Vh=0.8, look into specification and obtain Kh=0.24, then Sv=KhVh=0.192.Enter in instance analysis
Certain simplification is gone, parameters for tunnel, Analysis of Field Geotechnical Parameters and formation parameter are respectively such as table after rejecting the calculating value of some complexity
3.1st, shown in 3.2,3.3.
3.1 parameters for tunnel of table
3.2 Analysis of Field Geotechnical Parameters of table
3.3 formation parameter of table
By above-mentioned parameter is carried out bringing in tunnel stress formula (formula 3.27), The present invention gives from layered halfspace
Angle, edpth of tunnel, shear wave velocity etc. analyze tunnel STRESS VARIATION and the impact provided fortification against earthquakes to tunnel, specifically, referring to figure
6- Figure 11.
Shown in Fig. 6 be the present invention layered halfspace angle to tunnel-liner buckling and the influence curve of axial stress
Figure.
It will be appreciated from fig. 6 that layered halfspace angle is very big to the stress influence in tunnel.Maximum tunnel axial stress is with seismic wave
The increase of incident angle and first increase and then be gradually reduced, when incident angle is 45 °, tunnel axial stress reaches maximum；
The maximum stress in bend in tunnel then reduces with the increase at layered halfspace angle, when angle of incidence is 0 °, tunnel bending stress
Reach maximum.45 ° of angle of incidence can be used for calculating and set up defences length.But typically when seismic wave vibrations direction is vertical with tunnel
When, earthquake is maximum to the destruction in tunnel, so it is general in Tunnel Engineering with tunnel bending stress providing fortification against earthquakes.
It is influence curve figure of the edpth of tunnel of the present invention to tunnel-liner buckling and axial stress shown in Fig. 7.
When edpth of tunnel changes, the predominant period also changes therewith, it is assumed that the hardness in place is constant, its average clearance method
Also it is constant.As shown in Figure 7, axial stress change when buried depth is less than 50m in tunnel is not clear aobvious；When buried depth is more than 50m, tunnel should
Power is strongly reduced as edpth of tunnel increases；It is possible thereby to infer：The length of setting up defences in tunnel shortens with the increase of buried depth,
Therefore it is bigger for the impact of the Portal Section regional earthquake to tunnel in shallow tunnel or tunnel；In the condition of instance analysis
Under, if using tunnel bending stress as standard, buried depth needs to consider that tunnel is set up defences when being less than 50m.Tunnel portal section is generally oblique
Long side slope, buried depth is typically than shallower, and soil layer is unstable, is the keypoint part of tunnel antidetonation.As long as therefore measuring tunnel portal
The buried depth of section, just can determine that its anti-seismic fortified length.
It is influence curve figure of the shear wave velocity of the present invention to tunnel-liner buckling and axial stress shown in Fig. 8.
As shown in Figure 8, under ground seismic wave function, tunnel stress reduces with the increase of soil layer shear wave velocity, wherein
The comparison that bending stress reduces is quicker, and stratum shear wave velocity is relevant with its soft or hard degree, and in this hard soil layer of explanation, tunnel will
Better than the anti-seismic performance of soft soil tunnel, length of setting up defences reduces with the increase of shear wave velocity；Shearing can be analyzed according to figure
Velocity of wave needs to consider that tunnel is set up defences less than the place of 150m/s or so.And native stone accumulation body or slide rock are generally in tunnel portal section
Body, shear wave velocity are less, therefore checking tunnel portal section is the emphasis provided fortification against earthquakes again.As long as measuring the soil body with instrument to cut
Cut velocity of wave, it is possible to determine the anti-seismic fortified length in tunnel.
Fig. 9-Figure 11 is impact of the edpth of tunnel to tunnel stress under seismic wave incidence angles degree, specifically, shown in Fig. 9
It is seismic wave of the invention edpth of tunnel and longitudinal stress graph of relation in 15 ° of angle of incidence, is of the invention shown in Figure 10
Seismic wave edpth of tunnel and longitudinal stress graph of relation in 45 ° of angle of incidence are the seismic wave of the present invention shown in Figure 11 at 60 °
Edpth of tunnel and longitudinal stress graph of relation during angle of incidence.
