CN113221220A - Method for calculating shearing resistance and bearing capacity of grouting type mortise joint of assembled underground structure - Google Patents

Method for calculating shearing resistance and bearing capacity of grouting type mortise joint of assembled underground structure Download PDF

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CN113221220A
CN113221220A CN202110509962.XA CN202110509962A CN113221220A CN 113221220 A CN113221220 A CN 113221220A CN 202110509962 A CN202110509962 A CN 202110509962A CN 113221220 A CN113221220 A CN 113221220A
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杨秀仁
林放
黄美群
彭智勇
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Beijing Urban Construction Design and Development Group Co Ltd
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Abstract

A method for calculating the shear bearing capacity of a slip casting type mortise joint comprises the following steps: the method comprises the following steps: calculating the shear-resistant bearing capacity provided by the joint tenon and tenon; step two: calculating the shear-resisting bearing capacity provided by the axial force; step three: taking the small value of the bearing capacity of the shear keys on the left side and the right side as the shearing resistance bearing capacity of the grouting type mortise joint, and finally obtaining the shearing resistance bearing capacity of the grouting type mortise joint; therefore, the invention can overcome the defects of the prior art, realize the joint design and the verification of the shearing resistance and bearing capacity, effectively improve the stability of the underground structure and prolong the service life.

Description

Method for calculating shearing resistance and bearing capacity of grouting type mortise joint of assembled underground structure
Technical Field
The invention relates to the technical field of underground engineering, in particular to a method for calculating the shearing resistance and bearing capacity of a grouting type mortise joint of an assembled underground structure in a bending load action environment, wherein the grouting type mortise joint is adopted in the assembled underground structure.
Background
The assembly type construction technology is a great change of the construction mode of the building engineering and is one of the work which is intensively promoted in recent years by the department of housing construction. The prefabricated structure has high production efficiency of components and easy quality guarantee; the construction is mechanized, and the construction speed is high; the field operation is less, the environmental impact is less, and the like.
The conventional ground building structure is designed and built by adopting an equal cast-in-place concept, joint positions are connected by adopting a grouting sleeve steel bar connection and a secondary cast-in-place concrete connection mode, the bearing performance of the constructed structure is not different from that of the cast-in-place structure, and the shearing resistance problem of the joint positions does not need to be considered particularly. Due to the influence of factors such as large structural size, more steel bars and narrow operation environment, the prefabricated assembled structure of the underground engineering is generally not suitable for a joint connection method of the assembled structure of the ground building, a joint connection mode capable of realizing quick connection construction in the construction process is selected, and the grouting type mortise joint is a joint connection mode capable of meeting the assembly connection requirements of the underground structure. The joint connection mode is mainly characterized in that corresponding tenons and mortises are arranged at the end parts of two components to be connected, the two components can be conveniently and quickly butted together during connection, in order to ensure the force transmission performance of a connection part, filling grout is poured in gaps between the end parts of the butted components and the tenon mortises, and an integrated joint node is formed after the grout is solidified.
After the construction of the fabricated structure is completed, the joint part is in a bending action and a certain shear load environment state under the action of stratum load. Because the reinforcing steel bars of the components at the connecting parts of the slip casting type tongue-and-groove joints are discontinuous, and the difference between the physical and mechanical properties of a slip casting material and a concrete material is large, the bearing performance of the slip casting type tongue-and-groove joint cannot be considered according to a continuous structure, the traditional method for calculating the shearing resistance of the concrete structure is not suitable any more, and special research is needed.
The slip casting type mortise joint is used for the assembled underground structure for the first time at home and abroad, so the research aiming at the shear resistance of the joint in the past is blank.
