CN109359316A - The horizontal layered rock interlayer cohesive strength calculation method of simple beam structure - Google Patents
The horizontal layered rock interlayer cohesive strength calculation method of simple beam structure Download PDFInfo
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Abstract
The invention discloses the horizontal layered rock interlayer cohesive strength calculation methods of simple beam structure, freely-supported beam model after the tunnel roof mechanics model of different construction stages to be equivalent to excavation disturbance, while proposing the computation model of horizontal layered rock interlayer cohesive strength and the specific formula for calculation of cohesive strength；By the theoretical model for being implanted into horizontal layered rock interlayer cohesive strength in traditional excavation width model, the horizontal layered rock tunnel roof critical span consistent with practice of construction has been obtained, has been had great importance for the design and construction of Guidance Levels stratiform surrounding rock tunnel.
Description
Technical field
The invention belongs to technical field of tunnel construction in civil engineering, and in particular to a kind of level for considering interlayer cohesive strength
The horizontal layered rock interlayer cohesive strength that stratiform surrounding rock tunnel roof safety excavates simple beam structure in span calculation method calculates
Method.
Background technique
Beded rock mass is a kind of sedimentary rock with bedded structure.Whole world beded rock mass distributed pole is wide, and it is total to account for about land
The 66% of area.Beded rock mass distribution in China's is wider, reaches the 77% of national territorial area, is concentrated mainly on southwest, Central China and northern Shensi
Equal areas.Beded rock mass since with typical layer structure, not only deformation and intensity property have apparent anisotropy, and
And rock mass damage mechanism and mode are also significantly different from other rock mass.The deformation and failure characteristics of beded rock mass are mainly by rock stratum group
It closes and structural plane control often becomes extremely complex engineering problem under construction disturbance.Especially horizontal layer rock mass, by
It is in parallelly distribute in structural plane, causes it with apparent transverse isotropy, during constructing tunnel, arch easily occurs
The engineering problems such as chip off-falling falling rocks, absciss layer, bending or even partial collapse, out break.Arch chip off-falling falling rocks is horizontal layered rock tunnel
Common fault in road construction, seriously threatens construction safety, leads to casualties, increased costs, construction delay.
With the rapid development of China's communication, there is a large amount of Tunnel Engineering, inevitably encounter level
Stratiform surrounding rock tunnel, such as the Xishan Tunnel of romote antiquity high speed, the windburn mountain tunnel of often the sparrow small stream tunnel of lucky high speed, the sharp railway that changes
Deng.By many years tackling of key scientific and technical problems and engineering practice, some experiences are had accumulated, achieve some scientific achievements, but horizontal layer encloses
Engineering problem in rock constructing tunnel is not still solved effectively.To find out its cause, mainly to horizontal layered rock tunnel top
Plate mechanical characteristic lacks further investigation, does not establish reasonable horizontal layered rock tunnel mechanics computation model.With common rocks
Tunnel is compared, and the vault stability in horizontal layered rock tunnel is most important, and horizontal layered rock has apparent level
Layer structure and layered combinations thereof feature, Mechanical Characters of Composite Ground difference between each rock stratum considerably beyond their difference in terms of thickness, and
Single layer structure is compared, and interlayer cohesive strength is stronger.Therefore, reasonable tunnel roof mechanics model is established, can be horizontal layer
Surrounding rock tunnel stability analysis provides basis, and solves the key of engineering problem in horizontal layered rock constructing tunnel.
Currently, domestic and foreign scholars have carried out a large amount of research to horizontal layered rock tunnel mechanics computation model.It is overall next
It sees, mainly uses Slab, beam model, stratified half-space model and mole-coulomb criterion and Hoek-Brown criterion
Tunnel roof mechanical behavior is analyzed.Although having obtained some achievements, it generally ignores top in detail design
Slate body interlayer cohesive strength, the model for different phase of constructing and the practical goodness of fit be not high so that in constructing tunnel critical across
Degree parameter calculating differs greatly with practice of construction scene, affects construction cost and progress.
