CN110059370A - A kind of substrate load calculation method suitable for passing through compound stratum tunnel - Google Patents
A kind of substrate load calculation method suitable for passing through compound stratum tunnel Download PDFInfo
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Abstract
The substrate load calculation method that the invention discloses a kind of suitable for passing through compound stratum tunnel, belong to technical field of tunnel construction, wherein by establishing the slip field dynamics model passed through between compound stratum tunnel and compound stratum, soft according to compound stratum, hard stratum line of demarcation and tunnel center line positional relationship, it can accurately and rapidly determine the width of slip region in hard stratum, realize the calculating for passing through compound stratum Tunnel Base load.The substrate load calculation method for being suitable for passing through compound stratum tunnel of the invention, its derivation process is simple, it can effectively realize the calculating of substrate load when tunnel structure passes through compound stratum, ensure that calculated result and the measured value of Tunnel Base load are more close, it is more in line with the actual forced status that tunnel is located in compound stratum, substrate load when for Tunnel Passing compound stratum provides accurately and reliably calculation method, it ensure that construction and the operation safety in tunnel, it is scientific strong, with good application prospect and promotional value.
Description
Technical field
The invention belongs to technical field of tunnel construction, and in particular to a kind of substrate lotus suitable for passing through compound stratum tunnel
Carry calculation method.
Background technique
With the needs of the enlargement of China's traffic tunnel, deep layerization construction, tunnel construction section increases, buried depth increases, tunnel
The case that road construction meets with compound stratum is more and more.For example, China is in recent years in the Changjiang river, Pearl River Delta, one band of southeastern coast
Soft lower hard compound stratum is met with repeatedly in a large amount of Tunnel Engineering of construction；For another example System of Wuhan Yangtse Tunnel mainly passes through strong saturating
Water sand layer, partial section penetrating ground are the great layer of sand of soft or hard degree difference-argillaceous siltstoue compound stratum；For another example wide Shenzhen and Hong Kong
High iron lion ocean tunnel successively passes through weak soil, soft or hard uneven compound stratum, tunneling boring weathered rock formation etc..
In the design process of tunnel structure, the calculating of pressure from surrounding rock is to need to consider the problems of first.In existing tunnel
In road pressure from surrounding rock calculating process, using it is more be modified routine method, often assume that the stratum of tunnel structure periphery is bullet
Property isotropic body, and the interaction process of tunnel structure and stratum is reduced to model as shown in Figure 9.
The above method can meet pressure from surrounding rock for passing through the tunnel in common homogeneous formation region to a certain extent
It calculates；But the tunnel for passing through compound stratum, there are certain differences for the binding mode due to Different Strata to tunnel structure
It is different, if still using modified routine method that compound stratum equivalent-simplification is carried out to the calculating of country rock load for homogeneous formation, can lead
The generation for causing larger design error causes tunnel structure Reinforcement Design improper, influences the safety and stabilization of structure design of tunnel
Property.Meanwhile when Tunnel Passing compound stratum, tunnel top is often acted on by Soft Soil Layer, and the middle and lower part in tunnel is usually by pan soil
Layer effect, for the Soft Soil Layer on compound stratum top, usually can relatively accurately be realized using existing load calculation method
Simulation and calculating, such as utilize " the compound stratum shield tunnel vault loadometer disclosed in existing patent CN 106529150
Calculation method " can realize that the simulation of tunnel top country rock load calculates to a certain extent, obtain the vertical soil pressure of tunnel top
Power；But for the load computational problem of tunnel middle and lower part hard stratum, there is no reasonable calculation method at present, so that tunnel base
Bottom country rock is unable to get accurate calculating to the imposed load of tunnel structure, influences the standard of tunnel structure country rock load calculating
True property and comprehensive, causing structure design of tunnel, there are biggish limitations.
