1. A method for calculating the bending resistance and bearing capacity of a grouting type tongue-and-groove joint of an assembled underground structure is characterized by comprising the following steps:

the method comprises the following steps: determining the geometric dimension of the grouting type mortise joint of the fabricated underground structure;

step two: determining a 3-inflection point 4 broken line bending moment corner M-theta curve calculation model;

wherein, the pure concrete contribution bending moment M is calculated according to the axial force condition_1c、M_2c、M_3c、M_limcThen, coefficient correction is carried out, contribution element coefficients and geometric correction coefficients are determined, and bending moment M of each stage of the final joint is calculated₁、M₂、M₃And M_lim；

Step three: determining the bending rigidity;

wherein, k is firstly obtained according to the M-theta curve under the condition of variable rigidity input_θ-M bending stiffness curve; then, under the condition that only constant rigidity can be input, the equivalent rigidity value of the first two stages of the M-theta curve is used as a numerical calculation input value.

2. The method for calculating the bending resistance and bearing capacity of the grouting type mortise and tenon joint of the fabricated underground structure according to claim 1, wherein the method comprises the following steps: the geometric dimensions in the step one comprise tenon length, tenon width, inclination angle and tenon number.

3. The method for calculating the bending resistance and bearing capacity of the grouting type mortise and tenon joint of the fabricated underground structure according to claim 1, wherein the method comprises the following steps: and in the second step, the concrete contribution elements serving as the mechanical model foundation are subjected to joint stress analysis according to the plane, and the concrete steps of establishing the 3-inflection-point 4-stage broken line model are as follows:

step 2.1: corresponding to the contribution of concrete on contact surface, the state of whole section being pressed, the bearing capacity of joint structure being in linear stage, and the inflection point being corresponding to the limit state p of whole section being pressed₁The total stress of the joint is the stress generated by axial force and bending moment respectivelyAnd (3) superposing the force, and obtaining the following mechanical parameters in the stage by the following formula according to the force and moment balance conditions:

d₁＝p₁/K (6)

d₂＝p₂/K (7)

θ＝(d₂-d₁)/h (8)

wherein:

n is axial force (kN);

m is a bending moment (kN.m);

t is the prestressing force (kN) of a stress application rod;

p₁、p₂the magnitude of the stress (kPa) on the tension side and the compression side;

h is the length of the contact surface, namely the length (m) of the grouting section;

b is the joint width (m);

h_Tthe distance (m) from the stress application rod to the center of the contact surface;

t is positive at the pressure side and negative at the pull side, d₁And d₂Is p₁And p₂Respectively corresponding displacements (m);

and solving each mechanical parameter at the inflection point of the extreme state to obtain the following result:

p₁＝0 (9)

step 2.2: when M > M₁The concrete develops a tensile stress state, where h₀The effective height contributed by the joint concrete, namely the effective compression area of the joint concrete, and the mechanical parameters at the stage are solved as follows:

d₂＝p₂/K (2)

the inflection point of the extreme state is as follows:

p₂＝α(N)·f_c (4)

wherein:

f_ca design value (kPa) for the compressive strength of concrete;

alpha (N) is a correction coefficient which is a function of the change of the axial force,

and combining the analysis of the subsequent stage to find that the inflection point bending moment is calculated by the following formula:

M_2c＝M_1c+(M_3c-M_1c)/2 (5)

the rotation angle calculation formula is:

step 2.3: as the bending moment increases, the effective compression area of the joint concrete contribution gradually decreases until p₂＝f_cThe stress distribution is the same as the step 2.2, the calculation formula at the stage is the same as the step 2.2, and the inflection point of the limit state and various mechanical parameters are solved as follows:

step 2.4: stress p when₂Reach the design value f of the compressive strength of the concrete at the two sides of the joint_cThen, the joint concrete begins to enter a yield failure stage, the yield range extends to the pressed end along with the continuous increase of the bending moment, h₁Contributing a yield zone height, h, to the joint concrete₀And contributing effective compression height to joint concrete, solving the following mechanical parameters in the stage:

solving the mechanical parameters of the stage IV limit state as follows:

4. the method for calculating the bending resistance and bearing capacity of the grouting type mortise joint of the fabricated underground structure as claimed in claim 3, wherein: carrying out contribution element correction on the obtained concrete 3 inflection points 4 broken line model, and introducing a tenon contribution rate correction coefficient k₁、k₂、k₃And k_limAnd the corrected three inflection points and the ultimate bending moment of the bearing limit are as follows: m₁＝k₁M_1c；M₂＝k₂M_2c；M₃＝k₃M_3c；M_lim＝k_limM_limcCoefficient k of contribution of tenon₁、k₂、k₃And k_limThe actual turning point value and the limit value of each stage obtained by the joint test and the concrete contribution bending moment M_1c、M_2c、M_3c、M_limcThe ratio of (3) is obtained by regressing all the working condition ratios and the axial force, the correction coefficients are obtained, the corresponding matched correction coefficient k values exist in different tenon numbers, and a coefficient zeta is introduced₁、ζ₂、ζ₃Respectively as the proportion of three inflection points in the whole joint life cycle, and using zeta_limCalculate the whole joint life cycle M_limAnd multiplying the ratio of the life cycle of each inflection point by the ratio of the life cycle of each inflection point to obtain an actual inflection point value, wherein the final three inflection points and the ultimate bending moment of the bearing limit are as follows:

M₁＝ζ₁M_lim (15)

M₂＝ζ₂M_lim (16)

M₃＝ζ₃M_lim (17)

M_lim＝ζ_lim·M_limc (18)

wherein, when N is 0:

when N > 0, M_1c、M_2c、M_3cAnd M_limcCalculated according to equations 11, 17, 19 and 25, respectively.

