CN106644206B - A kind of pressure from surrounding rock calculation method for shallow tunnel - Google Patents
A kind of pressure from surrounding rock calculation method for shallow tunnel Download PDFInfo
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- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
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Abstract
The present invention relates to Tunnel Engineering technical fields.A kind of pressure from surrounding rock calculation method for shallow tunnel of the invention, comprising steps of choosing the convergent deformation monitoring point of country rock；In monitoring point structural texture mechanical model；Derive the calculation relational expression between convergent deformation and pressure from surrounding rock；Engineering real data and convergence monitoring data band are entered into relational expression and calculate the displacement of monitoring point arranged on left and right sides and the convergent deformation of monitoring point；Country rock is calculated and calculates angle of friction and pressure from surrounding rock.The relationship between convergent deformation and pressure from surrounding rock that this method passes through side wall country rock in analysis two side-wall pilot tunnel constructing tunnel, establish model of structural mechanics, pressure from surrounding rock is acquired by field monitoring data inverse, compared to the existing calculation method for relying on empirical parameter, practical pressure from surrounding rock more acurrate, more representative of tunnel, and the convergent deformation data in tunnel be easier to obtain, convenience of calculation it is accurate.
Description
Technical field
The present invention relates to Tunnel Engineering technical field, in particular to a kind of pressure from surrounding rock calculating side for shallow tunnel
Method.
Background technique
Pressure from surrounding rock is blocking of the surrouding rock deformation by supporting construction during the raw stress redistribution of the disturbed movable property of rock mass
And the generated pressure on the contact surface of supporting and country rock, it directly influences the choosing of the structure design and construction method in tunnel
It selects.For shallow tunnel since buried depth is shallower, the influence caused by excavating more will directly influence earth's surface and neighboring buildings.
Pressure from surrounding rock caused by tunnel excavation is influenced by many factors, not only with rock mass structure, geological structure, rock object
It is related to manage mechanical property, underground water, the geologic(al) factors such as initial field stress, also with tunnel shape, size, excavation construction side
Human factor caused by the engineering activities such as method, support form is related.In Tunnel Engineering practice, Accurate Prediction tunnel excavation causes
Pressure from surrounding rock it is significant for making smooth advances for constructing tunnel.
Empirical formula method is to be widely used and develop more mature determination pressure from surrounding rock method at present, it is with a large amount of real
Based on the engineering data of border, by the summary of experience that different surrounding rock rank proposes, it is conveniently and efficiently asked convenient for engineers and technicians
Obtain the size and distribution pattern of pressure from surrounding rock.Such as current domestic application most wide " vcehicular tunnel design specification ", " railway tunnel is set
Meter specification " in pressure from surrounding rock calculation formula be exactly to obtain empirical parameter according to a large amount of previous analysis of project example and calculate to ask
Obtain pressure from surrounding rock.But empirical formula method still having some limitations property: referenced by the calculating parameter value in empirical formula method
Case history can only represent limited engineering geological condition, and with the progress of technique of design and construction level, tunnel
Construction geology condition becomes increasingly complex, and the engineering geological condition of engineering in practice has its particularity, in this case using biography
System empirical formula method is unable to get accurate pressure from surrounding rock value.
Summary of the invention
It is an object of the invention to overcome use empirical formula method determine Tunnel Surrounding Rock Pressure when, based on empirical parameter
The mechanical property in tunnel can not be represented well, therefore accurate pressure from surrounding rock value is unable to get using Conventional wisdom equation
The technical issues of, a kind of pressure from surrounding rock calculation method for shallow tunnel is provided, this method passes through analysis two side-wall pilot tunnel
Relationship in constructing tunnel between the convergent deformation and pressure from surrounding rock of side wall country rock, establishes model of structural mechanics, by field monitoring
Data inverse acquires pressure from surrounding rock, compared to the existing calculation method for relying on empirical parameter, reality more acurrate, more representative of tunnel
Border pressure from surrounding rock, and the convergent deformation data in tunnel be easier to obtain, convenience of calculation it is accurate.