Summary of the invention
It is abundant in calculating the invention proposes a kind of horizontal layered rock interlayer cohesive strength calculation method of simple beam structure
Influence of the interlayer cohesive strength of tunnel roof mechanics model and horizontal layered rock to span is excavated is considered, so that calculating
As a result more meet Practical Project, the design and construction to horizontal layered rock tunnel have important directive significance, and are effectively reduced
Construction cost, improves tunnelling progress.
A kind of horizontal layered rock interlayer cohesive strength calculation method of simple beam structure of the invention, comprising the following steps:
[1] horizontal layered rock is taken to excavate two layers of rock mass sample of region roof supporting or more, measurement obtains upper layer respectively
The elasticity modulus of rock mass is E1Elasticity modulus with lower layer rock mass is E2, in E2<E1In the case where, according to step [2] and step
[3] interlayer cohesive strength g is calculated_ freely-supported；
[2] upper layer rock mass and lower layer's rock mass are equivalent to respectively to the upper layer beam and lower layer's beam of simple beam structure support, and pressed
The load q of upper layer beam is calculated separately according to the actual parameter of site operationOn, lower layer's beam load qUnder, upper layer beam amount of deflection ωOnWith under
The amount of deflection ω of layer beamUnder, wherein
qOn=q1+γ1h1+g_ freely-supported；
qUnder=q1+γ1h1+γ2h2-g_ freely-supported；
In formula, q1For the vertical active force of country rock, upper layer depth of stratum is h1, bulk density γ1, lower layer's depth of stratum is h2, hold
Weight is γ2, g_ freely-supportedFor the interlayer cohesive strength of simple beam structure；Upper layer beam the moment of inertia is I1, lower layer's beam the moment of inertia is I2, b1For upper layer
The longitudinal length of beam, b2For the longitudinal length of lower layer's beam, a is that roof rock mass excavates span, the office that x is established by top plate beam section
X-axis coordinate value in portion's coordinate system；
[3] under the conditions of cooperative transformation, the amount of deflection ω of upper layer beamOnWith the amount of deflection ω of lower layer beamUnderIt is identical, it is calculated
The as interlayer cohesive strength of simple beam structure.
The horizontal layered rock interlayer cohesive strength calculation method of above-mentioned simple beam structure, in step [2]
q1=γ H
H=0.45 × 2s-1ω
Wherein H is the height equivlent of tunnel load, and γ is the severe (kN/m of country rock3), s is Grades of Surrounding Rock, and ω is width
Influence coefficient, ω=1+i (B-5)；The pressure from surrounding rock increment rate that i is that B is every when increasing 1m, B is tunnel width, when B < 5m, takes i
=0.2；When B > 5m, i=0.1 is taken.
The advantageous effects that the present invention has are as follows:
(1) present invention combines the detailed process of conventional tunnel construction, by the tunnel roof mechanics meter of different construction stages
It calculates model to be equivalent to excavate the freely-supported beam model after the anchoring beam model of initial stage and excavation disturbance, so that model is more in line with
The practice of construction process in tunnel.
(2) present invention calculates theoretical model for excavation width in current constructing tunnel and practice of construction difference is biggish asks
Topic analyzes the problem of existing excavation width calculates theoretical model, and it is viscous innovatively to propose horizontal layered rock interlayer
The computation model of poly- power and the specific formula for calculation of cohesive strength；It is enclosed by being implanted into horizontal layer in traditional excavation width model
The theoretical model of cohesive strength between rock stratum, obtained the horizontal layered rock tunnel roof critical consistent with practice of construction across
Degree, has great importance for the design and construction of Guidance Levels stratiform surrounding rock tunnel.
(3) interlayer cohesive strength model of the invention is easily understood, and the tunnel roof critical span formula derived
And alphabetical meaning in pilot process formula is clear, relevant parameter is easily obtained, there is stronger operability, and by with
The deformation and compared analysis by force parameter that Practical Project (crossbeam loess hills tunnel) monitors, demonstrate the correctness of model.