5. The method for calculating the bending resistance and bearing capacity of the grouting type mortise and tenon joint of the fabricated underground structure as claimed in claim 4, wherein: correction system ζ₁、ζ₂、ζ₃The values are shown in table 1:

TABLE 1 correction factor ζ₁、ζ₂、ζ₃Value-taking meter

6. The method for calculating the bending resistance and bearing capacity of the grouting type mortise and tenon joint of the fabricated underground structure as claimed in claim 5, wherein: correction coefficient ζ_limThe calculation method and the value-taking rule are as follows: zeta_lim＝ζ_lim,t·ζ_lim,h；ζ_lim,tFor the tenon related coefficients, use as per table 2; zeta_lim,hFor the highly correlated coefficients, as used in table 3,

TABLE 2 tenon correlation coefficient ζ_lim,tValue-taking meter

TABLE 3 tenon correlation coefficient ζ_lim,hValue-taking meter

7. The method for calculating the bending resistance and bearing capacity of the grouting type mortise and tenon joint of the fabricated underground structure as claimed in claim 6, wherein: the rotation amount is analyzed by the contribution factor of the concrete in the material influence range l_efOther contribution factors are considered, secondary correction is not needed, and the calculation is as follows:

θ₁＝θ_1c (23)

θ₂＝θ_2c (24)

θ₃＝θ_3c (25)

θ_lim＝θ_limc (26)

wherein, when N ═ 0, single tenon joint:

when N is equal to 0, the double tenon joint:

when N > 0, theta₁、θ₂、θ₃And theta_limcCalculated according to equations 35-38, respectively.

8. The method for calculating the bending resistance and bearing capacity of the grouting type mortise joint of the fabricated underground structure as claimed in claim 7, wherein: l_efThe middle correlation parameter is calculated and valued as follows: mu.s_efFor the compression modulus correlation coefficient, 1.2 is taken for single tenon, and 1.0 is taken for double tenon and multiple tenon; beta is a_ef,1Is the correlation coefficient of the compression modulus, beta, of stage I_ef,1＝β_ef,1o·β_ef,h，β_ef,1oUsing, according to Table 4, beta_ef,2Is the phase II coefficient of compression modulus, beta_ef,2＝4.4·β_ef,h；β_ef,3Is the stage III compression modulus correlation coefficient, beta_ef,3＝β_ef,3o·β_ef,h，β_ef,3oUsed as in Table 5; beta is a_ef,limIs the phase IV compression modulus correlation coefficient, beta_ef,lim＝β_ef,lim0·β_ef,hβ_ef,1oAdopted according to Table 6; beta is a_ef,hLinear interpolation as per table 7; mu.s_efFor the coefficient of compression modulus dependence, 1 is taken for the single tenon2, taking 1.0 out of double tenons and multiple tenons;

TABLE 4 correlation coefficient of compression modulus beta_ef,1oValue-taking meter

TABLE 5 coefficient of correlation of compression modulus beta_ef,3oValue-taking meter

TABLE 6 correlation coefficient of compression modulus beta_ef,limoValue-taking meter

TABLE 7 correlation coefficient of compression modulus beta_ef,hValue-taking meter

h/m ≤1 1.5 2 2.5 3 β_ef,1h 1 1.18 1.36 1.58 1.8

。

9. The method for calculating the bending resistance and bearing capacity of the grouting type mortise joint of the fabricated underground structure as claimed in claim 8, wherein: calculating to obtain M and theta values corresponding to each stage, and finally forming a four-fold line M-theta curve, and according to a mathematical formula, calculating M and theta values_3cRequireFor M_limcRequireWith N_max≤f_cbh; taking the above minimum value, N is required to be not more than

10. The method for calculating the bending resistance and bearing capacity of the grouting type mortise joint of the fabricated underground structure as claimed in claim 9, wherein: by using the joint test result, a tenon length coefficient alpha is introduced_S＝s_l/s_h(s_lIs the length of the tenon, s_hTenon width), the general coefficient relationship of different tenon lengths can be obtained by researching the relationship between the tenon length coefficients of the joints with different tenon lengths and the bearing key values of each stage under the action of different axial forces. When alpha is_SLess than or equal to 0.32, and the length-tenon width ratio reduction coefficient alpha of the tenon is obtained according to the following table_sM to be solved according to the previous algorithm₁、M₂、M₃And M_limMultiplied by alpha_sI.e. the final value when α is_S≥0.65，α_sWhen 1, when η₁When the ratio is between 0.32 and 0.65, according to alpha_sLinear interpolation is performed for 1 and the following table values;