In order to achieve the above-mentioned object of the invention, the present invention provides following technical schemes:
A kind of pressure from surrounding rock calculation method for shallow tunnel, comprising the following steps:
The convergent deformation monitoring point of S1 selection country rock: researching and analysing the tunnel using two side-wall pilot tunnel construction,
Choosing the point on the pilot tunnel excavated at first by sequence of excavation is convergent deformation monitoring point；
S2 is in monitoring point structural texture mechanical model；Structural texture mechanical model at pilot tunnel is excavated in advance by practical；
S3 derives the calculation relational expression between convergent deformation and pressure from surrounding rock；
S4 brings engineering real data and convergence monitoring data in the relational expression of step S3 into, calculate separately monitoring point it is left,
The displacement of right two sides and the convergent deformation of monitoring point；
S5 is calculated country rock and calculates angle of friction and pressure from surrounding rock；
Between convergent deformation and pressure from surrounding rock of this method by side wall country rock in analysis two side-wall pilot tunnel constructing tunnel
Relationship, establish model of structural mechanics, horizontal adjoining rock pressure and vertical pressure from surrounding rock acquired by field monitoring data inverse, compared
In the existing calculation method for relying on empirical parameter, practical pressure from surrounding rock more acurrate, more representative of tunnel, and the convergence in tunnel becomes
Graphic data be easier to obtain, convenience of calculation it is accurate.
Preferably, choosing left base tunnel top bar in step S2 or right base tunnel top bar is analyzed, tectonic dynamics model.
After the left base tunnel excavated at first according to practical construction experience or the construction of right base tunnel top bar, convergent deformation increases steadily in one week
Add, convergence rate slows down after a week, basicly stable after two weeks, therefore can take among left base tunnel and right base tunnel face one
A monitoring point, its convergent deformation after monitoring data are basicly stable in one to two weeks can represent the change that pressure from surrounding rock effect generates
Shape convergence.
Done when preferably, establishing model it is assumed hereinafter that: left base tunnel top bar or right base tunnel top bar are considered as sector；On
Step right wall and circular arch part are reduced to rigid material；Each node of simplified model is considered as rigid connection.
Preferably, monitoring point two sides are respectively seen as statically indeterminate beam and indeterminate arch is analyzed, calculate separately super quiet
The displacement of beam and indeterminate arch is determined to obtain the convergent deformation of monitoring point.
Preferably, the statically indeterminate beam of monitoring point displacement calculate the following steps are included:
S211 analyzes statically indeterminate beam load: statically indeterminate beam load q firstlFor horizontal loading qsAnd vertical load
qcIn the sum of the component perpendicular to beam direction, i.e. ql=qs·sinα+qcCos α, and by load qlIt is divided into evenly load ql1, line
Property load ql2, wherein α is the angle between fan-shaped two radius；Since beam both ends are consolidation, do not influenced by xial feed, therefore only
Consider horizontal loading and vertical load in the effect perpendicular to beam direction load；
S212 lists load q respectivelyl1、ql2Calculating formula；
S213 calculates the calculation of Bending Moment formula on statically indeterminate beam using the force method principle of structural mechanics；
S214 combination load and calculation of Bending Moment formula respectively obtain monitoring point by load ql1、ql2Displacement calculating formula, will survey
Tunnel pressure data bring calculating formula into, respectively obtain the displacement of load；
S215 obtains the total displacement amount ω of statically indeterminate beaml。
Preferably, when being calculated in above-mentioned steps S212: it will be the direction x along the direction definition of statically indeterminate beam, it is perpendicular
Direction is the direction y；
S2121 calculates ql1When:
The moment of flexure of statically indeterminate beam any position in the x direction is calculated by the force method principle of structural mechanics:R is fan-shaped radius in formula, and M (x) is the moment of flexure in the direction x；
According to the relational expression of moment of flexure in the mechanics of materials and amount of deflection:Wherein EI is constant, and ω is deformation
Amount；
Double integral is asked to obtain moment of flexure:
ωl1(x) EI=∫ ∫ [M (x) dx] dx+C1x+D1, ω in formulal1It (x) is monitoring point by ql1Load is in y-direction