Detailed description of the invention
Fig. 1 is the present invention in tunnel excavation initial stage country rock diagrammatic cross-section；
Fig. 2 is the present invention in tunnelling intermediate stage country rock diagrammatic cross-section；
Fig. 3 is the present invention in tunnelling later stage country rock diagrammatic cross-section；
Fig. 4 is that tunnel surrounding of the present invention anchors beam model beam body stress sketch；
Fig. 5 is that tunnel surrounding of the present invention anchors beam model beam body shear diagram；
Fig. 6 is that tunnel surrounding of the present invention anchors beam model beam body bending moment diagram；
Fig. 7 is tunnel surrounding beam body model representative section coordinate system axis figure of the present invention；
Fig. 8 is tunnel surrounding simply supported beam model beam body stress sketch of the present invention；
Fig. 9 is tunnel surrounding simply supported beam model beam body shear diagram of the present invention；
Figure 10 is tunnel surrounding simply supported beam model beam body bending moment diagram of the present invention.
Appended drawing reference are as follows: 3-cracks；4-tunnel contours；5-upper layer rock mass；6-lower layer's rock mass.
Specific embodiment
In order to which objects and advantages of the present invention are more clearly understood, below in conjunction with attached drawing and case history, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
Fig. 1-3 gives tunnel excavation initial stage, intermediate stage and later stage country rock diagrammatic cross-section, 5 and 6 in figure
Upper layer rock mass and lower layer's rock mass are respectively indicated, 3 excavate the crack in intermediate stage and the formation of later stage rock mass, and 4 indicate tunnel
Profile.
In Fig. 1, the hair wide open digging initial stage in tunnel, the disturbance that country rock is subject to is smaller, the support of tunnel roof rock mass both ends
Position rock mass still has preferable integrality, and more than top plate two layers of rock mass is constrained by upper and lower rock stratum at this time, is neither able to rotate, also not
It can move up and down, therefore tunnel roof rock mass can be reduced to anchoring beam model as shown in Figure 1.Further, due to anchor
Gu Liang bears biggish tensile stress on anchored end top, in addition the interference of tunnel ensuing blast construction, so that anchoring beam upper end reaches
To the ultimate tensile of rock mass, so that the cracking starts perforation from top to down carries out (as shown in Figure 2), two layers of rock of final top plate
The end of body is cracked perforation (as indicated at 3), and two layers of beam body can be rotated along respective end at this time, then tunnel top at this time
Plate it is visual be freely-supported beam model.
It should be noted that excavating the functional relation that span a and tunnel width B is not determined in figure, tunnel width B is only
Width at tunnel maximum excavation line, for calculating country rock vertical pressure, and excavates span a and refers to tunnel tunnel roof rock mass
Face sky span, is that simulation is simplified to tunnel roof rock mass.
In the anchoring beam model of Fig. 1, design parameter assumes as follows: tunnel excavation span is B, and it is a that span is excavated on top；
First layer depth of stratum is h from top to bottom at the top of tunnel excavation1, rock stratum elasticity modulus is E1, Poisson's ratio μ1, cohesive force c1,
Bulk density is γ1, internal friction angle isSecond layer depth of stratum is h2, rock stratum elasticity modulus is E2, Poisson's ratio μ2, cohesive force is
c2, bulk density γ2, internal friction angle is
In traditional tunnel excavation design and simulation calculate, influence of the structure of rock stratum to parameter is not considered generally,
So that notional result and the practical biggish difference of generation.It is viscous that the present invention innovatively proposes horizontal layered rock interlayer in calculating
The computation model of poly- power and the specific formula for calculation of cohesive strength.It needs to make explanations: if E1>E2, i.e., first layer rock stratum is rigid
Degree is greater than second layer rock stratum, then there are cohesive strengths between two layers of rock stratum, and first layer rock mass is by downward cohesive strength, second layer rock
Body is by upward cohesive strength.If E1<E2, i.e., first layer rock stratum rigidity is less than second layer rock mass layer rock stratum, then first layer rock stratum meeting
Downward additional force is generated to second layer rock stratum, cohesive strength is not present at this time, therefore this example is only to E1>E2The case where account for.