TABLE 8 Table for taking value of tenon length-tenon width ratio reduction coefficient alphas

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 fabricated structure is designed and built by adopting an equal cast-in-place concept, joint positions are connected by adopting grouting sleeve steel bars and a secondary cast-in-place concrete connection mode, and the bearing performance of the constructed structure is not different from that of the cast-in-place structure. The prefabricated underground structure is usually not suitable for a joint connection method adopting a ground building fabricated structure due to the influence of factors such as large structural size, more steel bars, narrow operation environment and the like, a joint connection mode capable of realizing quick connection construction in the construction process is selected, and the grouting 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 the ends of two components to be connected are provided with corresponding tenons and mortises, the two components can be conveniently and quickly butted together during connection, in order to ensure the force transmission performance of the connection part, filling grout is filled in gaps between the butted component ends and the tenon mortises, and after the grout is solidified, an integrated joint node is formed (the concrete structure of the grouting type mortise joint is shown in figure 1). 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.

The discontinuity of the fabricated underground structure joint steel bars enables the bending rigidity of the joint part to be smaller than that of a continuous cast-in-place structure, and the difference of the mechanical properties of the joints causes the difference of the mechanical behaviors of a fabricated structure system and a cast-in-place structure system. However, the research of mechanical models of the fabricated station component joint by the previous academic community is almost blank, and under the situation that green construction and building industrialization are vigorously advocated in China and the application of a fabricated underground structure system is in reserve, the research of mechanical behaviors of the fabricated underground structure joint is necessary.

The grouting type mortise and tenon joint has multiple structural elements and complex material properties. The joint concrete is not in direct contact, but is in connection contact through grouting materials, a single tenon joint is taken as an example in fig. 1, a reinforcing rod 20 is arranged between concrete layers 10 for fastening connection, a grouting section 40 is arranged between tenon and tenon 30 of the concrete layers 10, two ends of the grouting section 40 are respectively sealed through sealing gaskets 50, the reinforcing rod 20 can be an auxiliary connecting bolt, under the action of axial force and bending moment, stress on a contact surface is not uniformly distributed, but continuously changes along with a loading process, and mechanical behavior is complex. Under the influence of all the factors, the actual stress distribution of the joint presents a nonlinear characteristic with weak regularity along with the change of the axial force and the bending moment of the joint, even if the sectional stress integration is carried out, the solution can not be displayed by utilizing the mechanical balance condition and the reasonable boundary, and the complicated computer iteration solution is needed, so that the method is not suitable for being adopted by designers when the joint is designed.

Therefore, in view of the above defects, the designer of the invention researches and designs a method for calculating the bending resistance and bearing capacity of the grouting type tongue-and-groove joint of the fabricated underground structure by combining the experience and the result of the related industry for many years 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 bending resistance and the bearing capacity of a grouting type tongue-and-groove joint of an assembled underground structure, which can effectively overcome the defects of the prior art, can be completely used for joint design and bearing capacity verification of the underground structure, and can improve the service environment and the service life of the underground structure.

In order to achieve the purpose, the invention discloses a method for calculating the bending resistance and the bearing capacity of a grouting type tongue-and-groove joint of an assembled underground structure, which is characterized by comprising the following steps of:

the method comprises the following steps: determining the geometric dimension of the grouting type mortise joint of the fabricated underground structure;

step two: determining a 3-inflection point 4 broken line bending moment corner M-theta curve calculation model;

wherein, the pure concrete contribution bending moment M is calculated according to the axial force condition_1c、M_2c、M_3c、M_limcThen, coefficient correction is carried out, contribution element coefficients and geometric correction coefficients are determined, and bending moment M of each stage of the final joint is calculated₁、M₂、M₃And M_lim；

Step three: determining the bending rigidity;

wherein, k is firstly obtained according to the M-theta curve under the condition of variable rigidity input_θ-M bending stiffness curve; then, under the condition that only constant rigidity can be input, the equivalent rigidity value of the first two stages of the M-theta curve is used as a numerical calculation input value.

Wherein: the geometric dimensions in the step one comprise tenon length, tenon width, inclination angle and tenon number.

Wherein: and in the second step, the concrete contribution elements serving as the mechanical model foundation are subjected to joint stress analysis according to the plane, and the concrete steps of establishing the 3-inflection-point 4-stage broken line model are as follows:

step 2.1: corresponding to the contribution of concrete on contact surface, the state of whole section being pressed, the bearing capacity of joint structure being in linear stage, and the inflection point being corresponding to the limit state p of whole section being pressed₁The total stress of the joint is the superposition of the stress generated by the axial force and the bending moment respectively, and according to the force and moment balance condition, the mechanical parameters at the stage are obtained by the following formula as follows:

d₁＝p₁/K (6)

d₂＝p₂/K (7)