Displacement, since beam and arch are consolidation, so ω (0)=0, ω (r)=0, substituting into above formula be can be calculated:
And ql1=qc·cosα+e1Sin α, wherein
e1For tunnel top lateral pressure/kPa, q is obtainedl1Value, and then obtain in load ql1Act on the displacement of lower statically indeterminate beam
ωl1；
S2122 calculates ql2Value:
The moment of flexure on statically indeterminate beam at the x of any position is calculated by the force method principle of structural mechanics:
Ask double integral that can obtain moment of flexure:
ω in formulal2It (x) is prison
Measuring point is by ql2The displacement of load in y-direction；And ql2=(e2-e1) sin α, e in formula2For tunnel bottom lateral pressure/
KPa is obtained in load ql2Act on the displacement of lower statically indeterminate beam；
In the calculating process, ql1、ql2Displacement by actual measurement tunneling data inverse obtain, i.e., by the e of actual measurement1Tunnel top
Lateral pressure, e2Tunnel bottom lateral pressure is brought into derivation formula, and load q is obtainedl1And ql2Value, and then respectively obtain super quiet
Beam is determined by load ql1、ql2Displacement, obtain the displacement of statically indeterminate beam, lay the foundation to calculate the displacement of monitoring point, it is real
The data of survey are more accurate reliable come the more traditional mode calculated by empirical formula method of the displacement of the statically indeterminate beam calculated, fit
Ying Xinggeng is wide.
Preferably, the indeterminate arch of monitoring point displacement calculate the following steps are included:
Horizontal direction load decomposition suffered by indeterminate arch is evenly load q by S2211, linear load q2, further include vertical side
To load q3；The constraint load for the horizontal direction that the intersection point of indeterminate arch and horizontal plane is subject to is denoted as x3, vertical direction load
It is denoted as x2, the torque which is subject to is denoted as x1；
S222 is rigid connection node according to indeterminate arch and the intersection point of horizontal plane, obtains the intersection point in three directions
Displacement relation under unit load effect；
S223 lists displacement relation formula of the indeterminate arch with the intersection point of horizontal plane under three direction load actions；
S224 lists the calculation of Bending Moment formula of arbitrary point on indeterminate arch；
S225 brings the data of coordinate points into above formula and obtains the displacement ω of indeterminate arch since beam and arch are consolidationg。
Preferably, can be obtained in above-mentioned steps S222 according to the rigid connection of model point:
Δ in formulaiqFor by load q generate along xiDirection
Displacement, δijFor by unit force xj=1 generate along xiThe displacement in direction, wherein i=1,2 or 3, j=1,2 or 3, and according to this
The characteristic of rigid connection point, δ12=δ21、δ13=δ31、δ23=δ32；And calculate the displacement δ of indeterminate arch arbitrary pointijWhen:
R is fan-shaped radius in formula, and α is fan-shaped
Angle between two radius；
And it calculates separately in load q1、q2、q3Displacement under effectiq:
Load q can be acquired using above formula1、q2、q3Constraint x under effect1、x2、x3, then can acquire and encircle the curved of upper arbitrary point
Square:
,
Ask double integral that can obtain moment M (x):
X=r in formula(I.e.It is 0 to a value between α), C2For, D2To ask the normal system generated during double integral to moment of flexure
Number；
ω (0)=0, ω (α)=0 are substituted into above formula, C can be acquired2、D2, obtain the displacement ω of indeterminate archg。
Preferably, the convergent deformation of monitoring point is the sum of the displacement deformation of statically indeterminate beam and indeterminate arch: ω=ωl·
sinα+ωg。
Preferably, when calculating angle of friction:
S51 first determines whether tunnel is shallow tunnel, determines Grades of Surrounding Rock according to convergent deformation ω and field data；
When S52 is shallow tunnel, its vertical pressure from surrounding rock q is calculated:In formula
Q is vertical uniform load/kNm-2, γ is tunnel above rock severe/kNm-3；H is edpth of tunnel/m；BtIt is wide for tunnel
Degree/m, λ are lateral pressure coefficient, θ be country rock angle of friction/°；
S53 wherein, lateral pressure coefficient λ:
In formula: β is broken
The angle of broken face and horizontal plane/°,For country rock calculate angle of friction/°, and then obtain:
Lateral pressure are as follows:
e1=γ H λ
e2=γ h λ, H is edpth of tunnel/m in formula, and h is tunnel height/m；
S54 according to Grades of Surrounding Rock by specification recommend value obtain γ,And λ value, θ degree is calculated according to design drawing
Number, finally acquires horizontal adjoining rock pressure and vertical pressure from surrounding rock.