Summary of the invention
One or more of aiming at the above defects or improvement requirements of the prior art, the present invention provides one kind to be applicable in
In the substrate load calculation method for passing through compound stratum tunnel, wherein by establish pass through compound stratum tunnel and compound stratum it
Between slip field dynamics model, soft according to compound stratum, hard stratum line of demarcation and tunnel center line positional relationship, can it is accurate,
The width of slip region in hard stratum is quickly determined, then realizes the calculating of Tunnel Base load, so that calculating Tunnel Base lotus
Result and the measured value of load are more closely, be more in line with the actual forced status that tunnel is located in compound stratum, for Tunnel Passing
Substrate load when compound stratum provides accurately and reliably calculation method, guarantees construction and the operation safety in tunnel.
To achieve the above object, the present invention provides a kind of substrate load calculating side suitable for passing through compound stratum tunnel
Method, which comprises the steps of:
S1: obtaining the exploration parameter in tunnel, and the exploration parameter includes: the distance between tunnel top and level ground,
The positional relationship and tunnel two sides pan soil of the horizontal boundary line of Soft Soil Layer and hard stratum and tunnel horizontal center line in compound stratum
The vertical load when internal friction angle and the hard stratum of layer reach plastic limit state at the horizontal boundary line；
S2: the cunning of compound stratum is established according to the positional relationship of the horizontal boundary line of soft, hard stratum and tunnel horizontal center line
Field of line mechanical model；The just tangent curve with tunnel bottom, the i.e. sliding of hard stratum are determined in the slip field dynamics model
Line, the skid wire include linear the first skid wire and the second skid wire in log spiral, respectively correspond slip field
In active stressed zone and unfair stress area, the boundary lines of two stressed zones be the first linear stress section, the first stress section
Two-end-point be respectively the intersection point of the first skid wire and the second skid wire and the intersection point of the horizontal boundary line and tunnel circumference；
S3: according to the relative position in hard stratum line of demarcation and tunnel center line soft in compound stratum, in conjunction with skid wire and circle
The position of all tangent condition and point of contact calculates the width of slip region；
When the horizontal boundary line is not less than the tunnel horizontal center line, the width of slip region can be counted by following formula
It calculates:
In formula 1, b is the width of slip region；A is the radius of a circle in tunnel；For the angle of friction of hard stratum；θ1Connect for first
Angle formed by line and the first stress section, first line are continuous, the institute of arbitrary point and the first point of interface on the second skid wire
State the intersection point that the first point of interface is the horizontal boundary line and tunnel circumference；
When the horizontal boundary line is lower than the tunnel horizontal center line, the width of slip region can be counted by following formula
It calculates:
In formula 2, b is the width of slip region；A is the radius of a circle in tunnel；For the angle of friction of hard stratum；θ3Connect for second
The angle of line and tunnel horizontal center line, second line are the line of the first point of interface and the tunnel center of circle, θ3< 0；
S4: calculating the load intensity that tunnel is born at first point of interface, and calculation formula is as follows:
In formula 3, q2For the load intensity at first point of interface；q1It is the hard stratum at the horizontal boundary line
Reach vertical load when plastic limit state；
The load intensity on circumference being had a common boundary due to tunnel and hard stratum is with the increase with the first point of interface distance
And reduce, then the load intensity of any position can be carried out by following formula between the first point of interface and point of contact on tunnel circumference
It calculates:
qx=q2-λlx(formula 4)
In formula 4, qxTake up an official post for camber line in slip region the load intensity anticipated at the X of position；q2For the load collection at the first point of interface
Degree；Lx be position X and the first point of interface circumferentially at a distance from；λ is the reduction coefficient of load intensity.
As a further improvement of the present invention, arbitrary point can pass through at a distance from the first point of interface on second skid wire
Following formula is calculated:
In formula 5, r0For the length of the first stress section；θ '=θ1。
As a further improvement of the present invention, the derivation process of step S3 Chinese style 1 may include following steps:
S31: using the first point of interface as polar coordinate center point, the line in the first point of interface and the tunnel center of circle is that x-axis establishes pole
Coordinate system, and following formula can be obtained according to geometrical relationship:
In formula 6, θ2For the angle of the 4th line and x-axis, the 4th line is that the tunnel circumference contacted with slip region is taken up an official post
Line of the meaning point with the first point of interface；
S32: according to second skid wire and the tangent condition of tunnel circumference, θ is calculated1Size, formula is as follows:
S33: joint type 6 and formula 7, and in conjunction with second skid wire and the tangent condition of tunnel circumference, derivation can be corresponded to
Formula 1 out.