θ＝(d₂-d₁)/h (8)

wherein:

n is axial force (kN);

m is a bending moment (kN.m);

t is the prestressing force (kN) of a stress application rod;

p₁、p₂the magnitude of the stress (kPa) on the tension side and the compression side;

h is the length of the contact surface, namely the length (m) of the grouting section;

b is the joint width (m);

h_Tthe distance (m) from the stress application rod to the center of the contact surface;

t is positive at the pressure side and negative at the pull side, d₁And d₂Is p₁And p₂Respectively corresponding displacements (m);

and solving each mechanical parameter at the inflection point of the extreme state to obtain the following result:

p₁＝0 (9)

step 2.2: when M > M₁The concrete develops a tensile stress state, where h₀The effective height contributed by the joint concrete, namely the effective compression area of the joint concrete, and the mechanical parameters at the stage are solved as follows:

d₂＝p₂/K(2)

the inflection point of the extreme state is as follows:

p₂＝α(N)·f_c (4)

wherein:

f_ca design value (kPa) for the compressive strength of concrete;

alpha (N) is a correction coefficient which is a function of the change of the axial force,

and combining the analysis of the subsequent stage to find that the inflection point bending moment is calculated by the following formula:

M_2c＝M_1c+(M_3c-M_1c)/2 (5)

the rotation angle calculation formula is:

step 2.3: as the bending moment increases, the effective compression area of the joint concrete contribution gradually decreases until p₂＝f_cThe stress distribution is the same as the step 2.2, the calculation formula at the stage is the same as the step 2.2, and the inflection point of the limit state and various mechanical parameters are solved as follows:

step 2.4: stress p when₂Reach the designed value of the compressive strength of the concrete at the two sides of the jointf_cThen, the joint concrete begins to enter a yield failure stage, the yield range extends to the pressed end along with the continuous increase of the bending moment, h₁Contributing a yield zone height, h, to the joint concrete₀And contributing effective compression height to joint concrete, solving the following mechanical parameters in the stage:

solving the mechanical parameters of the stage IV limit state as follows:

wherein: carrying out contribution element correction on the obtained concrete 3 inflection points 4 broken line model, and introducing a tenon contribution rate correction coefficient k₁、k₂、k₃And k_limAnd the corrected three inflection points and the ultimate bending moment of the bearing limit are as follows: m₁＝k₁M_1c；M₂＝k₂M_2c；M₃＝k₃M_3c；M_lim＝k_limM_limcCoefficient k of contribution of tenon₁、k₂、k₃And k_limThe actual turning point value and the limit value of each stage obtained by the joint test and the concrete contribution bending moment M_1c、M_2c、M_3c、M_limcThe ratio of (a) to (b),all the working condition ratios and the axial force are regressed to obtain correction coefficients, the number of different tenons has corresponding matched correction coefficient k values, and a coefficient zeta is introduced₁、ζ₂、ζ₃Respectively as the proportion of three inflection points in the whole joint life cycle, and using zeta_limCalculate the whole joint life cycle M_limAnd multiplying the ratio of the life cycle of each inflection point by the ratio of the life cycle of each inflection point to obtain an actual inflection point value, wherein the final three inflection points and the ultimate bending moment of the bearing limit are as follows:

M₁＝ζ₁M_lim (15)

M₂＝ζ₂M_lim (16)

M₃＝ζ₃M_lim (17)

M_lim＝ζ_lim·M_limc (18)

wherein, when N is 0:

when N > 0, M_1c、M_2c、M_3cAnd M_limcCalculated according to equations 11, 17, 19 and 25, respectively.

Wherein: correction system ζ₁、ζ₂、ζ₃The values are shown in Table 9:

TABLE 1 correction factor ζ₁、ζ₂、ζ₃Value-taking meter

Wherein: correction coefficient ζ_limThe calculation method and the value-taking rule are as follows: zeta_lim＝ζ_lim,t·ζ_lim,h；ζ_lim,tFor the tenon related coefficients, adopt according to table 10; zeta_lim,hFor the highly correlated coefficients, as per table 11,

TABLE 2 tenon correlation coefficient ζ_lim,tValue-taking meter

TABLE 3 tenon correlation coefficient ζ_lim,hValue-taking meter

Wherein: the rotation amount is analyzed by the contribution factor of the concrete in the material influence range l_efOther contribution factors are considered, secondary correction is not needed, and the calculation is as follows:

θ₁＝θ_1c (23)

θ₂＝θ_2c (24)

θ₃＝θ_3c (25)

θ_lim＝θ_limc (26)

wherein, when N ═ 0, single tenon joint:

when N is equal to 0, the double tenon joint:

when N > 0, theta₁、θ₂、θ₃And theta_limcCalculated according to equations 35-38, respectively.