The international research on the shearing resistance of the concave-convex mortise basically focuses on the condition of pure shearing actionThere is no practical method for calculating the shearing resistance of the concave-convex tenon under the condition of the action of the axial force, and there is no method for calculating the shearing resistance of the grouting type mortise joint under the condition of the action of the axial force. The method for calculating the shearing resistance of the concave-convex mortise under the action of pure shear load is given in the first book of the general theory of prefabricated buildings compiled by the Association of prefabricated buildings of the Japanese society of Law, the method for calculating the shearing resistance bearing capacity and the calculation formula for transmitting the shear force through the occlusion of the concave-convex mortise concrete structure are given, and the method for calculating the shearing failure bearing capacity Q through the shear key is providedsAnd the bearing capacity Q of the shear key surface in excess of the compressive strength failurebComing to check the shear-resistant bearing capacity Q of the two sides of the joint1 and Q 2And taking the smaller bearing capacity value of the left and right shear keys as the shear bearing capacity of the joint. The specific calculation formula is as follows:
Q1=min(Q1s,Q1b);
Q2=min(Q2s,Q2b);
Figure BDA0003059905830000031
Figure BDA0003059905830000032
Figure BDA0003059905830000033
Figure BDA0003059905830000034
in the formula :
n is the number of shear keys generating bearing stress;
wiis the width of the shear key;
xiheight (mm) of the shear key contact surface;
f'c1the compressive strength (N/mm) of the concrete on the left side of the boundary surface2);
f'c2Compressive strength (N/mm) of concrete on the right side of the boundary surface2);
Alpha is a pressure-bearing coefficient which is equal to 1.0;
aithe length (mm) of the bottom of the mortise side shear key;
biis the length (mm) of the bottom of a tenon side shear key
The method does not consider the axial force action of the joint at all, and requires that the shear keys have good fit contact relation so as to synchronously and effectively transfer the shear force action.
Joints of fabricated underground structures are subjected to typical axial forces, bending moments and shear. The joint seam of the mortise joint is subjected to grouting treatment, the force transmission is more definite and reliable, the stress of the joint part is obviously influenced by the axial force, the shearing mechanism of the joint is more complex than the simple shearing action, and the Japanese formula is only suitable for checking calculation of the pure shearing stress and cannot be applied.
In the past, a mature method for calculating shearing resistance of the grouting type mortise joint of the assembled underground structure is not provided at home.
In a word, the research and the proposal of the calculation method of the shearing resistance of the grouting type mortise joint under the action of the axial force have very important significance for the application of the technology of supporting the assembled underground structure.
Therefore, in view of the above defects, the designer of the invention researches and designs a shear-resistant bearing capacity calculation method for a grouting type tongue-and-groove joint of an assembled underground structure by combining experience and achievement of related industries for a long time through careful research and design so as to overcome the above defects.
Disclosure of Invention
The invention aims to provide a method for calculating the shearing resistance and bearing capacity of a grouting type mortise joint of an assembled underground structure, which can overcome the defects of the prior art, realize joint design and shearing resistance and bearing capacity verification, and effectively improve the stability and the service life of the underground structure.
In order to achieve the purpose, the invention discloses a method for calculating the shear bearing capacity of a slip casting type tongue-and-groove joint, which is characterized by comprising the following steps of:
the method comprises the following steps: calculating the shear-resistant bearing capacity provided by the joint tenon and tenon;
for this purpose, step one comprises the following substeps:
step 1.1: calculating the shear bearing capacity on the left side of the tenon and mortise through formula 1:
Q1M=min(Q1s,Q1b) (1)
wherein ,
Figure BDA0003059905830000041
n is the number of shear keys generating bearing stress; w is aiWidth (mm) of shear key; x is the number ofiHeight (mm) of the shear key contact surface; f'c1The compressive strength (N/mm) of the concrete on the left side of the boundary surface2) (ii) a Alpha is a pressure-bearing coefficient which is equal to 1.0; a isiThe length (mm) of the bottom of the left side of the shear key;
step 1.1: calculating the right shear bearing capacity of the tenon and the mortise through a formula 2:
Q2M=min(Q2s,Q2b) (2)
wherein ,
Figure BDA0003059905830000051
f'c2compressive strength (N/mm) of concrete on the right side of the boundary surface2);biThe length (mm) of the bottom of the right side of the shear key;
step two: calculating the shear-resisting bearing capacity provided by the axial force;
and the smaller of the left side and the right side is calculated according to the formulas 3 and 4 as follows:
left side:
Figure BDA0003059905830000052
right side:
Figure BDA0003059905830000053
wherein ,σnTo joint face normal stress(MPa), taking
Figure BDA0003059905830000054
When the force application rod of the additional tension device acts,
Figure BDA0003059905830000055
wherein N and T are respectively axial force and stress application bar acting force (kN), h is the height (mm) of the joint grouting surface, and b is the width (mm) of the joint;
step three: the bearing capacity of the shear keys on the left side and the right side is a small value as the shear bearing capacity of the grouting type mortise joint, and the shear bearing capacity is determined through formulas 5 and 6 as follows:
shear resistance of the left shear key: q1=Q1M+Q1N (5)
Shear resistance of right side shear key: q2=Q2M+Q2N (6)
And finally, obtaining the shear bearing capacity of the grouting type mortise joint through a formula 7:
Qsk=min(Q1,Q2) (7)。
wherein: and determining the shear resistance calculation of the grouting type mortise joint through a four-point shear failure test of the 1:1 prototype joint.