As a further improvement of the present invention, the reduction coefficient λ of load intensity can by moment of flexure at the first point of interface and
Derivation calculating is carried out for 0, i.e.,
∑MB=MAB+MAC+MCD+MBD+MW=0 (formula 8)
In formula 8, MBFor the moment of flexure of the first point of interface；MABIt is the load on horizontal boundary line to the moment of flexure of the first point of interface；
MACIt is the load on the first skid wire to the moment of flexure of the first point of interface；MCDIt is the load on the second skid wire to the first point of interface
Moment of flexure；MBDIt is the load on camber line in slip region to the moment of flexure of the first point of interface；MWIt is gravity to the moment of flexure of the first point of interface.
Above-mentioned improved technology feature can be combined with each other as long as they do not conflict with each other.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, have below beneficial to effect
Fruit:
(1) the substrate load calculation method for being suitable for passing through compound stratum tunnel of the invention, is passed through again by establishing
The slip field dynamics model between formation tunnel and compound stratum is closed, in, hard stratum line of demarcation soft according to compound stratum and tunnel
The positional relationship of heart line can accurately and rapidly determine the width of slip region in hard stratum, realize the accurate meter of Tunnel Base load
It calculates, so that the result and measured value that calculate Tunnel Base load are more closely, be more in line with the reality that tunnel is located in compound stratum
Border stress, substrate load when for Tunnel Passing compound stratum provide accurately and reliably calculation method, ensure that tunnel
Construction and operation safety；
(2) the substrate load calculation method for being suitable for passing through compound stratum tunnel of the invention, by establishing polar coordinates
Length requirement and the slope requirement for being and combining skid wire at point of contact, can effectively determine the correlation between corresponding angle,
Then the calculation formula of sliding sector width is accurately obtained, derivation process is simple, and accuracy is high, can effectively ensure the standard of calculated result
True property；
(3) the substrate load calculation method for being suitable for passing through compound stratum tunnel of the invention, derivation process are simply bright
, can effectively realize the calculating of substrate load when tunnel structure passes through compound stratum, it is ensured that the calculated result of Tunnel Base load
It is Tunnel Passing compound stratum with measured value more closely, being more in line with the actual forced status that tunnel is located in compound stratum
When substrate load provide accurately and reliably calculation method, ensure that construction and the operation safety in tunnel, it is scientific strong, have
Preferable application prospect and promotional value.
Detailed description of the invention
Fig. 1 is the load mode schematic diagram that compound stratum tunnel is passed through in the embodiment of the present invention；
Fig. 2 is the slip field dynamics model schematic that compound stratum tunnel is passed through in the embodiment of the present invention by formation function；
Fig. 3 is the slip field in the embodiment of the present invention when the stratum line of demarcation of compound stratum is located above tunnel center line
Mechanical model schematic diagram；
Slip field dynamics when Fig. 4 is the concordant tunnel center line in stratum line of demarcation in the embodiment of the present invention when compound stratum
Model schematic；
Fig. 5 is the slip field in the embodiment of the present invention when the stratum line of demarcation of compound stratum is located at below tunnel center line
Mechanical model schematic diagram；
Fig. 6 is the sectional schematic diagram of Tunnel Passing compound stratum in the specific embodiment of the invention；
Fig. 7 is the slip field dynamics model schematic that tunnel is acted on by compound stratum in the specific embodiment of the invention；
Fig. 8 is calculated with load calculation method of the invention in the specific embodiment of the invention and with modified routine method
The contrast schematic diagram of pressure from surrounding rock calculated value and pressure from surrounding rock measured value out；
Fig. 9 be in current modified routine method tunnel by the Load Model schematic diagram of formation function；
In all the appended drawings, same appended drawing reference indicates identical technical characteristic.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that described herein, specific examples are only used to explain the present invention, not
For limiting the present invention.
In addition, as long as technical characteristic involved in the various embodiments of the present invention described below is each other not
Constituting conflict can be combined with each other.