Wherein: l_efThe middle correlation parameter is calculated and valued as follows: mu.s_efFor the compression modulus correlation coefficient, 1.2 is taken for single tenon, and 1.0 is taken for double tenon and multiple tenon; beta is a_ef,1Is the correlation coefficient of the compression modulus, beta, of stage I_ef,1＝β_ef,1o·β_ef,h，β_ef,1oUsing, according to Table 12, beta_ef,2Is the phase II coefficient of compression modulus, beta_ef,2＝4.4·β_ef,h；β_ef,3Is the stage III compression modulus correlation coefficient, beta_ef,3＝β_ef,3o·β_ef,h，β_ef,3oAdopted according to Table 13; beta is a_ef,limIs the phase IV compression modulus correlation coefficient, beta_ef,lim＝β_ef,lim0·β_ef,hβ_ef,1oAs used in Table 14; beta is a_ef,hLinear interpolation using table 15；μ_efFor the compression modulus correlation coefficient, 1.2 is taken for single tenon, and 1.0 is taken for double tenon and multiple tenon;

TABLE 4 correlation coefficient of compression modulus beta_ef,1oValue-taking meter

TABLE 5 coefficient of correlation of compression modulus beta_ef,3oValue-taking meter

TABLE 6 correlation coefficient of compression modulus beta_ef,limoValue-taking meter

TABLE 7 correlation coefficient of compression modulus beta_ef,hValue-taking meter

h/m	≤1	1.5	2	2.5	3
						βef,1h	1	1.18	1.36	1.58	1.8

。

Wherein: calculating to obtain M and theta values corresponding to each stage, and finally forming a four-fold line M-theta curve, and according to a mathematical formula, calculating M and theta values_3cRequireFor M_limcRequireWith N_max≤f_cbh; taking the above minimum value, N is required to be not more than

Wherein: by using the joint test result, a tenon length coefficient alpha is introduced_S＝s_l/s_h(s_lIs the length of the tenon, s_hTenon width), the general coefficient relationship of different tenon lengths can be obtained by researching the relationship between the tenon length coefficients of the joints with different tenon lengths and the bearing key values of each stage under the action of different axial forces. When alpha is_SLess than or equal to 0.32, and the length-tenon width ratio reduction coefficient alpha of the tenon is obtained according to the following table_sM to be solved according to the previous algorithm₁、M₂、M₃And M_limMultiplied by alpha_sI.e. the final value when α is_S≥0.65，α_sWhen 1, when η₁When the ratio is between 0.32 and 0.65, according to alpha_sLinear interpolation is performed for 1 and the following table values;

TABLE 8 Table for taking value of tenon length-tenon width ratio reduction coefficient alphas

According to the content, the method for calculating the bending resistance and the bearing capacity of the grouting type mortise joint of the fabricated underground structure has the following effects:

1. the joint design and bearing capacity calibration device can be used for joint design and bearing capacity calibration of an underground structure, and improves the service environment and service life of the underground structure.

2. The method is simple and easy to use, can be calculated by hands, is convenient for designers to use in practice, and has wide popularization.

3. The method can be applied to different non-rigid connection joints, and can be used for joints with larger difference of contact surface materials and types only by updating and correcting parameters.

4. The grouting type tongue-and-groove joint mechanics theory is constructed, and the application and the development of an assembly type underground structure system can be effectively supported.

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 the contact surface of a fabricated underground structure grouted tongue and groove joint of the present invention.

Fig. 2 shows a schematic diagram of a joint 3 inflection point 4 broken line mechanical model of the invention.

FIG. 3 shows a schematic view of the load contribution of the slip casting tongue and groove joint of the present invention.

Fig. 4 shows a schematic view of the deformed state of the joint of the present invention.

FIG. 5 shows a schematic view of the calculation steps for the bending resistance and load bearing of the grouting-type tongue-and-groove joint of the present invention.

FIG. 6 shows a schematic of the phase I concrete contributing stress distribution of the present invention.

Figure 7 shows a schematic of the phase ii and iii joint concrete contributing stress profiles of the present invention.

Figure 8 shows a schematic of the stage iv joint concrete contributing stress distribution of the present invention.

Fig. 9A, 9B and 9C are graphs of calculated values versus trial M-theta for different joint styles.

Reference numerals:

10. a concrete layer; 20. a force application rod; 30. a tenon and a mortise; 40. a grouting section; 50. and a gasket.

Detailed Description

Referring to fig. 2 to 8, a method for calculating the bending resistance and the bearing capacity of the grouted mortise joint of the fabricated underground structure according to the present invention is shown.

The inventor of the method for calculating the bending resistance and bearing capacity of the assembled underground structure grouting type tongue-and-groove joint conducts a large number of prototype failure tests on various types of grouting type tongue-and-groove joints, linearly approximates the mechanical property of the joint to a four-stage broken line divided by three inflection points by using a bending moment corner M-theta characteristic curve obtained by the joint test, and provides a joint 3 inflection point 4 broken line M-theta characteristic curve calculation model (as shown in figure 2). And under the condition of considering a certain degree of safety, the bending moment value corresponding to the second inflection point in the model is used as a design bearing limit value considering the degree of safety of the joint.