Wherein: the slip casting formula tongue-and-groove connects and is formed with the boss on concrete layer, and the boss of both sides passes through the reinforcing bar fastening, and is equipped with outside additional tension device outside the boss, and has the slip casting section between the unsmooth tongue-and-groove between the concrete layer.
Wherein: the grouting section is an epoxy resin glue layer.
According to the above content, the method for calculating the shearing resistance and bearing capacity of the grouting type mortise joint of the assembled underground structure has the following effects:
1. the design of the joint and the calibration of the shearing resistance and bearing capacity are realized, and the stability and the service life of the underground structure are effectively improved.
2. The method for calculating the shear-resisting bearing capacity of the grouting type mortise joint with the bending function based on the characteristics of the assembled underground structure is more approximate to the practical situation of engineering and has guiding significance for the design of the assembled underground structure joint.
3. The calculation method considering the axial force effect can be applied to different non-rigid connecting joints of the above-ground and underground structures.
4. The method is simple and easy to calculate, is convenient for designers to use, and has high popularization value.
5. And a grouting type tongue-and-groove joint mechanical theory is constructed, and a solid foundation is laid for popularization and application of the prefabricated underground structure.
The details of the present invention can be obtained from the following description and the attached drawings.
Drawings
FIG. 1 shows a schematic view of a fabricated underground slip-cast tongue and groove joint of the present invention.
Figure 2 shows a schematic view of the shear bearing of the tongue and groove joint of the present invention.
FIG. 3 shows a schematic diagram of a four-point shear test of a joint of the present invention.
Figure 4 shows a schematic of the shear test ultimate failure mode of the present invention.
Fig. 5 shows the asperity planar stress state of the asperity of the invention.
Figure 6 shows the moll circle of the infinitesimal body of the present invention.
FIG. 7 shows the process of the present invention.
10. A concrete layer; 20. a boss; 30. a force application rod; 40. an external additional tension device; 50. and (5) grouting.
Detailed Description
Referring to fig. 1 and 2, a method for calculating the shear bearing capacity of a grouted mortise joint of a fabricated underground structure according to the present invention is shown.
The basic idea of the shear-resistant bearing capacity calculation method of the grouting type mortise joint of the assembled underground structure is that a method for calculating the shear-resistant bearing capacity of the concave-convex mortise under the pure shearing condition (hereinafter referred to as a pure shearing method) is used as the basis for researching the shear-resistant bearing capacity of the grouting type mortise joint under the pure shearing condition, a 1:1 four-point pure shearing test of the grouting type mortise joint is carried out, the test result is compared with the calculation result, and whether the pure shearing method can be suitable for the grouting type mortise joint or not is judgedCalculating the pure shear of the joint; according to the crack development condition (crack development position and included angle with horizontal direction) of the test joint, researching the relation between the joint main tensile stress azimuth angle and the shearing failure mode; an expression is then derived for the effect of the axial force (with the external additional tension device 40, as shown in phantom in FIG. 1) on the principal tensile stress of the joint, according to which the ultimate tensile strength f is reachedtThe principle is that the crack generates a root cause, and a vertical shear stress expression under the action of axial force is provided; extracting the direct shear reduction coefficient of the joint grouting bonding surface according to the test data; an expression of the shear bearing capacity of the joint is formed, and the expression is decomposed to form a calculation expression of the shear bearing capacity of the joint, which consists of two parts (such as a calculation diagram shown in figure 2) influenced by pure shear and axial force. The first part is consistent with the expression of a pure shearing method, and the second part is a calculation formula for the increase of the shearing resistance and the bearing capacity of the joint under the action of the axial force; and finally, carrying out example verification and providing main operation steps for calculating the shearing resistance of the grouting type mortise joint by applying the invention result.