Grades of Surrounding Rock is determined according to the convergent deformation amount of monitoring point that the data that tunnel is surveyed obtain, and by Grades of Surrounding Rock
Recommend value to obtain related coefficient and country rock calculating angle of friction numerical value according to specification, brings horizontal adjoining rock pressure and vertical country rock pressure into
The calculating formula of power obtains pressure value.
Compared with prior art, beneficial effects of the present invention:
The convergent deformation and pressure from surrounding rock that the calculation method passes through side wall country rock in analysis two side-wall pilot tunnel constructing tunnel
Between relationship, establish model of structural mechanics, horizontal adjoining rock pressure and vertical pressure from surrounding rock acquired by field monitoring data inverse,
Compared to the existing calculation method for relying on empirical parameter, practical pressure from surrounding rock more acurrate, more representative of tunnel, and the receipts in tunnel
Hold back deformation data be easier to obtain, convenience of calculation it is accurate.
Detailed description of the invention:
Fig. 1 is existing two side-wall pilot tunnel construction schematic diagram.
Fig. 2 is the left base tunnel top bar simplified model figure of the present invention.
The illustraton of model for the horizontal direction load that Fig. 3 statically indeterminate beam is subject to.
The illustraton of model for the vertical load that Fig. 4 statically indeterminate beam is subject to.
Fig. 5 is indeterminate to encircle the horizontal direction Load Model figure being subject to.
Fig. 6 is indeterminate to encircle the vertical load illustraton of model being subject to.
Fig. 7 statically indeterminate beam load calculates illustraton of model.
The indeterminate arch load of Fig. 8 calculates illustraton of model.
Marked in the figure: the left base tunnel top bar of 1-, the left base tunnel of 2- are got out of a predicament or an embarrassing situation, the right base tunnel top bar of 3-, the right base tunnel of 4- is got out of a predicament or an embarrassing situation,
Base tunnel top bar in 5-, base tunnel is got out of a predicament or an embarrassing situation in 6-, the left base tunnel top bar convergent point of 7-, 8- up/down steps line of demarcation, 9-
One layer of preliminary bracing, 10- second layer preliminary bracing.
Specific embodiment
Below with reference to test example and specific embodiment, the present invention is described in further detail.But this should not be understood
It is all that this is belonged to based on the technology that the content of present invention is realized for the scope of the above subject matter of the present invention is limited to the following embodiments
The range of invention.