The invention respectively peels off various contributing factors (concrete + grouting layer + tenon + reinforcing bar, as shown in figure 3) for providing the bending resistance of the joint, and the contributing factors are respectively used as the basis for the stress-strain relationship deduction, stress state judgment and bending resistance bearing capacity contribution calculation under the assumption of the concrete plane section. The contribution analysis of the bending resistance provided by each element after splitting is as follows:

1. concrete: firstly, the stress-strain relation of a joint contact plane (assumed as a plane) is analyzed according to a plane section assumption, and the stress-strain relation is used as the basis of subsequent contribution factor analysis; according to the shape of the M-theta curve of the joint and a 3-inflection-point 4-fold line mechanical model, the contact surface of the joint is divided into four stages, namely I, II, III and IV, and the bending resistance contribution values of concrete at three inflection points and the bending resistance contribution value of concrete under a bearing limit state are calculated.

2. Grouting layer: when the grouting layer is pulled at the joint contact surface, the tensile stress of the grouting layer can provide certain bending moment resisting effect. However, as can be seen from the failure mode of the joint test, since the tensile strength of the epoxy resin is greater than that of the concrete, after the joint contact surface is pulled, the epoxy resin bonding surface is not separated from the bonded concrete, but the concrete protective layer on the joint surface is pulled apart. Considering that the tensile strength of concrete is low and the contribution to the bending resistance is small, the contribution to the bending resistance is ignored (the contribution ratio is assumed to be 0) for the sake of simplifying the analysis.

3. Tenon and mortise: the theoretical calculation of the bending resistance contribution of the tenon and the mortise to the section is very complex, the bending resistance contribution rate of the tenon and the mortise is counted based on the joint loading failure test result, and an empirical formula is obtained through regression and used for correcting the assumed pure concrete model of the flat section;

4. a force application rod: from the results and the mechanism of action of the joint test, it is known that the reinforcing bar provided on the tension side can improve the bending resistance of the joint to some extent, suppress the deformation of the joint and delay the occurrence of cracks, while the reinforcing bar provided on the pressure side cannot improve the bending resistance of the joint and can also consume the resistance of the joint to some extent. In engineering design, the force bar is usually only used for fixing the member joint in the assembling process, and is not considered as the bearing capacity of the joint, and for this reason, the contribution rate of the force bar is assumed to be 0.

And correcting the values of the three inflection points of the 3-inflection-point 4-fold line mechanical model by using the contribution values of all the contribution elements, and then connecting the corrected 3 inflection points and the limit value point by using a straight line to obtain the joint theoretical bearing curve.

In the calculation method and model derivation of the bending resistance and the bearing capacity of the joint, the following assumed conditions are observed in linear and nonlinear sections:

(1) the plane assumption is that: the joint section comprises a concave-convex tenon surface and is kept as a plane in the bearing process;

(2) the contact plane is not under tension: although the joints are bonded by epoxy resin, the tensile strength of epoxy resin is greater than that of concrete, when the contact surface is pulled, the concrete protective layer which is the reinforcing steel bar of the joint is pulled, the tensile strength of concrete is low, the tensile effect is ignored, and the stress of the tensile stress part of the contact plane is assumed to be 0 (the deformation state of the joint is shown in figure 4);

(3) stress linear distribution: fitting stress is approximated to a linear form:

p ═ K · d (y) formula (1)

Wherein:

p is the stress (kPa) at the joint coordinate y

d (y) is the displacement (m) at the joint coordinate y

K is the compressive stiffness (kPa/m) of the joint³)

In the elastic phase, p ═ ε · E

Wherein:

epsilon is strain, and a joint strain influence depth index l is introduced for calculating the compression deformation of a certain part_efCompression deformation d ═ ε · l at a certain position_efThe uniform inelastic segment formula also adopts the expression of an elastic segment p;

the joint compressive stiffness K satisfies:

K＝E/l_efformula (2)

Wherein:

e is the modulus of elasticity (kPa) of the material

l_efIs the strain influence depth (m).

l_ef＝k_efH formula (3)

Wherein:

h is the effective contact surface height (m) of the joint

k_efFor the strain-influencing depth coefficient, k_ef＝μ_ef·β_efCoefficient of μ_efAnd beta_efRelated to the loading phase and the tenon type. The relevant parameters were obtained by regression analysis of the test data for the different linkers.

According to the joint mechanical model, the method for calculating the bending resistance and the bearing capacity of the grouting type tongue-and-groove joint of the fabricated underground structure comprises the following steps (shown in figure 5):

the method comprises the following steps: and determining the geometrical size of the grouting type mortise and tenon joint of the fabricated underground structure.

The mainly determined geometric dimensions may include tenon length, tenon width, inclination angle, number of tenons, and the like.

Step two: and determining a 3-inflection point and a 4-fold line bending moment corner M-theta curve calculation model.

Wherein, the pure concrete contribution bending moment M is calculated according to the axial force condition_1c、M_2c、M_3c、M_limcThen, coefficient correction is carried out, contribution element coefficients and geometric correction coefficients are determined, and bending moment M of each stage of the final joint is calculated₁、M₂、M₃And M_lim；

Step three: the bending stiffness was determined.

Wherein, k is firstly obtained according to the M-theta curve under the condition of variable rigidity input_θ-M bending stiffness curve; then, under the condition that only constant rigidity can be input, the equivalent rigidity value of the first two stages of the M-theta curve is used as a numerical calculation input value.