The calculation method can be suitable for calculating the shearing resistance and bearing capacity of the grouting type mortise joint under the conditions of axial force and no axial force.
The specific derivation steps of the invention are as follows:
firstly, developing an indoor test and verifying the applicability of the pure shearing method
Although the pure shear method is similar to the structural style of the slip-cast tongue and groove joint, there are significant differences in construction, particularly the less slip-cast joint after joint slip casting provides significant improvements in the close relationship of the tongue and groove connection. Therefore, a four-point shear failure test of a 1:1 prototype joint is specially developed indoors, and whether a pure shear method is suitable for calculating the shear resistance of the grouting type tongue-and-groove joint is researched and verified.
The loading mode of the four-point shear failure test is shown in figure 3, the test can effectively verify that the concave-convex tenon meshing effect of the grouting type mortise joint in the whole process of shearing resistance and bearing is very obvious, no obvious peeling occurs between the epoxy resin glue layer and the concrete (as shown in figure 4), and the method of filling grouting materials is adopted between the gaps of the tenon and the mortise to effectively ensure the synchronization of the stress of the tenon and the mortise, limit the dislocation deformation of the concave-convex tenon and ensure the integrity and the reliable bearing capacity of the shearing resistance key. Tests reveal that the grouting type mortise joint and tenon constraint conditions, deformation and cracking characteristics are completely consistent with the application conditions and mechanical characteristics of a pure shearing method.
In order to further verify the coincidence between the calculation result of the pure shearing method and the test data, the shear resistance and the bearing capacity of the test joint are calculated by adopting the pure shearing method, and the calculation parameters and the calculation result of the joint are listed in table 1.
TABLE 1 CALCULATING TABLE FOR CALCULAR JOINT AND CROSS-KEY
Figure BDA0003059905830000091
The theoretical shear load capacity of the joint was calculated to be 660.28 kN. The shear resistance and the bearing capacity of the joint obtained by the pure shear test carried out by the inventor on the joint are 668kN, which is very close to the theoretically calculated bearing capacity value.
It can be seen that the pure shear method can be used for the shear capacity calculation of the grouted dovetail joint with the axial force of 0.
And secondly, researching the relation between the main tensile stress azimuth angle of the joint and the shearing failure mode according to the crack development condition (crack development position and included angle with the horizontal direction) of the test joint.
The main tensile stress of the concrete reaches the ultimate tensile strength ftIs the root cause of crack generation. When the tenon and tenon are sheared along the root of the tenon or the main crack, the vertical shearing stress tau and the concrete tensile strength ftAnd joint face normal stress σnIn this connection, the plane stress state is shown in FIG. 5.
Next, the inventor researches the influence of joint axial force action on the shear resistance based on the shear resistance and the bearing capacity of the joint in a pure shearing method, and the shear resistance and the bearing capacity of the joint are expressed as a pure shearing state (sigma)n0) the shear-bearing capacity of the joint and the action of the axial force result in the shear-bearing capacity of the joint being increased by two partsStated differently. And a calculation formula of the shearing resistance and the bearing capacity of the joint under the action of the axial force is provided.