From Fig. 9 to Figure 11, tunnel-liner bending stress and axial stress reduce with the increase of edpth of tunnel；Tunnel
At road, stratum deformation is also tapered into as the depth apart from earth's surface is more deep；The change at layered halfspace angle is to tunnel-liner stress
Impact it is very sensitive, as seismic wave injects angle expansion, tunnel structure by gradually becoming tension and compression stress based on flexural loading is
Main, this point underground utilities little from cross-sectional area are different, and underground utilities can be ignored cross-bending stress and only consider axis tension and compression
Impact, and tunnel iso-cross-section accumulates big underground linear structure, and cross-bending stress really occupies larger proportion, is to neglect
Depending on.
It is that the tunnel stress curve and tunnel of the present invention is set up defences regional relation curve chart shown in Figure 12.Based on formation curvature
Evaluation methodology does not consider that tunnel surrounding interacts and carries out certain condition simplification and can obtain the Tunnel under ground seismic wave function
Mouth section anti-seismic fortified length is as shown in figure 12.
Assume that concrete flexural transverse stress feasible value [σ] is 0.5 × 1.3Mpa, wherein 1.3 improve coefficient for intensity during earthquake,
Then can obtain maximum anti-based on formation curvature evaluation tunnel by formula (3.19) tunnel bending stress and its offset yield stress
Shake length l of setting up defencesmaxFor：
Simplified：
Wherein, ImaxFor tunnel maximum anti-seismic fortified length, [σ] is concrete flexural transverse stress feasible value, VsCutting for soil layer
Cut velocity of wave, TsFor the natural period of oscillation of soil layer, elastic modelling quantity of the E for beam, distances of the H for basement rock to ground surface, SvIt is anti-for speed
The value that should be composed, wavelength of the λ ' for seismic wave,For the axis angle in incident direction and the tunnel of seismic wave, h is buried for tunnel center
It is deep, equivalent external diameters of the D for tunnel.
The flex point of curve chart can be obtained by Fig. 9 to Figure 11, according at flex point for numerical value, respectively 45 ° angle of incidence,
The power velocity of wave of 30m buried depths and 150m/s, substitutes into calculating and can obtain lmax≈25.18m。
It is when considering that tunnel surrounding interacts, equivalent to one layer of buffer layer is arranged around tunnel, calculated
Length of setting up defences most is worth can be smaller than 25.18m, and it is 1.04 numerical value to be substituted into Poisson ratio is calculated in formula (3.15),
This coefficient can be multiplied by bending stress feasible value to recalculate, may finally obtain tunnel portal length value of setting up defences is
24.37m, about 3 hole across.
A kind of tunnel portal section anti-seismic fortified length computational methods of the present invention, the length proposition of setting up defences to tunnel portal section
Clear and definite solution, improves the integrity degree and degree of accuracy of the length computation of setting up defences of the tunnel portal section of prior art.
The specific embodiment of the present invention is described in detail above in conjunction with accompanying drawing, but the present invention has been not restricted to
Embodiment is stated, in the case of the spirit and scope without departing from claims hereof, those skilled in the art can make
Go out various modifications or remodeling.
Claims (7)
1. a kind of tunnel portal section anti-seismic fortified length computational methods, it is characterised in that include：
A, ground beam element is analyzed, obtains the two dimensional motion differential equation in the tunnel under geological process；
B, introducing tunnel lateral direction deformation coefficient η1With Axial distortion parameter η2, obtain revised seismic wave shape displacement equation；
C, according to the two dimensional motion differential side in tunnel under the revised seismic wave shape displacement equation, the geological process
Journey, is calculated the Poisson ratio η1With Axial distortion parameter η2；
D, according to step B and step C, obtain corresponding maximum stress in bend equation and maximum axial stress equation；
E, the corresponding maximum stress in bend equation and the maximum axial stress equation are modified after, corrected
Maximum stress in bend equation afterwards and revised maximum axial stress equation；
F, each ginseng for determining the revised maximum stress in bend equation and the revised maximum axial stress equation
Number numerical value；
G, according to the parameters numerical computations tunnel maximum anti-seismic fortified length.