The stress condition of upper layer rock stratum is analyzed first.Excavation initial stage country rock is in lesser state of disturbance, therefore will at this time
Tunnel roof model simplification is anchoring beam model, and stress sketch are as shown in Figure 4.It acts in equivalent beam body and is vertically evenly distributed with lotus
Carry q (kN/m2) it is vertical active force q by country rock1(kN/m2), rock stratum weight stress q2(kN/m2) and interlayer cohesive strength be g
(kN/m2) be formed by stacking.Active force in horizontal direction is then the horizontal adjoining rock pressure q of country rock3(kN/m2).Vertical uniform load
The shearing of generation is acted in equivalent beam body by q as shown in figure 5, moment of flexure is as shown in Figure 6.
Further, to q1、q2、q3Specifically solved:
To q1Solve as follows:
q1=γ H
H=0.45 × 2s-1ω
In formula: H is the height equivlent of tunnel load, and γ is the severe (kN/m of country rock3)；S is Grades of Surrounding Rock；ω is width
Influence coefficient, ω=1+i (B-5)；The pressure from surrounding rock increment rate that i is that B is every when increasing 1m, B is tunnel width, when B < 5m, takes i
=0.2；When B > 5m, i=0.1 is taken.
To q2Solve as follows:
q2=γ1h1
q3=λ q1
In formula: λ is lateral pressure coefficient；Angle of friction (°) is calculated for country rock.
Then act on the vertical uniform load q in equivalent beam body are as follows:
Q=q1+q2+g
The internal force for further analyzing Equivalent Beam, at the spaning middle section (1-1) of the Equivalent Beam of Fig. 4
In formula: M1-1For the moment of flexure (kNm) at spaning middle section (1-1)；IzFor the moment of inertia of spaning middle section (1-1)；σ1-1
For the direct stress at spaning middle section (1-1)；F1sFor shearing suffered by the section (kN)；Other symbols are the same.Y is in representative section
Coordinate system axis, referring to Fig. 7.
When y is maximized, i.e. ymax=h1When/2, the direct stress that moment of flexure generates is also maximum value, then at section (1-1)
Upper limb and lower edge direct stress are as follows:
σ in formula1-1 pressureFor section upper limb compression, σ1-1 is drawnFor section lower edge tensile stress.
Act on the maximum (normal) stress of Equivalent Beam spaning middle section (1-1) upper limb
σOn 1-1=σ1-1 pressure+q3
Act on the maximum (normal) stress σ of Equivalent Beam spaning middle section (1-1) lower edgeUnder 1-1Are as follows:
σUnder 1-1=σ1-1 is drawn-q3
And in Fig. 4 at the end cross-sectional (2-2) of Equivalent Beam
In formula: M2-2For the moment of flexure (kNm) at end cross-sectional (2-2)；IzFor the moment of inertia of end cross-sectional (2-2)；σ2-2
For the direct stress at end cross-sectional (2-2)；F2sFor shearing suffered by the section (kN)；Other symbols are the same.
When y is maximized, i.e. ymax=h1/ 2, the direct stress that moment of flexure generates also should be maximum value, then cut in equivalent beam end
The upper limb and lower edge direct stress in face (2-2) are as follows:
σ in formula2-2 is drawnFor section upper limb tensile stress, σ2-2 pressureFor section lower edge compression.
Act on the maximum (normal) stress σ of Equivalent Beam end cross-sectional (2-2) upper limbOn 2-2Are as follows:
σOn 2-2=σ2-2 is drawn-q3
Act on the maximum (normal) stress σ of Equivalent Beam end cross-sectional (2-2) lower edgeUnder 2-2Are as follows:
σUnder 2-2=σ2-2 pressure+q3
Shear stress at Equivalent Beam end cross-sectional (2-2) are as follows:
F in formula2sFor shear stress suffered by Equivalent Beam end cross-sectional (2-2),Equivalent Beam end cross-sectional (2-2) is to neutral axis
Static moment, other symbols are the same.