Joint shear test (sigma)n0) to obtain an included angle alpha between the main tensile stress and the horizontal direction of about 37 degrees, at the moment, the joint reaches the limit of shearing-resistant bearing capacity, and the main tensile stress reaches the strength f of the concrete tensile strengthtAt this time, the infinitesimal molar stress circle is shown in fig. 6, and the following relationship exists:
Figure BDA0003059905830000101
in addition, according to the stress relation in the unit body: tau isx=τy=τ and σx=σnAnd the vertical shear stress when the tenon shear key concrete is damaged can be obtained as follows:
Figure BDA0003059905830000102
for grouting type tongue-and-groove joints, the coefficient alpha is reduced by introducing glue jointssThe calculation formula for obtaining the shearing resistance and bearing capacity of the cemented tenon and the tenon is as follows:
Qsk=αsτAs=1.327αsAs(ftn) Formula (1-1)
in the formula ,αs-reduction factor, according to the pure shear failure test, axial force N is 0, i.e. σnCalculated when the value is 0, preferably 0.81;
Astotal area of rebate shear failure face (mm)2),
Figure BDA0003059905830000103
Or
Figure BDA0003059905830000104
ftConcrete axial tensile strength (N/mm)2);
σnThe joint plane shouldForce (MPa), take
Figure BDA0003059905830000105
When the force application rod acts on the force application rod,
Figure BDA0003059905830000106
wherein h is the height (mm) of the joint grouting surface, and b is the width (mm) of the joint;
decomposing the formula (1) as follows:
Figure BDA0003059905830000107
wherein :σnShear key bearing capacity that shears when 0 pure shearing operating mode:
Figure BDA0003059905830000108
shear bearing capacity provided by the joint contact surface under the action of axial force:
Figure BDA0003059905830000111
thirdly, verification and comparison are carried out by utilizing the calculation method and the pure shearing method
Table 2 shows the derivation of sigma for several types of jointsnShear key shear bearing capacity under pure shear condition of 0 DEG C
Figure BDA0003059905830000112
And comparing the calculation result with the calculation formula of the shear key of the pure shearing method.
TABLE 2 comparison of pure shearing method and slip casting type mortise joint shearing calculation method results
Tenon type QPure shearing method(kN) QGrouting type mortise(kN)
Single tenon short joint 660.28 658.34
Single tenon long joint 660.28 658.34
Double tenon joint 796.89 794.54
As can be seen from the calculation results in the table above, the results of the two calculation methods are basically consistent, so that the correctness of the calculation result of the calculation method under the condition of 0 axial force is verified.
Fourthly, concrete flow for calculating bearing capacity of shear key of slip casting type mortise joint
As can be seen from the above description and fig. 7, the method for calculating the shear-resisting bearing capacity of the grouting-type tongue-and-groove joint of the present invention includes the following steps:
the method comprises the following steps: the shear resistance provided by the joint rebate is calculated.
For this purpose, step one comprises the following substeps:
step 1.1: calculating the shear bearing capacity on the left side of the tenon and mortise through formula 1:
Q1M=min(Q1s,Q1b) (1)
wherein ,
Figure BDA0003059905830000113
n is the number of shear keys generating bearing stress; w is aiWidth (mm) of shear key; x is the number ofiHeight (mm) of the shear key contact surface; f'c1The compressive strength (N/mm) of the concrete on the left side of the boundary surface2) (ii) a Alpha is a pressure-bearing coefficient which is equal to 1.0; a isiThe length (mm) of the bottom of the left side of the shear key.
Step 1.1: calculating the right shear bearing capacity of the tenon and the mortise through a formula 2:
Q2M=min(Q2s,Q2b) (2)
wherein ,
Figure BDA0003059905830000121
f'c2compressive strength (N/mm) of concrete on the right side of the boundary surface2);biThe length (mm) of the bottom of the right side of the shear key.
Step two: the shear bearing capacity provided by the axial force is calculated.
And the smaller of the left side and the right side is calculated according to the formulas 3 and 4 as follows:
left side:
Figure BDA0003059905830000122
right side:
Figure BDA0003059905830000123
wherein ,σnTaking the positive stress (MPa) of the joint face
Figure BDA0003059905830000124
When the force application rod of the additional tension device acts,
Figure BDA0003059905830000125
wherein N and T are respectively axial force and stress application rod acting force (kN), h is the height (mm) of the joint grouting surface, and b is the width (mm) of the joint.
