CN109359316B - Calculation method for cohesive force between horizontal layered surrounding rock layers of simply supported beam structure - Google Patents
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Abstract
The invention discloses a calculation method of cohesive force between horizontal layered surrounding rock layers of a simply supported beam structure, wherein mechanical calculation models of tunnel roofs in different construction stages are equivalent to a simply supported beam model after excavation disturbance, and meanwhile, a calculation model of the cohesive force between the horizontal layered surrounding rock layers and a specific calculation formula of the cohesive force are provided; by implanting a theoretical model of cohesive force between horizontal layered surrounding rock layers into a traditional excavation width model, the critical excavation span of the top plate of the horizontal layered surrounding rock tunnel consistent with actual construction is obtained, and the method has important significance for guiding the design and construction of the horizontal layered surrounding rock tunnel.
Description
Technical Field
The invention belongs to the technical field of tunnel construction in civil engineering, and particularly relates to a horizontal layered surrounding rock interlayer cohesive force calculation method of a simply supported beam structure in a horizontal layered surrounding rock tunnel roof safe excavation span calculation method considering interlayer cohesive force.
Background
A stratified rock mass is a sedimentary rock with a stratified structure. The stratified rock mass is widely distributed all over the world and occupies about 66 percent of the total land area. The stratified rock mass in China is distributed more widely, reaches 77% of the territory area of China, and is mainly concentrated in regions such as southwest, China, northern Shaanxi and the like. Because of the typical layered structure, the layered rock has obvious anisotropy in deformation and strength properties, and the rock failure mechanism and mode are obviously different from other rocks. The deformation and destruction characteristics of the stratified rock mass are mainly controlled by rock stratum combination and structural planes, and the stratified rock mass often becomes a very complicated engineering problem under construction disturbance. Especially, the horizontal stratified rock has obvious transverse isotropy due to the parallel distribution of the structural planes, and the engineering problems of lump falling, rock falling, bed separation, bending, even local collapse, over excavation and the like easily occur in the arch part in the tunnel construction process. The arch part chipping and falling rocks are common diseases in the construction of horizontal layered surrounding rock tunnels, seriously threaten the construction safety, and cause personal casualties, increased cost and delayed construction period.
With the rapid development of the traffic industry in China, a large amount of tunnel engineering appears, and horizontal layered surrounding rock tunnels such as Taigu high-speed west tunnels, very-high-speed que xi tunnels, and volcanic tunnels of Yuli railways are inevitably encountered. Through years of scientific and technological attack and engineering practice, some experiences are accumulated, some scientific achievements are obtained, but the engineering problem in the construction of the horizontal layered surrounding rock tunnel is still not effectively solved. The reason is that the stress characteristics of the top plate of the horizontal layered surrounding rock tunnel are not deeply researched, and a reasonable mechanical calculation model of the horizontal layered surrounding rock tunnel is not established. Compared with a common rock tunnel, the vault stability of the horizontal layered surrounding rock tunnel is of great importance, the horizontal layered surrounding rock has obvious horizontal layered structure and layered combination characteristics, the mechanical property difference between rock layers is far more than the difference of the rock layers in the aspect of layer thickness, and compared with a single-layer structure, the interlayer cohesive force is stronger. Therefore, a reasonable tunnel roof mechanical calculation model is established, a foundation can be provided for stability analysis of the horizontal layered surrounding rock tunnel, and the method is also a key for solving engineering problems in horizontal layered surrounding rock tunnel construction.
At present, scholars at home and abroad carry out a great deal of research on a mechanical calculation model of a horizontal layered surrounding rock tunnel. In a general view, a plate model, a beam model, an elastic layered semi-space model, a mole-coulomb criterion and a Hoek-Brown criterion are mainly adopted to analyze the mechanical behavior of the tunnel roof. Although some achievements are obtained, the cohesive force between roof rock mass layers is generally ignored in the construction design, the model and actual goodness of fit at different construction stages is not high, so that the difference between the critical excavation span parameter calculation and the actual construction site in the tunnel construction is large, and the construction cost and the construction progress are influenced.