And the concrete contribution element serving as the mechanical model foundation in the step two is subjected to joint stress analysis according to a plane, and the concrete steps of establishing the 3-inflection-point 4-stage broken line model are as follows:

step 2.1: corresponding to the contribution of concrete on contact surface, the state of whole section being pressed, the bearing capacity of joint structure being in linear stage, and the inflection point being corresponding to the limit state p of whole section being pressed₁The total joint stress can be considered as a superposition of the axial force and the bending moment respectively generating stress, as shown in fig. 6.

According to the force and moment balance conditions, the following mechanical parameters are obtained through the following formula:

d₁＝p₁/K (6)

d₂＝p₂/K (7)

θ＝(d₂-d₁)/h (8)

wherein:

n is axial force (kN);

m is a bending moment (kN.m);

t is the prestressing force (kN) of a stress application rod;

p₁、p₂the magnitude of the stress (kPa) on the tension side and the compression side;

h is the length of the contact surface, namely the length (m) of the grouting section;

b is the joint width (m);

h_Tthe distance (m) from the stress application rod to the center of the contact surface;

t is positive at the pressure side and negative at the pull side, d₁And d₂Is p₁And p₂Respectively corresponding displacements (m).

And solving each mechanical parameter at the inflection point of the extreme state to obtain the following result:

p₁＝0 (9)

step 2.2: when M > M₁The concrete is in a tensile stress state (only from the perspective of the concrete, the contact surface is actually still in a full contact state under the action of other contributing factors, and the stage is in a quasi-linear change stage from the test result. FIG. 7 shows the stress distribution of the joint at this stage, where h₀The effective height contributed to the joint concrete, i.e. the effective compression area of the joint concrete. The mechanical parameters at this stage are solved as follows:

d₂＝p₂/K (36)

the inflection point of the extreme state is as follows:

p₂＝α(N)·f_c (38)

wherein:

f_ca design value (kPa) for the compressive strength of concrete;

alpha (N) is a function of the correction coefficient as a function of the axial force.

As the function alpha (N) is not strong in regularity and is more complex to calculate, the following formula is combined with the analysis of the subsequent stage to calculate the inflection point bending moment by the following formula:

M_2c＝M_1c+(M_3c-M_1c)/2 (39)

the rotation angle calculation formula is:

step 2.3: as the bending moment increases, the effective compression area of the joint concrete contribution gradually decreases until p₂＝f_cThe stress distribution is as shown in step 2.2, fig. 7. The calculation formula of the stage is the same as the step 2.2, and the solution of the inflection point of the extreme state and various mechanical parameters is as follows:

step 2.4: stress p when₂Reach the design value f of the compressive strength of the concrete at the two sides of the joint_cThereafter, the joint concrete starts to advanceIn the yield failure stage, as the bending moment continues to increase, the yield range extends to the pressed end, the distribution of the contribution stress of the joint concrete is shown in figure 8, wherein h is₁Contributing a yield zone height, h, to the joint concrete₀Contributing an effective compression height to the joint concrete. The mechanical parameters at this stage are solved as follows:

solving the mechanical parameters of the stage IV limit state as follows:

then, the contribution element correction is carried out on the obtained concrete 3-inflection-point 4 broken line model:

the contribution factor correction mainly considers the contribution rate correction of the tenon and the mortise which play a main bearing control role. Introducing a tenon contribution rate correction coefficient k through statistical analysis and regression of test results₁、k₂、k₃And k_limAnd the corrected three inflection points and the ultimate bending moment of the bearing limit are as follows: m₁＝k₁M_1c；M₂＝k₂M_2c；M₃＝k₃M_3c；M_lim＝k_limM_limc. Tenon contribution rate correction coefficient k₁、k₂、k₃And k_limThe actual turning point value and the limit value of each stage obtained by the joint test and the concrete contribution bending moment M_1c、M_2c、M_3c、M_limcThe ratio of (2) is obtained by regressing the ratio of all working conditions and the axial force (converted into each linear meter), and the number of different tenons has corresponding matched correction coefficient k values. Considering the rapid and convenient calculation, the coefficient zeta is introduced by summarizing the M-theta curve of the test piece under each working condition₁、ζ₂、ζ₃(k₁、k₂、k₃And k_limThe coefficient is integrated into the coefficient after being subjected to regression analysis) respectively as three inflection points to account for the proportion of the whole joint life cycle, and zeta is utilized_limCalculate the whole joint life cycle M_limAnd multiplying the ratio of the life cycle of each inflection point by the ratio of the life cycle of each inflection point to obtain an actual inflection point value, wherein the final three inflection points and the ultimate bending moment of the bearing limit are as follows:

M₁＝ζ₁M_lim (49)

M₂＝ζ₂M_lim (50)

M₃＝ζ₃M_lim (51)

M_lim＝ζ_lim·M_limc (52)

wherein, when N is 0:

when N > 0, M_1c、M_2c、M_3cAnd M_limcCalculated according to equations 11, 17, 19 and 25, respectively.