The load mode that compound stratum tunnel is passed through in the preferred embodiment of the present invention is as shown in fig. 1, by being not difficult in diagram
Find out, the compound stratum that tunnel structure passes through in preferred embodiment is upper soft lower hard soil layer, i.e., on the top of tunnel structure, ground
Layer is Soft Soil Layer, and in the lower section of tunnel structure, stratum is hard stratum.Since tunnel structure passes through compound stratum, so that tunnel knot
The load mode and have certain difference as passed through the load mode that the tunnel structure of homogeneous formation is born in Fig. 9 that structure is born
Different, difference is mainly reflected on the force modes of tunnel structure two sides.By Fig. 1 it is not difficult to find out that, in soft, hard stratum boundary
Place, the lateral load that tunnel structure is born can mutate, and the difference of lateral loading pattern makes tunnel structure correspond to hard stratum
Two sides there is slip region, as shown in Figure 2.
Further, for passing through the tunnel structure of compound stratum in the present invention, the calculating of substrate pressure from surrounding rock is main
It is carried out around active earth pressure and passive resisting force.Wherein, active earth pressure is mainly generated by the phorogenesis of lower part hard stratum,
Slip Line Theory can be used to be solved；Elastic foundation method solution can be used in passive soil pressure.Correspondingly, it is upper it is soft it is lower it is hard compoundly
The magnitude of the active earth pressure generated when stratum slides to tunnel bottom lining cutting is covered under layer, taking its counter-force is compoundly
Layer Tunnel Base load, and be overlapped when tunnel left and right sides skid wire overlaps.
Specifically, the present invention is preferably as follows suitable for the substrate load calculation method for passing through compound stratum tunnel:
S1: the substrate Load Model for passing through compound stratum tunnel is established
For existing calculation method as shown in Figure 9, i.e. modified routine method, wherein by the phase of tunnel structure and stratum
Interreaction force is reduced to the increased active force of depth, which includes the stratum drag and upper and lower subgrade reaction of two sides.
The Load Model can reflect the load situation of tunnel structure in homogeneous formation to a certain extent, but for tunnel as shown in Figure 1
Road structure, since Soft Soil Layer, hard stratum have differences with the effect of tunnel structure respectively, thus its stress load mode there is also
Certain difference.In consideration of it, the present invention is put forward for the first time for the otherness of compound stratum weak soil, pan soil and tunnel structure effect
It is suitable for passing through the load mode of compound stratum tunnel structure as shown in Figure 1.
Specifically, the top of tunnel structure is Soft Soil Layer, vertical soil of the Soft Soil Layer to tunnel structure in compound stratum
Pressure P1It can be unfolded according to Traditional calculating methods as shown in Figure 9.And when for the calculating of soil lateral pressure, due to soft
Soil and pan soil have different lateral pressure coefficients and stratum resistance coefficient, so that the soil lateral pressure of soft or hard soil layer intersection exists
Mutation.When realistic simulation calculates, for the stratum drag of side, the stratum spring being correspondingly arranged should be respectively set different
Parameter；Simultaneously as the soil body bonds effect to tunnel segment structure presence in stratum, so that can generate during tunnel deformation tangential
Power, it is therefore desirable to radially and tangentially spring be respectively set when stratum spring is arranged, as shown in fig. 1.In addition, for tunnel bottom
Portion's soil layer often only acts on active earth pressure P to tunnel bottom2, therefore, the substrate passive earth pressure of tunnel structure bottom is past
It is past to be simulated by setting stratum spring.
S2: the slip field dynamics model of compound stratum is established
According to the Mohr's circle of stress of Plastic flow of soil stress state it is found that working as vertical suffered by the hard stratum of tunnel structure two sides
Load will generate failure by shear when reaching plastic limit state, and then be formed as shown in Figure 2 in the two sides of tunnel structure
Slip region.