Disclosure of Invention
The invention provides a method for calculating the interlayer cohesive force of horizontal layered surrounding rocks of a simply supported beam structure, wherein the influence of a tunnel top plate mechanical calculation model and the interlayer cohesive force of the horizontal layered surrounding rocks on the excavation span is fully considered in the calculation, so that the calculation result is more in line with the actual engineering, the method has important guiding significance on the design and construction of horizontal layered surrounding rock tunnels, the construction cost is effectively reduced, and the tunnel excavation progress is improved.
The invention discloses a method for calculating cohesive force between horizontal layered surrounding rock layers of a simply supported beam structure, which comprises the following steps of:
【1】 Taking two layers of rock mass samples above a supporting top plate of a horizontal layered surrounding rock excavation area, and respectively measuring to obtain the elastic modulus E of an upper layer rock mass 1 And the elastic modulus of the lower rock mass is E 2 At E 2 <E 1 In the case of (1), the interlayer cohesion g is calculated according to the step [ 2 ] and the step [ 3 ] Brief support ；
【2】 Respectively equating the upper rock mass and the lower rock mass as an upper beam and a lower beam supported by a simply supported beam structure, and respectively calculating the load q of the upper beam according to the actual parameters of field construction Upper part of Load q of lower beam Lower part Upper beam deflection omega On the upper part And the deflection omega of the lower layer beam Lower part Wherein
q On the upper part ＝q 1 +γ 1 h 1 +g Brief support ；
q Lower part ＝q 1 +γ 1 h 1 +γ 2 h 2 -g Brief support ；
In the formula, q 1 The vertical acting force of the surrounding rock is provided, and the thickness of the upper rock layer is h 1 Volume weight of gamma 1 Thickness of lower rock layer is h 2 Volume weight of gamma 2 ，g Brief support The interlayer cohesive force of the simply supported beam structure; moment of inertia of the upper beam is I 1 The lower beam has a moment of inertia of I 2 ，b 1 Is the longitudinal length of the upper beam, b 2 The longitudinal length of a lower layer beam is defined, a is the top plate rock mass excavation span, and x is an x-axis coordinate value in a local coordinate system established by the top plate beam section;
【3】 Deflection omega of upper beam under cooperative deformation condition On the upper part And the deflection omega of the lower layer beam Lower part Same, calculated to obtain
Namely the interlayer cohesive force of the simply supported beam structure.
The method for calculating the cohesive force between the horizontal layered surrounding rock layers of the simply supported beam structure comprises the step (2)
q 1 ＝γH
H＝0.45×2 s-1 ω
Wherein H is the equivalent height of the tunnel load, and gamma is the weight of the surrounding rock (kN/m) 3 ) S is the surrounding rock level, ω is the width influence coefficient, ω is 1+ i (B-5); i is the surrounding rock pressure increase rate when B increases by 1m, B is the tunnel width, and when B is less than 5m, i is 0.2; when B is more than 5m, i is 0.1.
The invention has the following beneficial technical effects:
(1) the method combines the concrete process of the conventional tunnel construction, and enables the tunnel roof mechanical calculation models in different construction stages to be equivalent to the anchoring beam model in the initial excavation stage and the simply supported beam model after excavation disturbance, so that the models are more consistent with the actual construction process of the tunnel.
(2) Aiming at the problem that the difference between an excavation width calculation theoretical model and actual construction in the current tunnel construction is large, the invention analyzes the problems existing in the existing excavation width calculation theoretical model and innovatively provides a calculation model of the cohesion force between horizontal layered surrounding rock layers and a specific calculation formula of the cohesion force; by implanting the theoretical model of the cohesion between the horizontal layered surrounding rock layers into the traditional excavation width model, the critical excavation span of the horizontal layered surrounding rock tunnel top plate consistent with the actual construction is obtained, and the method has important significance for guiding the design and construction of the horizontal layered surrounding rock tunnel.
(3) The interlayer cohesion model is simple and easy to understand, letters in a derived tunnel top plate critical excavation span formula and a middle process formula are definite in significance, relevant parameters are easy to obtain, strong operability is achieved, and the model correctness is verified through comparison and analysis of deformation and stress parameters monitored by actual projects (girder and loess hills tunnels).