Correction system ζ₁、ζ₂、ζ₃The values are shown in Table 9:

TABLE 9 correction factor ζ₁、ζ₂、ζ₃Value-taking meter

Correction coefficient ζ_limThe calculation method and the value-taking rule are as follows: zeta_lim＝ζ_lim,t·ζ_lim,h；ζ_lim,tFor the tenon related coefficients, adopt according to table 10; zeta_lim,hFor the highly correlated coefficients, the following table 11 was used.

TABLE 10 tenon correlation coefficient ζ_lim,tValue-taking meter

TABLE 11 tenon correlation coefficient ζ_lim,hValue-taking meter

The rotation amount is analyzed by the contribution factor of the concrete in the material influence range l_efOther contribution factors are considered, secondary correction is not needed, and the calculation is as follows:

θ₁＝θ_1c (57)

θ₂＝θ_2c (58)

θ₃＝θ_3c (59)

θ_lim＝θ_limc (60)

wherein, when N ═ 0, single tenon joint:

when N is equal to 0, the double tenon joint:

when N > 0, theta₁、θ₂、θ₃And theta_limcCalculated according to equations 35-38, respectively.

l_efThe middle correlation parameter is calculated and valued as follows: mu.s_efFor the compression modulus correlation coefficient, 1.2 is taken for single tenon, and 1.0 is taken for double tenon and multiple tenon; beta is a_ef,1Compression modulus phase relation for stage INumber, beta_ef,1＝β_ef,1o·β_ef,h，β_ef,1oUsing, according to Table 12, beta_ef,2Is the phase II coefficient of compression modulus, beta_ef,2＝4.4·β_ef,h；β_ef,3Is the stage III compression modulus correlation coefficient, beta_ef,3＝β_ef,3o·β_ef,h，β_ef,3oAdopted according to Table 13; beta is a_ef,limIs the phase IV compression modulus correlation coefficient, beta_ef,lim＝β_ef,lim0·β_ef,hβ_ef,1oAs used in Table 14; beta is a_ef,hLinear interpolation is adopted according to the specification table 15; mu.s_efFor the compression modulus correlation coefficient, the single tenon is 1.2, and the double tenon and the multiple tenons are 1.0.

TABLE 12 correlation coefficient of compression modulus beta_ef,1oValue-taking meter

TABLE 13 coefficient of correlation of compression modulus beta_ef,3oValue-taking meter

TABLE 14 correlation coefficient of compression modulus beta_ef,limoValue-taking meter

TABLE 15 correlation coefficient of compression modulus beta_ef,hValue-taking meter

h/m	≤1	1.5	2	2.5	3
						βef,1h	1	1.18	1.36	1.58	1.8

And according to the series formulas, calculating and obtaining M and theta values corresponding to each stage, and finally forming a four-fold line M-theta curve. In addition, according to the mathematical formula, for M_3cRequireFor M_limcRequireWith N_max≤f_cbh; taking the above minimum value, N is required to be not more than

By using the joint test result, a tenon length coefficient alpha is introduced_S＝s_l/s_h(s_lIs the length of the tenon, s_hTenon width), the general coefficient relationship of different tenon lengths can be obtained by researching the relationship between the tenon length coefficients of the joints with different tenon lengths and the bearing key values of each stage under the action of different axial forces. When alpha is_SLess than or equal to 0.32, and the length-tenon width ratio reduction coefficient alpha of the tenon is obtained according to the following table_sM to be solved according to the previous algorithm₁、M₂、M₃And M_limMultiplied by alpha_sI.e. the final value. When alpha is_S≥0.65，α_s1. When eta₁When the ratio is between 0.32 and 0.65, according to alpha_sLinear interpolation was performed as 1 and the values in the table below.

TABLE 16 Tab Length tenon Width ratio reduction coefficient alphas value-taking table

By adopting the slip casting type tongue-and-groove joint bending resistance bearing calculation method, compared with a joint test (such as three typical joint types shown in fig. 9A, 9B and 9C), it can be seen that the degree of bonding is high in the first three stages, the proposed design bearing limit value inflection point is provided, and the calculated value is basically consistent with the test value; the calculated value of the turning angle of the double-tenon forcing rod in the drawing side joint of the figure 9C is slightly different from the tested value, mainly because the forcing rod has a certain limiting effect on the turning angle, but the contribution rate is not high.

In general, the calculated value obtained by the joint theoretical calculation method provided by the invention has the same trend with the relation curve of the test value M-theta, and the linear and inflection point goodness of fit is high.

In conclusion, the algorithm of the invention is based on the characteristic curve of the joint 3 inflection point 4 broken line M-theta, and the parameters of the basic concrete contribution element model are fitted and corrected by the joint test value through independently decomposing and analyzing each contribution element of the joint, so as to obtain the final bearing bending moment value and the final bearing turning angle value of each stage. From the aspect of example performance, the calculated value of the algorithm has good correspondence with the tested value, the inflection point is basically consistent, the algorithm is feasible, and the method has guiding significance for the design of the assembled underground structure joint.

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.