Step three: the bearing capacity of the shear keys on the left side and the right side is a small value as the shear bearing capacity of the grouting type mortise joint, and the shear bearing capacity is determined through formulas 5 and 6 as follows:
shear resistance of the left shear key: q1=Q1M+Q1N (5)
Shear resistance of right side shear key: q2=Q2M+Q2N (6)
And finally, obtaining the shear bearing capacity of the grouting type mortise joint through a formula 7:
Qsk=min(Q1,Q2) (7)。
it should be apparent that the foregoing description and illustrations are by way of example only and are not intended to limit the present disclosure, application or uses. While embodiments have been described in the embodiments and depicted in the drawings, the present invention is not limited to the particular examples illustrated by the drawings and described in the embodiments as the best mode presently contemplated for carrying out the teachings of the present invention, and the scope of the present invention will include any embodiments falling within the foregoing description and the appended claims.

Claims (4)

1. A method for calculating the shear bearing capacity of a slip casting type mortise joint is characterized by comprising the following steps:
the method comprises the following steps: calculating the shear-resistant bearing capacity provided by the joint tenon and tenon;
for this purpose, step one comprises the following substeps:
step 1.1: calculating the shear bearing capacity on the left side of the tenon and mortise through formula 1:
Q1M=min(Q1s,Q1b) (1)
wherein ,
Figure FDA0003059905820000011
n is the number of shear keys generating bearing stress; w is aiWidth (mm) of shear key; x is the number ofiHeight (mm) of the shear key contact surface; f'c1The compressive strength (N/mm) of the concrete on the left side of the boundary surface2) (ii) a Alpha is a pressure-bearing coefficient which is equal to 1.0; a isiThe length (mm) of the bottom of the left side of the shear key;
step 1.1: calculating the right shear bearing capacity of the tenon and the mortise through a formula 2:
Q2M=min(Q2s,Q2b) (2)
wherein ,
Figure FDA0003059905820000012
f′c2compressive strength (N/mm) of concrete on the right side of the boundary surface2);biThe length (mm) of the bottom of the right side of the shear key;
step two: calculating the shear-resisting bearing capacity provided by the axial force;
and the smaller of the left side and the right side is calculated according to the formulas 3 and 4 as follows:
left side:
Figure FDA0003059905820000013
right side:
Figure FDA0003059905820000014
wherein ,σnTaking the positive stress (MPa) of the joint face
Figure FDA0003059905820000015
When the force application rod of the additional tension device acts,
Figure FDA0003059905820000021
wherein N and T are respectively axial force and stress application bar acting force (kN), h is the height (mm) of the joint grouting surface, and b is the width (mm) of the joint;
step three: the bearing capacity of the shear keys on the left side and the right side is a small value as the shear bearing capacity of the grouting type mortise joint, and the shear bearing capacity is determined through formulas 5 and 6 as follows:
shear resistance of the left shear key: q1=Q1M+Q1N (5)
Shear resistance of right side shear key: q2=Q2M+Q2N (6)
And finally, obtaining the shear bearing capacity of the grouting type mortise joint through a formula 7:
Qsk=min(Q1,Q2) (7)。
2. the method for calculating the shear-resistant bearing capacity of the grouting-type mortise-tenon joint according to claim 1, wherein: and determining the shear resistance calculation of the grouting type mortise joint through a four-point shear failure test of the 1:1 prototype joint.
3. The method for calculating the shear-resistant bearing capacity of the grouting-type mortise-tenon joint according to claim 1, wherein: the slip casting formula tongue-and-groove connects and is formed with the boss on concrete layer, and the boss of both sides passes through the reinforcing bar fastening, and is equipped with outside additional tension device outside the boss, and has the slip casting section between the unsmooth tongue-and-groove between the concrete layer.
4. The method for calculating the shear-resistant bearing capacity of the grouting-type mortise-tenon joint according to claim 1, wherein: the grouting section is an epoxy resin glue layer.
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Cited By (1)

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CN114135731A (en) * 2021-11-30 2022-03-04 西北工业大学上海闵行协同创新中心 Method for determining annular tenon of pipe joint and pipe joint with annular tenon

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