Embodiment
As shown in Figures 1 to 8, the present embodiment is calculated by taking certain urban road tunnel as an example, edpth of tunnel be 7.21m~
13.45m, the wide 12m in tunnel, tunnel trunk is V grade of country rock, using two side-wall pilot tunnel partial excavation, the pressure from surrounding rock in the tunnel
Calculation method the following steps are included:
The convergent deformation monitoring point of S1 selection country rock: successively excavating as shown in Figure 1, tunnel is divided into 6 parts, point
Not Wei left base tunnel top bar 1, left base tunnel get out of a predicament or an embarrassing situation 2, right base tunnel top bar 3, right base tunnel get out of a predicament or an embarrassing situation 4, middle base tunnel top bar 5, in
Base tunnel is got out of a predicament or an embarrassing situation 6 and up/down steps line of demarcation 8, and it is detection position that the present embodiment, which chooses left base tunnel top bar convergent point 7,
1. the second layer preliminary bracing 10 of first layer preliminary bracing 9, internal layer in work progress equipped with outer layer, the present embodiment are chosen in figure
After pilot tunnel is excavated in portion, choose by the point on pilot drift is excavated as the monitoring point of convergent deformation, the excavation width of the pilot tunnel is
5.16m, i.e. tunnel width Bt=5.16m, by the judgement of load height equivlent, the tunnel is shallow embedding or deep tunnel:
Hp=(2~2.5) hq, H in formulapFor shallow tunnel boundary depth/m, hqLoad height equivlent/m, and hq=0.45 ×
2s-1ω, wherein S is Grades of Surrounding Rock, the present embodiment S=5, and ω is widths affect coefficient, ω=1+i (B-5), B be tunnel width/
M, the present embodiment Bt=5.16m, i be B it is every increase and decrease 1m when pressure from surrounding rock gradient, vertically uniformly pressed with the country rock of B=5m
Subject to power, as B < 5m, i=0.2 is taken；When B > 5m, i=0.1 is taken；Due to for V grade of country rock, Hp=2.5hq, therefore obtain:
hq=0.45 × 2s-1ω=7.32m, Hp=2.5hq=18.29m, therefore the tunnel is shallow tunnel.
S2 is in the monitoring point structural texture mechanical model:
Done when establishing model it is assumed hereinafter that: left base tunnel top bar is considered as sector；Top bar right wall and circular arch simplified partial
For rigid material；Each node of simplified model is considered as rigid connection.
Therefore, it as shown in Fig. 2, monitoring point two sides are respectively seen as statically indeterminate beam and indeterminate arch is analyzed, counts respectively
The displacement of statically indeterminate beam and indeterminate arch is calculated to obtain the convergent deformation of monitoring point.
The displacement of the statically indeterminate beam of monitoring point calculate the following steps are included:
S211 is as shown in Figure 3 and Figure 4, first analysis statically indeterminate beam load: statically indeterminate beam load qlFor level
Load qsWith vertical load qcIn the sum of the component perpendicular to beam direction, i.e.,And
By load qlIt is divided into evenly load ql1, linear load ql2, wherein α is the angle between fan-shaped two radius；Since beam both ends are
Consolidation, is not influenced by xial feed, therefore only considers horizontal loading and vertical load in the effect perpendicular to beam direction load；
S212 lists load q respectivelyl1、ql2Calculating formula:
Calculate ql1When:
As shown in Figure 3 and Figure 4, the curved of statically indeterminate beam any position in the x direction is calculated by the force method principle of structural mechanics
Square:R is fan-shaped radius in formula, and M (x) is the moment of flexure in the direction x；
According to the relational expression of moment of flexure in the mechanics of materials and amount of deflection:Wherein EI is constant, and ω is deformation
Amount；
Double integral is asked to obtain moment of flexure:
ωl1(x) EI=∫ ∫ [M (x) dx] dx+C1x+D1, ω in formulal1It (x) is monitoring point by ql1Load is in y-direction
Displacement, since beam and arch are consolidation, so ω (0)=0, ω (r)=0, substituting into above formula be can be calculated:
And ql1=qc·cosα+e1Sin α, wherein
e1For tunnel top lateral pressure/kPa, q is obtainedl1Value, and then obtain in load ql1Act on the displacement of lower statically indeterminate beam
ωl1；
Calculate ql2Value:
The moment of flexure on statically indeterminate beam at the x of any position is calculated by the force method principle of structural mechanics:
Ask double integral that can obtain moment of flexure:
ω in formulal2It (x) is prison
Measuring point is by ql2The displacement of load in y-direction；And ql2=(e2-e1) sin α, e in formula2For tunnel bottom lateral pressure/
