Method for obtaining concrete interface shear stiffness in modular reinforced soil retaining wall

Abstract

The invention discloses a method for obtaining the shear stiffness of the concrete interface in a modular reinforced earth retaining wall, and belongs to the technical field of reinforced earth retaining wall design. H、 Module Heavy c b , interface friction angle #imgabs0#; the interface normal stress is calculated using formula #imgabs1# s n ; Use formula #imgabs2# to calculate the fitting function x ( s n ); Use formula #imgabs3# to calculate the fitting function or ( s n ); the concrete interface shear stiffness is calculated using formula #imgabs4# K st The method of the present invention does not require an interface direct shear test, which solves the technical problems of the existing method, such as a cumbersome test process, a long test cycle, high requirements for test personnel, and the need for professional test equipment. The method of the present invention only needs to obtain three parameters to obtain the interface shear stiffness K st The number of parameters required is small and the required parameters are easy to obtain. The method of the present invention is simple and has high accuracy.

Description

Technical Field

[0001] The invention relates to a method for obtaining the shear stiffness of a concrete interface in a modular reinforced earth retaining wall, and belongs to the technical field of reinforced earth retaining wall design. Background Art

[0002] Modular reinforced earth retaining walls are beautiful in appearance, easy to construct and low in cost. They are widely used in engineering fields such as construction, transportation, water conservancy, and land resources. Modular reinforced earth retaining walls are complex structures with many structural surfaces. The wall surface is made of small-sized concrete blocks stacked and laid dry. The wall modules are connected by pins or concave-convex grooves. The bottom module is placed on a horizontal base made of plain concrete, and the horizontal base is buried in the foundation soil. This forms multiple module interfaces, as well as module-base interface and base-foundation interface. In addition, there are wall module-filler interface and reinforcement material-filler interface. The strength and stiffness of these interfaces have an important influence on the deformation behavior of the retaining wall, especially the parameters of the wall module interface and the module-base interface. This is because the horizontal earth pressure acting on the wall is transmitted downward to the wall toe through the shear bonds between the wall modules. The friction resistance generated on the module-base interface at the wall toe and the tension of the reinforcement material balance the horizontal earth pressure to constrain the lateral deformation of the filler and the retained body.

[0003] At present, numerical simulation has become one of the main means of designing reinforced earth retaining walls. For modular reinforced earth retaining walls, the selection of parameters of each concrete interface at the wall surface is crucial to its numerical simulation results. In various geotechnical engineering numerical software (such as PLAXIS, FLAC, ABAQUS, ZSOIL, etc.), the interface model usually requires four parameters, namely cohesion, friction angle, shear stiffness and normal stiffness. Since the concrete interface is unbonded and there is generally no deformation in the normal direction at low stress levels, the cohesion of the interface is 0, and the normal stiffness is generally 1000MPa. Finally, the friction angle and shear stiffness become two parameters to be determined. The friction angle of the concrete interface can be obtained by a large-scale interface direct shear test or by an extremely simple inclined plate test. The shear stiffness value is defined as the ratio of shear stress to shear displacement when the shear displacement is 2mm, so the shear stiffness value can only be obtained through an interface direct shear test where shear stress and shear displacement can be measured. The use of the interface direct shear test method to obtain the interface shear stiffness has the following shortcomings: the test process is cumbersome, the test cycle is long, the requirements for test personnel are high, and there are few existing large-scale shear instruments, and design units rarely meet the test conditions. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned deficiencies of the prior art and to provide a method for obtaining shear stiffness without performing an interface direct shear test, that is, a method for obtaining the shear stiffness of the concrete interface in a modular reinforced earth retaining wall.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] The method for obtaining the shear stiffness of the concrete interface in the modular reinforced earth retaining wall comprises the following steps:

[0007] S1: Get the wall height H and the wall concrete module weight γ b , concrete interface friction angle

[0008] S2: Using the formula σ n =H·γ b Calculate the concrete interface normal stress σ n ;

[0009] S3: σ obtained by calculation n , using the formula Calculate the fitting function χ(σ n ), where P a is a standard atmospheric pressure, i.e. 101.3 kPa, a1, b1, c1 are fitting parameters, a1 = 336.4, b1 = -114.0, c1 = 141.4;

[0010] S4: σ obtained by calculation n , using the formula Calculate the fitting function η(σ n );where P a is a standard atmospheric pressure, i.e. 101.3 kPa, a2, b2, c2 are fitting parameters, a2 = 824.4, b2 = 7.5, c2 = 187.5;

[0011] S5: According to And the calculated σ n , χ(σ n ) and η(σ n ) Using the formula Calculate the concrete interface shear stiffness K st The wall height H refers to the wall height above the concrete interface where the shear stiffness is required.

[0012] The concrete interface friction angle It can be obtained by means of inclined plate test.

[0013] The concrete interface includes the wall toe interface between the module and the foundation and the interface between the modules.

[0014] The modules of the modular reinforced earth retaining wall are concrete modules.