Maximum shear stress is at the center end cross-sectional (2-2) when i.e. y=0, shear stress are as follows:
It is calculated above as can be seen that calculating the active force for knowing to be subject at anchoring most by the actual loading for anchoring beam
Greatly.Moreover, because the tensile strength of rock mass is much smaller than compression strength, so influenced excavating the later period by blast working, compared with
The rock mass on the anchored end top of big tensile stress reaches tensile failure at first, cracking as shown in Figures 2 and 3 is generated, to make tunnel
Road top plate mechanical model is converted to simply supported beam.
The stress sketch of freely-supported beam model as shown in figure 8, shear diagram as shown in figure 9, bending moment diagram is as shown in Figure 10.
In freely-supported beam model, force analysis process is identical as anchoring beam.Anchor beam model and freely-supported beam model difference portion
The stress value of position see the table below listed:
Further, the interlayer cohesive strength of two kinds of beam models is calculated.
It is assumed that two layers of beam is cooperative transformation state, i.e. its amount of deflection is identical.According to structural mechanics theory, beam deflection formula is anchored
Are as follows:
Wherein a is that roof rock mass excavates span, the x-axis coordinate value in the local coordinate system that x is established by top plate beam section.
The load q that upper layer beam is subject toOnFor vertical strata pressure q1, weight stress γ1h1With the resultant force of cohesive strength g are as follows:
qOn=q1+γ1h1+g
The load q that lower layer's beam is subject toUnderFor vertical strata pressure q1+γ1h1, weight stress γ2h2With the resultant force of cohesive strength g
Are as follows:
qUnder=q1+γ1h1+γ2h2-g
Upper layer beam deflection are as follows:
Lower layer's beam deflection are as follows:
According to compatible deformation condition (upper and lower level beam deflection is identical), cohesive strength g is obtained_ anchoringAre as follows:
By upper layer beam the moment of inertia and lower layer's beam the moment of inertiaAbove formula is substituted into respectively, can obtain cohesive strength g_ anchoringAre as follows:
Simply supported beam deflection formula are as follows:
The amount of deflection of upper layer beam are as follows:
The amount of deflection of lower layer's beam are as follows:
Similarly with anchoring beam model, according to compatible deformation condition (upper and lower level beam deflection is identical), cohesive strength g is obtained_ freely-supportedAre as follows:
It is analyzed according to above in relation to constructing tunnel stage different beam model Force Calculation, in anchoring beam anchoring end section
Top margin, simply supported beam spaning middle section bottom edge suffered by tensile stress it is maximum, with the gradually application of load, corresponding site reaches at first
The ultimate tensile intensity of rock mass, that is, reach destruction at first.Critical span in its destruction, it can by corresponding critical
State computation.
According to structural mechanics theory, anchoring back plate critical load is
Anchoring the critical span of back plate is
Simply supported beam span centre bottom edge critical load is
The critical span of simply supported beam top plate is
Finally, incorporation engineering actually verifies the critical span formula proposed.
Country rock relevant parameter is as follows:
It should be noted that fully consider excavation initial stage in the calculating of tunnel critical span and excavate later period rank
Requirement under section anchoring two kinds of model cases of beam and simply supported beam, it is to be ensured that excavate the calculated value of span, two can be met simultaneously
The requirement of kind model structure.Under normal conditions, critical span takes the minimum value of the theoretical calculation in two kinds of models.
Specific verifying example is given below:
Crossbeam loess hills tunnel is separate tunnel, and corresponding country rock is IV grades；According to field geology sketch situation, top plate upper layer is taken
Rock mass sandstone h1=0.5m, lower layer rock mass mud stone h2The longitudinal width b of=0.05~0.1m, beam take unit length 1m；Lower layer's rock mass
Ultimate tensile strength [σt]=0.7MPa.E1=10Gpa, E2=5Gpa.The critical span of two kinds of beam models is calculated, as a result
It see the table below listed.