KPa is obtained in load ql2The displacement of lower statically indeterminate beam is acted on, and then obtains the total displacement amount ω of statically indeterminate beaml。
And the indeterminate arch of monitoring point displacement calculate the following steps are included:
Horizontal direction load decomposition suffered by indeterminate arch is evenly load q as shown in Fig. 5 to Fig. 8 by S2211, linear lotus
Carry q2, further include the load q of vertical direction3；The constraint load for the horizontal direction that the intersection point of indeterminate arch and horizontal plane is subject to is remembered
For x3, vertical direction load is denoted as x2, the torque which is subject to is denoted as x1；
S222 is the characteristic of rigid connection node according to the intersection point of indeterminate arch and horizontal plane, obtains the intersection point three sides
Displacement relation under upward unit load effect:
It can be obtained according to rigid connection point:
Δ in formulaiqFor by load q generate along xiDirection
Displacement, δijFor by unit force xj=1 generate along xiThe displacement in direction, wherein i=1,2 or 3, j=1,2 or 3, and according to this
The characteristic of rigid connection point, δ12=δ21、δ13=δ31、δ23=δ32；And calculate the displacement δ of indeterminate arch arbitrary pointijWhen:
R is fan-shaped radius in formula, and α is fan-shaped
Angle between two radius；
And it calculates separately in load q1、q2、q3Displacement under effectiq:
Load q can be acquired using above formula1、q2、q3Constraint x under effect1、x2、x3, then can acquire and encircle the curved of upper arbitrary point
Square:
, ask double integral that can obtain moment M (x):
X=r in formula C2For, D2To seek the constant coefficient generated during double integral to moment of flexure；
ω (0)=0, ω (α)=0 are substituted into above formula, C can be acquired2、D2, obtain the displacement ω of indeterminate archg, monitoring point
Convergent deformation be statically indeterminate beam and indeterminate arch the sum of displacement deformation:
When judging tunnel for shallow tunnel, its vertical pressure from surrounding rock q is calculated:
Q is vertical uniform load/kNm in formula-2, γ is tunnel above rock severe/kNm-3；H is edpth of tunnel/m；BtFor tunnel
Width/m, λ are lateral pressure coefficient, θ be country rock angle of friction/°；
Wherein, lateral pressure coefficient λ:
In formula: β is rupture
The angle of face and horizontal plane/°,For country rock calculate angle of friction/°, and then obtain:
Lateral pressure are as follows:
e1=γ H λ
e2=γ h λ, H is edpth of tunnel/m in formula, and h is tunnel height/m；
The data of the present embodiment are brought into obtain, accumulative deformation ω (x)=15.5mm in digging process, edpth of tunnel H
=13.31m, EI=7.354 × 106N·m2, and tunnel is V grade of country rock, recommends value, tunnel above rock severe by specification
γ=19kNm-3, Reference Design drawing can be calculated model right wall angle with horizontal plane θ=71.68 °, substitutes into above-mentioned calculating formula
It acquires:
λ=0.19, q=199.41kPa, e1=47.35kPa, e2=17.22kPa,
V grade of country rock calculates angle of friction in vcehicular tunnel design specificationSuggestion value interval be 40 °~50 °, following table isThe vertical pressure from surrounding rock and horizontal adjoining rock pressure value acquired when taking 40 °, 45 °, 50 ° respectively according to proper calculation:
It can see by the table, the pressure from surrounding rock acquired by the calculation method of this programme is by " vcehicular tunnel design specification "
Within the scope of calculated result, it was demonstrated that this method is feasible, and accuracy is higher.
The calculation method of the present embodiment by analysis two side-wall pilot tunnel constructing tunnel in side wall country rock convergent deformation with
Relationship between pressure from surrounding rock, establishes model of structural mechanics, by field monitoring data inverse acquire horizontal adjoining rock pressure with it is vertical
Pressure from surrounding rock, compared to it is existing rely on empirical parameter calculation method, practical pressure from surrounding rock more acurrate, more representative of tunnel,
And the convergent deformation data in tunnel be easier to obtain, convenience of calculation it is accurate.
All features disclosed in this specification or disclosed all methods or in the process the step of, in addition to mutually exclusive
Feature and/or step other than, can combine in any way.
Any feature disclosed in this specification (including any accessory claim, abstract and attached drawing), except non-specifically chatting
It states, can be replaced by other alternative features that are equivalent or have similar purpose.That is, unless specifically stated, each feature is only
It is an example in a series of equivalent or similar characteristics.