Drawings
FIG. 1 is a schematic view of a section of a surrounding rock at an initial stage of tunnel excavation according to the invention;
FIG. 2 is a schematic cross-sectional view of the surrounding rock at an intermediate stage of tunneling according to the present invention;
FIG. 3 is a schematic cross-sectional view of the surrounding rock at the later stage of tunnel excavation according to the present invention;
FIG. 4 is a schematic diagram of the stress of the beam body of the tunnel surrounding rock anchoring beam model of the invention;
FIG. 5 is a beam body shear diagram of the tunnel surrounding rock anchoring beam model of the invention;
FIG. 6 is a beam body bending moment diagram of the tunnel surrounding rock anchoring beam model of the invention;
FIG. 7 is an axial view of an equivalent cross-sectional coordinate system of a tunnel surrounding rock beam model according to the present invention;
FIG. 8 is a schematic diagram of the stress of the beam body of the tunnel surrounding rock simply-supported beam model;
FIG. 9 is a shear diagram of a simple beam model of tunnel surrounding rock according to the invention;
FIG. 10 is a beam body bending moment diagram of the tunnel surrounding rock simply-supported beam model.
The reference signs are: 3-cracking; 4-tunnel profile; 5-upper rock mass; 6-lower rock mass.
Detailed Description
In order to make the objects and advantages of the invention more apparent, the invention is further described in detail below with reference to the accompanying drawings and engineering examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1-3 show the section schematic diagrams of surrounding rocks at the initial stage, the middle stage and the later stage of tunnel excavation, wherein 5 and 6 respectively represent an upper rock body and a lower rock body, 3 excavates cracks formed by the rock bodies at the middle stage and the later stage, and 4 represents a tunnel profile.
In figure 1, at the initial stage of tunnel cave excavation, the disturbance that the surrounding rock received is less, and tunnel roof rock mass both ends support position rock mass still has better integrality, and two-layer rock mass above the roof is retrained by upper and lower rock stratum at this moment, can not rotate, also can not move about from top to bottom, so can simplify tunnel roof rock mass to the anchor beam model as shown in figure 1. Furthermore, because the anchoring beam bears great tensile stress on the upper part of the anchoring end, and the interference of the subsequent blasting construction of the tunnel, the upper end of the anchoring beam reaches the tensile limit of the rock mass, and then the cracking starts to be run through from top to bottom (as shown in fig. 2), finally the end parts of the two layers of rock masses of the top plate are all cracked and run through (as shown in fig. 3), at the moment, the two layers of beam bodies can rotate along the respective end parts, and the tunnel top plate at the moment can be seen as a simply supported beam model.
It should be noted that, in the drawing, there is no definite functional relationship between the excavation span a and the tunnel width B, the tunnel width B is only the width at the maximum excavation line of the tunnel and is used for calculating the vertical pressure of the surrounding rock, and the excavation span a is the adjacent space span of the tunnel roof rock mass, and is a simplified simulation of the tunnel roof rock mass.
In the anchored beam model of fig. 1, the specific parameters are assumed as follows: the tunnel excavation span is B, and the upper excavation span is a; the thickness of the first rock stratum at the top-down of the tunnel excavation top is h 1 The elastic modulus of the rock formation is E 1 Poisson's ratio of μ 1 The adhesive force is c 1 Volume weight of gamma 1 Internal angle of friction of
Thickness of second layer rock layer is h 2 The elastic modulus of the rock formation is E 2 Poisson's ratio of μ 2 The adhesive force is c 2 Volume weight of gamma 2 Internal angle of friction of
In the traditional tunnel excavation design and simulation calculation, the influence of the structure of the rock stratum on the parameters is generally not considered, so that the theoretical result is greatly different from the actual result. The invention provides a calculation model of the cohesion force between horizontal layered surrounding rock layers and a specific calculation formula of the cohesion force in calculation. It should be explained that: if E 1 >E 2 That is, the rigidity of the first rock stratum is greater than that of the second rock stratum, cohesive force exists between the two rock strata, the first rock mass is subjected to downward cohesive force, and the second rock mass is subjected to upward cohesive force. If E 1 <E 2 That is, the rigidity of the first rock stratum is less than that of the second rock stratum, the first rock stratum will produce downward additional force to the second rock stratum, and no cohesive force exists, so that the embodiment is only for E 1 >E 2 The situation of (a) is considered.