2. a kind of tunnel portal section anti-seismic fortified length computational methods according to claim 1, it is characterised in that described two
Tieing up differential equation of motion is：
Wherein, elastic modelling quantity of the E for beam, the moment of inertias of the I for beam section, v (x, t) are tunnel lateral direction displacement, and u (x, t) is tunnel
Axial displacement, ρ be beam density, s be beam cross-sectional area, klFor grade beam Poisson ratio, kaFor grade beam axial deformation
Coefficient, gl(x, t) is foundation soil lateral displacement, ga(x, t) is foundation soil axial displacement.
3. a kind of tunnel portal section anti-seismic fortified length computational methods according to claim 1, it is characterised in that described to repair
Seismic wave shape displacement equation after just is：
Wherein, v (x, t) is tunnel lateral direction displacement, lateral displacements of the u (x, t) for foundation soil, circular frequency of the w for seismic wave, and λ ' is
The wavelength of seismic wave, amplitudes of the A ' for seismic wave,For the axis angle in incident direction and the tunnel of seismic wave, t is the time, x
For the propagation displacement of ripple.
4. a kind of tunnel portal section anti-seismic fortified length computational methods according to claim 3, it is characterised in that the horizontal stroke
To deformation coefficient η1With Axial distortion parameter η2Respectively：
Wherein, E for beam elastic modelling quantity, I for beam section the moment of inertia, ρ be beam density, s be beam cross-sectional area, klFor ground
Beam Poisson ratio, kaFor grade beam Axial distortion parameter, wavelength of the λ ' for seismic wave, w are the circular frequency of seismic wave,For
The incident direction of seismic wave and the axis angle in tunnel.
5. a kind of tunnel portal section anti-seismic fortified length computational methods according to claim 4, it is characterised in that described right
The maximum stress in bend equation and maximum axial stress equation answered is respectively：
Wherein,
σlmaxFor maximum stress in bend, σamaxFor maximum axial stress, elastic modelling quantity of the E for beam, the moment of inertias of the I for beam section, kl
For grade beam Poisson ratio, kaFor grade beam Axial distortion parameter, ρ is beam density, and s is beam cross-sectional area, and H is basement rock
To the distance of ground surface, SvFor the value of velocity response spectrum, λ ' is the wavelength of seismic wave,For the incident direction and tunnel of seismic wave
Axis angle, h be tunnel center buried depth, D for tunnel equivalent external diameter, VsFor the shear wave velocity of soil layer, TsFor the intrinsic of soil layer
Vibration period, wherein, Ts=4H/Vs。
6. a kind of tunnel portal section anti-seismic fortified length computational methods according to claim 5, it is characterised in that described to repair
Maximum stress in bend equation and revised maximum axial stress equation after just is respectively：
Wherein, σlmaxcorFor revised maximum stress in bend, σamaxcorFor revised maximum axial stress, elasticity of the E for beam
Modulus, distances of the H for basement rock to ground surface, SvFor the value of velocity response spectrum, λ ' is the wavelength of seismic wave,Entering for seismic wave
Penetrate the axis angle in direction and tunnel, h is tunnel center buried depth, equivalent external diameters of the D for tunnel, TsFor the intrinsic vibration week of soil layer
Phase, Ts=4H/Vs, wherein, VsFor the shear wave velocity of soil layer.
7. a kind of tunnel portal section anti-seismic fortified length computational methods according to claim 6, it is characterised in that the tunnel
Road maximum anti-seismic fortified length computing formula be：
Wherein, lmaxFor tunnel maximum anti-seismic fortified length, [σ] is concrete flexural transverse stress feasible value, VsFor the shearing wave of soil layer
Speed, TsFor the natural period of oscillation of soil layer, elastic modelling quantity of the E for beam, distances of the H for basement rock to ground surface, SvFor velocity response spectrum
Value, λ ' for seismic wave wavelength,For the axis angle in incident direction and the tunnel of seismic wave, h is tunnel center buried depth, D
For the equivalent external diameter in tunnel.
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