Claims (7)
1. a kind of pressure from surrounding rock calculation method for shallow tunnel, which comprises the following steps:
The convergent deformation monitoring point of S1 selection country rock: the tunnel using two side-wall pilot tunnel construction is researched and analysed, is chosen
Point on the pilot tunnel excavated at first by sequence of excavation is convergent deformation monitoring point；
S2 chooses left base tunnel top bar or right base tunnel top bar is analyzed, and in monitoring point structural texture mechanical model, establishes mould
Done when type it is assumed hereinafter that: left base tunnel top bar or right base tunnel top bar are considered as sector；By left base tunnel top bar right wall and circular arch
Simplified partial is rigid material；Each node of simplified model is considered as rigid connection, by monitoring point two sides be respectively seen as statically indeterminate beam and
Indeterminate arch is analyzed, and calculates separately the displacement of statically indeterminate beam and indeterminate arch to obtain the convergent deformation of monitoring point；
S3 derives the calculation relational expression between convergent deformation and pressure from surrounding rock；
S4 brings engineering real data and convergence monitoring data in the relational expression of step S3 into, calculates separately monitoring point left and right two
The displacement of side and the convergent deformation of monitoring point；
S5 is calculated country rock and calculates angle of friction and pressure from surrounding rock.
2. pressure from surrounding rock calculation method according to claim 1, which is characterized in that the displacement meter of the statically indeterminate beam of monitoring point
Calculate the following steps are included:
S211 analyzes statically indeterminate beam load: statically indeterminate beam load q firstlFor horizontal loading qsWith vertical load qc?
Perpendicular to the sum of the component in beam direction, i.e. ql=qs·sinα+qcCos α, and by load qlIt is divided into evenly load ql1, linear lotus
Carry ql2, wherein α is the angle between fan-shaped two radius；
S212 lists load q respectivelyl1、ql2Calculating formula；
S213 calculates the calculation of Bending Moment formula on statically indeterminate beam using the force method principle of structural mechanics；
S214 combination load and calculation of Bending Moment formula respectively obtain monitoring point by load ql1、ql2Displacement calculating formula, by the tunnel of actual measurement
Road pressure data brings calculating formula into, respectively obtains the displacement of load；
S215 obtains the total displacement amount ω of statically indeterminate beaml。
3. pressure from surrounding rock calculation method according to claim 2, which is characterized in that when being calculated in step S212: will be along super
The direction definition of statically determinate beam is the direction x, and perpendicular direction is the direction y；
S2121 calculates ql1When:
The moment of flexure of statically indeterminate beam any position in the x direction is calculated by the force method principle of structural mechanics:R is fan-shaped radius in formula, and M (x) is the moment of flexure in the direction x；
According to the relational expression of moment of flexure in the mechanics of materials and amount of deflection:Wherein EI is constant, and ω is deflection；
Double integral is asked to obtain moment of flexure:
ωl1(x) EI=∫ ∫ [M (x) dx] dx+C1x+D1, ω in formulal1It (x) is monitoring point by ql1The displacement of load in y-direction
Amount, C1For, D1To seek the constant coefficient generated during double integral to moment of flexure, since beam and arch are consolidation, so ω (0)=0,
ω (r)=0, substituting into above formula can be calculated:
And ql1=qc·cosα+e1Sin α, wherein e1For tunnel
Road top lateral pressure/kPa, obtains ql1Value, and then obtain in load ql1Act on the displacement ω of lower statically indeterminate beaml1；
S2122 calculates ql2Value:
The moment of flexure on statically indeterminate beam at the x of any position is calculated by the force method principle of structural mechanics:
Ask double integral that can obtain moment of flexure:
ω in formulal2It (x) is monitoring point
By ql2The displacement of load in y-direction；And ql2=(e2-e1) sin α, e in formula2For
Tunnel bottom lateral pressure/kPa, obtains in load ql2Act on the displacement of lower statically indeterminate beam.