The stress condition of the upper strata is firstly analyzed. The surrounding rock at the initial stage of excavation is in a small disturbance state, so that the tunnel roof model at the moment is simplified into an anchoring beam model, and the stress sketch of the anchoring beam model is shown in fig. 4. Vertically uniform load q (kN/m) acting on equivalent beam body 2 ) Is caused by vertical acting force q of surrounding rock 1 (kN/m 2 ) Self-weight stress q of rock formation 2 (kN/m 2 ) And interlayer cohesion of g (kN/m) 2 ) And (4) stacking. The horizontal force is the horizontal surrounding rock pressure q of the surrounding rock 3 (kN/m 2 ). The shearing force generated by the action of the vertically uniformly distributed load q on the equivalent beam body is shown in figure 5, and the bending moment is shown in figure 6.
Further, for q 1 、q 2 、q 3 Carrying out concrete solving:
to q is 1 The solution is performed as follows:
q 1 ＝γH
H＝0.45×2 s-1 ω
in the formula: h is the equivalent height of the tunnel load, and gamma is the weight of the surrounding rock (kN/m) 3 ) (ii) a s is the grade of surrounding rock; ω is the width influence coefficient, ω 1+ i (B-5); i is the surrounding rock pressure increase rate when B increases by 1m, B is the tunnel width, and when B is less than 5m, i is 0.2; when B is more than 5m, i is 0.1.
To q is 2 The solution is performed as follows:
q 2 ＝γ 1 h 1
q 3 ＝λq 1
in the formula: lambda is a lateral pressure coefficient;
the friction angle (°) was calculated for the surrounding rock.
Then the vertically uniform load q acting on the equivalent beam body is as follows:
q＝q 1 +q 2 +g
further analysis of the internal force of the equivalent beam, at midspan section (1-1) of the equivalent beam of FIG. 4
In the formula: m 1-1 Is bending moment (kN.m) at the midspan section (1-1); i is z Is the moment of inertia of the midspan section (1-1); sigma 1-1 Is the normal stress at the midspan section (1-1); f 1s The shear force (kN) to which the section is subjected; the other symbols are as before. y is the axis of the coordinate system on the equivalent cross-section, see fig. 7.
When y takes a maximum value, i.e. y max ＝h 1 At/2, the positive stress generated by the bending moment is also the maximum, and the positive stress at the upper edge and the lower edge of the section (1-1) is as follows:
in the formula sigma 1-1 pressure Is the compressive stress of the upper edge of the cross section, σ 1-1 pulling Is the tensile stress of the lower edge of the section.
Maximum positive stress acting on the upper edge of the cross section (1-1) of the equivalent beam
σ 1-1 thereon ＝σ 1-1 pressure +q 3
The maximum positive stress sigma acting on the lower edge of the midspan section (1-1) of the equivalent beam 1-1 is below Comprises the following steps:
σ 1-1 is below ＝σ 1-1 drawing -q 3
While the equivalent beam in fig. 4 is at the end section (2-2)
In the formula: m 2-2 Bending moment (kN.m) at the end section (2-2); i is z Is the moment of inertia of the end section (2-2); sigma 2-2 Is the normal stress at the end section (2-2); f 2s The shear force (kN) to which the section is subjected; the other symbols are as before.
When y takes a maximum value, i.e. y max ＝h 1 And 2, the positive stress generated by the bending moment is also the maximum value, and the positive stress at the upper edge and the lower edge of the equivalent beam end section (2-2) is as follows:
in the formula σ 2-2 drawing Is tensile stress of the upper edge of the cross section, σ 2-2 pressure Is the compressive stress of the lower edge of the section.