Specifically, as shown in Figure 2, on Tunnel Passing the case where soft lower hard compound stratum, hard stratum and tunnel
Two crosspoints (i.e. B point and E point) two sides of road structure reach plastic limit state because being acted on by biggish vertical pressure,
And then the lower part soil body is caused to generate rupture slide surface, i.e., the face ACD as shown in Figure 2.According to Rankine's earth pressure theory and Tai Sha
Base passive earth pressure calculation method, it is found that the skid wire of above-mentioned slide surface is the just tangent curve with tunnel bottom, by
This can determine the sliding sector width b at left and right sides of tunnel, and can determine that slip region boundary can be in along with horizontal lineThe direction of angle generates angle of rupture.
Further, it is preferable to which the slip region in embodiment, which can correspond to, is divided into ABC active stressed zone, 2, BCD unfair stress area
Region.Wherein, two skid wires AC, the BC in the region ABC are respectively straight line, can be by mole answering according to Hencky first theorem
Power circle calculates the direct stress of each position and the size of shearing stress on AC line, and then the stress shape of the every bit in the area ABC can be obtained
State.Simultaneously as the region BCD belongs to the Riemann problem of sharpening, therefore its CD skid wire is considered as equation and isLog spiral, and then the shape of CD line can be drawn out, the direct stress on CD line and shearing stress can also be with
It is calculated.Furthermore it is preferred that assuming the smooth outer surface of tunnel structure in embodiment, that is, disregard between tunnel surface and the soil body
Friction；Meanwhile in addition to the borderline stress state of skid wire, it is also necessary to consider active earth pressure of the effect to lining cutting of gravity
Influence, the position of gravity W is the center of gravity of entire slide mass, so the area of slide mass and gravity point slide it is linear
After formula determines, can accurately it learn.
S3: the range of slip field is determined according to formation characteristics
Specifically, in corresponding engineering overview, the determination key for sliding wire shaped is to determine skid wire and tunnel structure
Cusp position, i.e., D point as shown in Figure 1, then sliding sector width b is found out by the position of point of contact D.
Further, when tunnel structure passes through compound stratum, there are three types of the positional relationships of tunnel structure and compound stratum
Situation is as follows respectively:
Situation 1: the soft of compound stratum, hard stratum line of demarcation are located above tunnel center line, as shown in Figure 3, in the feelings
In shape, the relevant calculation process of slip field model is as follows:
(1) polar coordinate system is established:
Assuming that straight line OB and the horizontal angle for crossing the center of circle are θ3, using BO straight line as x-axis, B point is polar coordinate center point
Polar coordinate system is established, then the point of the upper any position of circle can be come out by polar coordinate representation, r2=2acos θ2, in formula: a
=tunnel radius；θ2The angle of any location point F and B point connected straight line BF and x-axis on=circle.
Further, it according to the log spiral equation of skid wire CD, can correspond to the point of any position on CD line
It is come out by polar coordinate representation, i.e.,In formula: r0Length equal to BC can be counted by geometrical relationship
It calculates, i.e.,θ1Equal to the folder of arbitrary point E on log spiral and the connected straight line BE and BC of B point
Angle.According to θ1And θ2Geometrical relationship, obtain relational expression:
(2) tangent in D point and circumference according to curve CD, then it should meet following condition at D point:
1. equal length r1=r2:
2. the equal r ' of slope1=r '2:
Joint type 2 and formula 3, can obtain:
In angle of frictionWith the θ for indicating soft or hard soil layer boundary line position3After determination, the position of point of contact D can be obtained, then
It can incite somebody to actionSubstitute into θ2Calculation formula in, can obtainAnd it willθ2It substitutes into public
In formula 1, it can obtain:
In the situation known to tunnel radius a, can be acquired according to above-mentioned formula 5 sliding sector width b, and then determine it is soft or hard not
When equal stratum line of demarcation is located above tunnel center line, lower part hard stratum generates the concrete shape of the skid wire of sliding.
Situation 2: the soft of compound stratum, hard stratum line of demarcation are located at tunnel centerline, as shown in Figure 4, in the situation
In, the relevant calculation process of slip field model is as follows:
At this point, straight line OB and the horizontal angle for crossing the center of circle are 0, i.e. θ3=0.Substituted into formula 4 above it is found thatIt can be reduced to
When the internal friction angle in Practical ProjectWhen, the θ that is calculated1=90 °, reach in log spiral at this time
θ1The value limit；Work as angle of frictionWhen, as shown in Figure 4；And then sliding sector width b can be found out by the way that formula 5 is corresponding,
And then when determining that hard-soft heterogeneous ground line of demarcation is located at tunnel centerline, lower part hard stratum generates the tool of the skid wire of sliding
Shape.