4. pressure from surrounding rock calculation method according to claim 1, which is characterized in that the displacement meter of the indeterminate arch of monitoring point
Calculate the following steps are included:
Horizontal direction load decomposition suffered by indeterminate arch is evenly load q by S2211, linear load q2, further include vertical direction
Load q3；The constraint load for the horizontal direction that the intersection point of indeterminate arch and horizontal plane is subject to is denoted as x3, vertical direction load is denoted as
x2, the torque which receives is denoted as x1；
S222 is rigid connection node according to the intersection point of indeterminate arch and horizontal plane, obtains the unit of the intersection point in three directions
Displacement relation under load action；
S223 lists displacement relation formula of the indeterminate arch with the intersection point of horizontal plane under three direction load actions；
S224 lists the calculation of Bending Moment formula of arbitrary point on indeterminate arch；
S225 brings the data of coordinate points into above formula and obtains the displacement ω of indeterminate arch since beam and arch are consolidationg。
5. pressure from surrounding rock calculation method according to claim 4, which is characterized in that according to rigid connection point in step S222
It can obtain:
Δ in formulaiqFor by load q generate along xiThe position in direction
It moves, δijFor by unit force xj=1 generate along xiThe displacement in direction, wherein i=1,2 or 3, j=1,2 or 3, and according to the rigidity
The characteristic of tie point, δ12=δ21、δ13=δ31、δ23=δ32；
And calculate the displacement δ of indeterminate arch arbitrary pointijWhen:
R is fan-shaped radius in formula, and α is fan-shaped two halves
Angle between diameter；
And it calculates separately in load q1、q2、q3Displacement under effectiq:
Load q can be acquired using above formula1、q2、q3Constraint x under effect1、x2、x3, it then can acquire the moment of flexure for encircleing upper arbitrary point:
,
Ask double integral that can obtain moment M (x):
In formula C2For, D2To seek the constant coefficient generated during double integral to moment of flexure；
ω (0)=0, ω (α)=0 are substituted into above formula, C can be acquired2、D2, obtain the displacement ω of indeterminate archg。
6. pressure from surrounding rock calculation method according to claim 5, which is characterized in that the convergent deformation of monitoring point is indeterminate
The sum of the displacement deformation of beam and indeterminate arch: ω=ωl·sinα+ωg。
7. pressure from surrounding rock calculation method according to claim 6, which is characterized in that when calculating angle of friction:
S51 first determines whether tunnel is shallow tunnel, determines Grades of Surrounding Rock according to convergent deformation ω and field data；
When S52 is shallow tunnel, its vertical pressure from surrounding rock q is calculated:Q is vertical in formula
Straight evenly load/kNm-2, γ is tunnel above rock severe/kNm-3；H is edpth of tunnel/m；BtFor tunnel width/m, λ
For lateral pressure coefficient, θ be country rock angle of friction/°；
S53 wherein, lateral pressure coefficient λ:
In formula: β is rupture
The angle of face and horizontal plane/°,For country rock calculate angle of friction/°, and then obtain:
Lateral pressure are as follows:
H is edpth of tunnel/m in formula, and h is tunnel height/m；
S54 according to Grades of Surrounding Rock by specification recommend value obtain γ,And λ value, it finally acquires horizontal adjoining rock pressure and is enclosed with vertical
Rock pressure power.
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| CN108801505B (en) * | 2018-06-11 | 2019-11-29 | 中国科学院武汉岩土力学研究所 | The cell cube method and device of Disturbance stress measurement |
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| CN109684744B (en) * | 2018-12-27 | 2022-11-25 | 石家庄铁道大学 | Method for calculating surrounding rock pressure of soft rock tunnel |
| CN110096833B (en) * | 2019-05-13 | 2022-09-09 | 中铁二院工程集团有限责任公司 | Surrounding rock load calculation method suitable for bedding bias tunnel |
| CN111141601B (en) * | 2019-12-24 | 2022-04-26 | 长安大学 | Method for testing stress safety of partition wall structure in shallow-buried ultra-large-span tunnel |
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