Calculated result shows: when considering interlayer cohesive strength, anchoring beam model critical span is 3.36~4.75m, letter
Branch beam model critical span is 2.74~3.88m；The minimum critical span in the tunnel is 2.74m under two kinds of models.Without
Consider interlayer cohesive strength when, anchoring beam model top plate critical span be 0.14~0.30m, freely-supported beam model critical across
Degree is 0.12~0.24m.And in practice of construction, when excavating 3~6m of span, there is flat-top phenomenon in vault in crossbeam loess hills tunnel, produces
Raw absciss layer and chip off-falling etc. are more than the situation that critical span just has, and illustrate that the present invention considers the top plate Mechanics Calculation mould of interlayer cohesive strength
Type more meets engineering practice, and the minimum critical span 2.74m being calculated matches with actual critical span.
And traditional computation model when not considering interlayer cohesive strength is then larger with Practical Project gap, therefore calculation method pair of the invention
Have great importance in the design and construction of Guidance Levels stratiform surrounding rock tunnel.
Claims (2)
1. the horizontal layered rock interlayer cohesive strength calculation method of simple beam structure, which comprises the following steps:
[1] horizontal layered rock is taken to excavate two layers of rock mass sample of region roof supporting or more, measurement obtains upper layer rock mass respectively
Elasticity modulus be E1Elasticity modulus with lower layer rock mass is E2, in E2<E1In the case where, it is counted according to step [2] and step [3]
Calculate interlayer cohesive strength g_ freely-supported；
[2] upper layer rock mass and lower layer's rock mass are equivalent to the upper layer beam and lower layer's beam of simple beam structure support respectively, and according to existing
The actual parameter of field construction calculates separately the load q of upper layer beamOn, lower layer's beam load qUnder, upper layer beam amount of deflection ωOnWith lower layer's beam
Amount of deflection ωUnder, wherein
qOn=q1+γ1h1+g_ freely-supported；
qUnder=q1+γ1h1+γ2h2-g_ freely-supported；
In formula, q1For the vertical active force of country rock, upper layer depth of stratum is h1, bulk density γ1, lower layer's depth of stratum is h2, bulk density is
γ2, g_ freely-supportedFor the interlayer cohesive strength of simple beam structure；Upper layer beam the moment of inertia is I1, lower layer's beam the moment of inertia is I2, b1For upper layer beam
Longitudinal length, b2For the longitudinal length of lower layer's beam, a is that roof rock mass excavates span, and the part that x is established by top plate beam section is sat
X-axis coordinate value in mark system；
[3] under the conditions of cooperative transformation, the amount of deflection ω of upper layer beamOnWith the amount of deflection ω of lower layer beamUnderIt is identical, it is calculated
The as interlayer cohesive strength of simple beam structure.
2. the horizontal layered rock interlayer cohesive strength calculation method of simple beam structure according to claim 1, feature exist
In in step [2]
q1=γ H
H=0.45 × 2s-1ω
Wherein H is the height equivlent of tunnel load, and γ is the severe (kN/m of country rock3), s is Grades of Surrounding Rock, and ω is widths affect system
Number, ω=1+i (B-5)；The pressure from surrounding rock increment rate that i is that B is every when increasing 1m, B is tunnel width, when B < 5m, takes i=0.2；B
When > 5m, i=0.1 is taken.
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| WO2018086085A1 (en) * | 2016-11-12 | 2018-05-17 | 苏州大学 | Method for calculating earth pressure load on tunnel |
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| CN106198208A (en) * | 2016-06-21 | 2016-12-07 | 中电建路桥集团有限公司 | A kind of interbedding of soft and hard rocks surrounding rock tunnel method for analog construction considering layer reason effect |
| WO2018086085A1 (en) * | 2016-11-12 | 2018-05-17 | 苏州大学 | Method for calculating earth pressure load on tunnel |
| CN107526873A (en) * | 2017-07-27 | 2017-12-29 | 西安理工大学 | A kind of shallow tunnel wall damage pattern-recognition and Calculation of support method |
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