Maximum positive stress sigma acting on the upper edge of the equivalent beam end section (2-2) 2-2 to Comprises the following steps:
σ 2-2 thereon ＝σ 2-2 drawing -q 3
Maximum positive acting on the lower edge of the equivalent beam end section (2-2)Stress sigma 2-2 of Comprises the following steps:
σ 2-2 of ＝σ 2-2 pressure +q 3
The shear stress at the equivalent beam end section (2-2) is:
in the formula F 2s Is equivalent to the shearing stress on the end section (2-2) of the beam,
the static moment of the equivalent beam end section (2-2) to the neutral axis is as before.
When the maximum shear stress is at the center of the end section (2-2), i.e. y is 0, the shear stress is:
the calculation shows that the maximum acting force at the anchoring position can be obtained through the actual stress calculation of the anchoring beam. Moreover, because the tensile strength of the rock mass is far less than the compressive strength, the rock mass at the upper part of the anchoring end with larger tensile stress is firstly damaged in tension under the influence of blasting construction in the later period of excavation, and cracks as shown in figures 2 and 3 are generated, so that the tunnel roof mechanical model is converted into a simply supported beam.
The stress diagram of the simple supporting beam model is shown in fig. 8, the shearing diagram is shown in fig. 9, and the bending moment diagram is shown in fig. 10.
In the simply supported beam model, the stress analysis process is the same as that of the anchoring beam. The stress values of different parts of the anchoring beam model and the simply supported beam model are listed in the following table:
further, interlayer cohesion of the two beam models is calculated.
The beams in the two layers are assumed to be in a cooperative deformation state, namely the deflection of the beams is the same. According to the theory of structural mechanics, the deflection formula of the anchoring beam is as follows:
wherein a is the excavation span of the roof rock mass, and x is the coordinate value of the x axis in the local coordinate system established by the roof beam section.
Load q to which the upper beam is subjected On the upper part Is the vertical formation pressure q 1 Self-weight stress gamma 1 h 1 And cohesive force g are the following combined forces:
q on the upper part ＝q 1 +γ 1 h 1 +g
Load q to which the lower beam is subjected Lower part Is the vertical formation pressure q 1 +γ 1 h 1 Self-weight stress gamma 2 h 2 And cohesive force g are the following combined forces:
q lower part ＝q 1 +γ 1 h 1 +γ 2 h 2 -g
The deflection of the upper beam is as follows:
the deflection of the lower layer beam is as follows:
obtaining cohesive force g according to the coordinated deformation conditions (the deflection of the upper and lower beams is the same) Anchoring device Comprises the following steps:
the inertia moment of the upper beam and the inertia moment of the lower beam
Respectively substituted into the above formulas to obtain cohesive force g Anchoring device Comprises the following steps:
the formula of the deflection of the simply supported beam is as follows:
the deflection of the upper beam is as follows:
the deflection of the lower beam is as follows:
obtaining cohesive force g according to the coordinated deformation conditions (the deflection of the upper layer beam and the lower layer beam is the same) by the same principle as the anchored beam model Brief support Comprises the following steps:
according to the stress calculation analysis of the beam models aiming at different tunnel construction stages, the top edge of the section of the anchoring end of the anchoring beam and the bottom edge of the midspan section of the simply supported beam are subjected to the largest tensile stress, and along with the gradual application of the load, the corresponding part firstly reaches the tensile ultimate strength of the rock mass, namely, the corresponding part is firstly damaged. The critical span at which it is destroyed can be calculated from the corresponding critical state.
According to the theory of structural mechanics, the critical load of the top plate of the anchoring beam is
The critical span of the top plate of the anchoring beam is
The critical load of the simply supported beam across the middle bottom edge is
The critical span of the simply supported beam top plate is
And finally, verifying the proposed critical excavation span formula by combining engineering practice.
The relevant parameters of the surrounding rock are as follows:
it should be noted that, in the calculation of the critical excavation span of the tunnel, the requirements of the two models of the anchoring beam and the simply supported beam at the initial excavation stage and the later excavation stage are fully considered, and the theoretical calculation value of the excavation span is ensured to meet the requirements of the two models. Typically, the critical span takes the minimum of theoretical calculations in both models.