Work as angle of frictionWhen, it is more than θ in log spiral1The value limit, at this moment log spiral also not with circle
Tunnel is tangent, and the specific discussion of such case is detailed in situation 3.
Situation 3: the soft of compound stratum, hard stratum line of demarcation are located at below tunnel center line, as shown in Figure 5, in the feelings
In shape, the relevant calculation process of slip field model is as follows:
At this point, straight line OB and the horizontal angle for crossing the center of circle are θ3< 0.Lead to θ1It is bigger than normal, exceed its value limit, such as
Fruit is in the value limit for reaching log spiral, when also not tangent with circular tunnel.It is so tangent with tunnel for skid wire DF, it cuts
Point is E.It is calculated by mathematics geometrical relationship, point of contact E and the line OE of tunnel central point are with horizontal angle
In situation 3, the calculation for sliding sector width b is different with the tangent mode in tunnel from log spiral, can
It is solved, and is obtained by mathematics geometrical relationship:
And then when determining that the soft of compound stratum, hard stratum line of demarcation are located at tunnel center line lower section, log spiral not with
When circular tunnel is tangent, lower part pan soil generates the concrete shape of the skid wire of sliding.
S4: the calculation formula of the native counter-force of tunnel bottom active is derived
Since the skid wire in the region ABC is straight line, then its stress is constant.Since the direct stress that acts on AB line and cutting is answered
Power is respectively as follows: σn=q1,τn=0, distinguished by the size that Mohr's circle of stress can calculate the direct stress on AC line and shearing stress
Are as follows:
Due to the radius and log spiral on each radius and log spiral on the log spiral BC of the region BCD
The normal of point of intersection atAngle, this point precisely due toIt is internal friction angle, therefore the normal stress on any unit of slide surface and rubs
Wipe power resultant force f also with this unit normal atAngle；Meanwhile the radial direction on the resultant direction on corresponding unit and the unit
It coincides.Because each radius on log spiral all passes through B point, therefore the resultant force f of direct stress and frictional force on CD line also leads to
Cross B point.In addition to this, the action direction of cohesive strength c and CD line are tangent.
Further, the small distribution in the big lower part in top is presented along camber line according to a certain percentage for the counter-force hypothesis on interior camber line BD
Rule.Correspondingly, the load intensity q of BD line top B point2Size it is related with the position of point of interface, and can carry out according to the following formula
It calculates:
Further, the load intensity on BD line at the X of any position are as follows:
qx=q2-λlxFormula 8
In formula, lxFor at the X of position at a distance from peak load intensity position B.
Under the premise of the position that hard-soft heterogeneous ground is located at tunnel determines, q2It is known, the only folding of load intensity
Subtracting coefficient lambda is unknown number, then passes through the moment of flexure and ∑ M to B pointB=0, the reduction coefficient λ of load intensity may finally be found out
Value.
The calculating process of λ is preferably as follows:
(1) moment of flexure of the load on AB line to B:
(2) moment of flexure of the load on AC line to B:
In formula:
(3) moment of flexure of the load on CD line to B: since CD line is helix, the resultant force of direct stress and frictional force on CD line
F does not have moment of flexure to B point by B point.The action direction of cohesive strength c and CD line are tangent, can be inquired by the unit of a length of ds, single
Cohesive strength on first body ds is cds, torque of the cds to B point are as follows:It is always glued along the face CD
Resultant couple of the poly- power to B point are as follows:
In formula:
(4) moment of flexure of the load on BD line (camber line in slip region) to B:
In formula: θ "=∠ BOD
(5) moment of flexure of the gravity to B:
MW=γ Ω d
In formula: γ be lower part hard stratum severe, Ω be slip region area, d be the slip region soil body center of gravity away from.If
On the left of B point, moment of flexure is positive center of gravity；Otherwise negative sign need to be added.