Specific examples of validation are given below:
the girder and loess hills tunnels are separated tunnels, and corresponding surrounding rocks are in grade IV; taking the rock sandstone h on the upper layer of the top plate according to the on-site geological sketch condition 1 0.5m, lower layer rock mass mudstone h 2 The length of the beam is 0.05-0.1 m, and the longitudinal width b of the beam is 1 m; ultimate tensile strength [ sigma ] of lower rock mass t ]＝0.7MPa。E 1 ＝10Gpa，E 2 5 Gpa. The critical span of the two beam models was calculated and the results are listed in the table below.
The calculation result shows that: when interlayer cohesive force is considered, the critical excavation span of the anchored beam model is 3.36-4.75 m, and the critical excavation span of the simply supported beam model is 2.74-3.88 m; the minimum critical span of the tunnel under both models is 2.74 m. And when the interlayer cohesive force is not considered, the critical excavation span of the top plate of the anchored beam model is 0.14-0.30 m, and the critical excavation span of the simply supported beam model is 0.12-0.24 m. In actual construction, when the excavation span of the girder and loess hills tunnel is 3-6 m, the arch crown is flat-topped, and the conditions that separation, block falling and the like exceed critical span are generated, which shows that the top plate mechanical calculation model considering interlayer cohesion in the invention is more in line with the actual condition of the project, and the minimum critical span 2.74m obtained by calculation is consistent with the actual critical excavation span. The traditional calculation model without considering the interlayer cohesive force has a large difference from the actual engineering, so the calculation method has important significance for guiding the design and construction of the horizontal layered surrounding rock tunnel.
Claims (2)
1. The method for calculating the cohesive force between the horizontal layered surrounding rock layers of the simply supported beam structure is characterized by comprising the following steps of:
【1】 Taking two layers of rock mass samples above a supporting top plate of a horizontal layered surrounding rock excavation area, and respectively measuring to obtain the elastic modulus E of an upper layer rock mass 1 And the elastic modulus of the lower rock mass is E 2 At E 2 <E 1 In the case of (1), the interlayer cohesion g is calculated according to the step [ 2 ] and the step [ 3 ] Brief support ；
【2】 Respectively equating the upper rock mass and the lower rock mass as an upper beam and a lower beam supported by a simply supported beam structure, and respectively calculating the load q of the upper beam according to the actual parameters of field construction On the upper part Load q of lower beam Lower part Upper beam deflection omega Upper part of And deflection omega of the lower beam Lower part Wherein
q On the upper part ＝q 1 +γ 1 h 1 +g Brief support ；
q Lower part ＝q 1 +γ 1 h 1 +γ 2 h 2 -g Brief support ；
In the formula, q 1 The vertical acting force of the surrounding rock is provided, and the thickness of the upper rock layer is h 1 Volume weight of gamma 1 Thickness of the lower rock layer is h 2 Volume weight of gamma 2 ，g 'Qin' support The interlayer cohesive force of the simply supported beam structure; moment of inertia of the upper beam is I 1 The lower beam has a moment of inertia of I 2 ，b 1 Is the longitudinal length of the upper beam, b 2 The longitudinal length of a lower layer beam is defined, a is the top plate rock mass excavation span, and x is an x-axis coordinate value in a local coordinate system established by the top plate beam section;
【3】 Deflection omega of upper beam under cooperative deformation condition On the upper part And deflection omega of the lower beam Lower part Same, calculated to obtain
Namely the interlayer cohesive force of the simply supported beam structure.
2. The method for calculating the cohesive force between horizontal layered surrounding rock layers of the simply supported beam structure according to claim 1, wherein the step [ 2 ]
q 1 ＝γH
H＝0.45×2 s-1 ω
Wherein H is the equivalent height of the tunnel load, and gamma is the weight of the surrounding rock (kN/m) 3 ) S is the grade of the surrounding rock, omega is the width influence coefficient, and omega is 1+ i (B-5); i is the surrounding rock pressure increase rate when B increases by 1m, B is the tunnel width, and when B is less than 5m, i is 0.2; when B is more than 5m, i is 0.1.
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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 |
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