Then, by ∑ MB=MAB+MAC+MCD+MBD+MW=0, λ can be found out:
S5: the load intensity at the X of any position is calculated
Relevant parameter, formula 7, formula 9 are updated to respectively in formula 8, can be obtained under soft lower hard compound stratum
The magnitude of the active earth pressure generated when stratum slides to tunnel bottom lining cutting is covered, taking its counter-force is compound stratum tunnel
Substrate load is overlapped when skid wire overlaps at left and right sides of tunnel.
In a specific embodiment, the setting situation of tunnel structure is as shown in figures 6 and 7, wherein Fig. 6 is shown
Section situation is tested, the load that Fig. 7 shows the section calculates mode.Specifically, Tunnel Passing muck soil, Extra-fine sand, cobble
The compound stratum that sand, middle sand are constituted, subjacent bed are middle layer of sand, and tunnel top is about 12m lower than the height of level ground.
At this point, expression skid wire is calculated according to slip field dynamics model, stratum physical and mechanical parameter and tunneling characteristics
With the cusp position and sliding sector width b of tunnel structure.The radius a=5.4m in tunnel in this section, lower part hard stratum it is interior
Angle of frictionIndicate the θ of soft or hard soil layer boundary line position3=34 °, it can be corresponded to according to formula 1 and formula 4 and θ is calculated1=
50 °, θ2=34 °.It can be corresponded to by formula 5 again and tunnel is calculated slide sector width b=4.667m, the cunning of you can get it this section
Field of line range.
Further, tunnel bottom actively soil is obtained according to the slip field of tunnel cross-section at this time diagram 7 and formation characteristics
The numerical value of parameter needed for counter-force calculation formula: q1=244.800kPa, q2=57.377kPa, τ1=72.786kPa, σ1=
157.004kPa θ "=∠ BOD=111 °, Ω=16.033m2, d=1.795m.
Then above-mentioned parameter is substituted into formula 9, reduction coefficient λ=1.231 for obtaining load intensity can be corresponded to, and according to formula
8 can correspond to the radial force q under calculating bottom most3=44.496kPa.To obtain Tunnel Base active earth pressure size and
Sphere of action, as shown in Figure 7.
Further, the meter by the substrate load calculation method for passing through compound stratum tunnel in the present invention will be used to obtain
Result is calculated compared with the calculated result obtained using existing modified routine method, comparing result is as shown in Figure 8, by being not difficult in diagram
Find out, the load mode of existing modified routine method excessively exaggerate substrate by dynamical reaction, cause calculated soil pressure and multiple
It closes the practical status under loading in soil layer tunnel bottom not being inconsistent, in contrast, be calculated using the substrate load calculation method in the present invention
Soil pressure and measured value are more identical, the left and right sides payload values compared with modified routine method load mode closer to measured value,
Although more bigger than actual measurement soil pressure at tunnel bottom, difference is only 3.2%, for this is compared with existing modified routine method,
The accuracy of calculated result is substantially improved.
It is suitable for passing through the substrate load calculation method in compound stratum tunnel in the present invention, step is simple, can effective mould
It is quasi- to calculate its substrate load when tunnel structure passes through compound stratum, so that the result and measured value that calculate Tunnel Base load are more
Be it is close, be more in line with the actual forced status that tunnel is located in compound stratum, be Tunnel Passing compound stratum when substrate lotus
It carries and accurately and reliably calculation method is provided, it is scientific strong to guarantee construction and the operation safety in tunnel, before there is preferable application
Scape and promotional value.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (4)
1. a kind of substrate load calculation method suitable for passing through compound stratum tunnel, which comprises the steps of:
S1: obtaining the exploration parameter in tunnel, and the exploration parameter includes: the distance between tunnel top and level ground, compound
The positional relationship and tunnel two sides hard stratum of the horizontal boundary line of Soft Soil Layer and hard stratum and tunnel horizontal center line in stratum
Vertical load when internal friction angle and the hard stratum reach plastic limit state at the horizontal boundary line；
S2: the slip field of compound stratum is established according to the positional relationship of the horizontal boundary line of soft, hard stratum and tunnel horizontal center line
Mechanical model；The just tangent curve with tunnel bottom, the i.e. skid wire of hard stratum, institute are determined in the slip field dynamics model
Stating skid wire includes linear the first skid wire and the second skid wire in log spiral, respectively corresponds the master in slip field
Dynamic stress area and unfair stress area, the boundary line of two stressed zones are the first linear stress section, the both ends of the first stress section
Point is respectively the intersection point of the first skid wire and the second skid wire and the intersection point of the horizontal boundary line and tunnel circumference；
S3: according to the relative position in hard stratum line of demarcation and tunnel center line soft in compound stratum, in conjunction with skid wire and circumference phase
The position of the condition and point of contact cut calculates the width of slip region；
When the horizontal boundary line is not less than the tunnel horizontal center line, the width of slip region be can be calculated by the following formula:
In formula 1, b is the width of slip region；A is the radius of a circle in tunnel；For the angle of friction of hard stratum；θ1For the first line with
Angle formed by first stress section, first line are the continuous of arbitrary point and the first point of interface on the second skid wire, described the
One point of interface is the intersection point of the horizontal boundary line and tunnel circumference；
When the horizontal boundary line is lower than the tunnel horizontal center line, the width of slip region be can be calculated by the following formula:
In formula 2, b is the width of slip region；A is the radius of a circle in tunnel；For the angle of friction of hard stratum；θ3For the second line with
The angle of tunnel horizontal center line, second line are the line of the first point of interface and the tunnel center of circle, θ3< 0；
S4: calculating the load intensity that tunnel is born at first point of interface, and calculation formula is as follows:
In formula 3, q2For the load intensity at first point of interface；q1Reach at the horizontal boundary line for the hard stratum
Vertical load when plastic limit state；
The load intensity on circumference being had a common boundary due to tunnel with hard stratum is subtracted with the increase with the first point of interface distance
Small, then the load intensity of any position can be counted by following formula between the first point of interface and point of contact on tunnel circumference
It calculates:
qx=q2-λlx(formula 4)
In formula 4, qxTake up an official post for camber line in slip region the load intensity anticipated at the X of position；q2For the load intensity at the first point of interface；
Lx be position X and the first point of interface circumferentially at a distance from；λ is the reduction coefficient of load intensity.
2. according to claim 1 be suitable for passing through the substrate load calculation method in compound stratum tunnel, wherein described the
Arbitrary point can be calculated by the following formula at a distance from the first point of interface on two skid wires:
In formula 5, r0For the length of the first stress section；θ '=θ1。
3. the substrate load calculation method according to claim 2 for being suitable for passing through compound stratum tunnel, wherein step S3
The derivation process of Chinese style 1 may include following steps:
S31: using the first point of interface as polar coordinate center point, the line in the first point of interface and the tunnel center of circle is that x-axis establishes polar coordinates
System, and following formula can be obtained according to geometrical relationship:
In formula 6, θ2For the angle of the 4th line and x-axis, the 4th line be on the tunnel circumference contacted with slip region arbitrary point with
The line of first point of interface；
S32: according to second skid wire and the tangent condition of tunnel circumference, θ is calculated1Size, formula is as follows:
S33: joint type 6 and formula 7, and in conjunction with second skid wire and the tangent condition of tunnel circumference, the formula of deriving can be corresponded to
1。
4. the substrate load calculation method described in any one of claim 1 to 3 for being suitable for passing through compound stratum tunnel,
Wherein, the reduction coefficient λ of load intensity can carry out derivation calculating by the moment of flexure at the first point of interface and for 0, i.e.,
∑MB=MAB+MAC+MCD+MBD+MW=0 (formula 8)
In formula 8, MBFor the moment of flexure of the first point of interface；MABIt is the load on horizontal boundary line to the moment of flexure of the first point of interface；MACFor
The moment of flexure of load on first skid wire to the first point of interface；MCDIt is the load on the second skid wire to the curved of the first point of interface
Square；MBDIt is the load on camber line in slip region to the moment of flexure of the first point of interface；MWIt is gravity to the moment of flexure of the first point of interface.
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