[0015] The base is a horizontal base made of plain concrete.

[0016] The wall surface is formed by stacking and dry-laying concrete blocks.

[0017] Furthermore, in order to more conveniently obtain the interface shear stiffness value, the interface shear stiffness K can be established: st Friction angle between wall height H and concrete interface The one-to-one correspondence curve of the interface shear stiffness K can be obtained through this curve. st Specifically, it is known that the density of concrete modules is generally 2200kg / m 3 , that is, the weight of the wall concrete module γ b 21.6kN / m 3 , the interface shear stiffness K can be established st Friction angle between wall height H and concrete interface One-to-one correspondence, such as Figure 7 As shown. Given the weight of the concrete module on the wall γ b With the wall height H, Figure 7 Directly obtain K st .

[0018] By using the method of the present invention, it is only necessary to know the wall height H, the wall concrete module weight γ b Friction angle between concrete and interface The interface shear stiffness can be obtained. By adopting the method of the present invention, not only the shear stiffness of the wall toe interface between the module and the base of the modular reinforced earth retaining wall can be obtained, but also the interface shear stiffness between the wall modules at any position in the modular reinforced earth retaining wall can be obtained. In addition, the method of the present invention is not only applicable to the acquisition of the concrete interface shear stiffness in the modular reinforced earth retaining wall, but also applicable to the acquisition of the concrete interface shear stiffness in any engineering.

[0019] The beneficial effects of the present invention are:

[0020] The method for obtaining the interface shear stiffness provided by the present invention only requires the wall height H, the wall concrete module weight γ b Friction angle between concrete and interface Three parameters are sufficient, and the number of parameters required is small. For modular reinforced earth retaining walls, the wall height H, the wall concrete module weight γ b Friction angle between concrete and interface These are three parameters that are easy to obtain. In addition, the interface shear stiffness value obtained by the method of the present invention is not much different from the shear stiffness value obtained by the direct shear test, and the relative error is within 5%. In short, the method for obtaining the interface shear stiffness provided by the present invention is simple and highly accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1.1is a shear stress and shear displacement relationship curve of the first group of interfaces in a specific embodiment of the present invention;

[0022] Figure 1.2 is a relationship curve between shear strength and normal stress of the first group of interfaces in a specific embodiment of the present invention;

[0023] Figure 2.1 is a shear stress and shear displacement relationship curve of the second group of interfaces in a specific embodiment of the present invention;

[0024] Figure 2.2 is a relationship curve between shear strength and normal stress of the second group of interfaces in a specific embodiment of the present invention;

[0025] Figure 3.1 is a shear stress and shear displacement relationship curve of the third group of interfaces in a specific embodiment of the present invention;

[0026] Figure 3.2 is a relationship curve between shear strength and normal stress of the third group of interfaces in a specific embodiment of the present invention;

[0027] Figure 4 is the relationship curve between shear stiffness and normal stress at different wall toe interfaces;

[0028] Figure 5 is the relationship curve between shear stiffness and friction angle under different normal stress conditions;

[0029] Figure 6 is the relationship curve between the fitting function and the normal stress;

[0030] Figure 7 It is a calculation model for the shear stiffness of the concrete interface in modular reinforced soil retaining walls;

[0031] Figure 8 This is a curve showing the relationship between concrete interface shear stress and shear displacement measured by the direct shear test in Example 1 of the present invention. DETAILED DESCRIPTION

[0032] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0033] The structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the limiting conditions for the implementation of the present invention, so they have no substantial technical significance. Any modification of the structure, change of the proportion relationship or adjustment of the size, without affecting the effects and purposes that can be achieved by the present invention, should still fall within the scope of the technical contents disclosed by the present invention. At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" quoted in this specification are only for the convenience of description, and are not used to limit the scope of the implementation of the present invention. The change or adjustment of their relative relationship should also be regarded as the scope of the implementation of the present invention without substantially changing the technical contents.

[0034] A large direct shear tester was used to carry out direct shear tests on concrete interfaces with three different degrees of roughness under different normal stress conditions. The relationship curve between shear stress and shear displacement was obtained, thereby obtaining the shear stiffness of the interface. The relationship curve between the interface shear stiffness and the interface friction angle and normal stress was also plotted.

[0035] Three groups of concrete interfaces with different roughness were made: six concrete slabs with dimensions of 600mm×400mm×100mm (length×width×height) were made and grouped in pairs to form three groups of interfaces; the first group of interfaces was not treated in any way; a polytetrafluoroethylene film was pasted on the contacting sides of the second group of concrete slabs to change the interface roughness; a 1.5mm thick flexible geomembrane (i.e., flexible PP board) was placed between the third group of concrete slabs to change the interface roughness.

[0036] The interface friction angles of the above three groups of interfaces were obtained by using the inclined plate test method; the interface friction angle of the first group of interfaces was 39°, the interface friction angle of the second group of interfaces was 13°, and the interface friction angle of the third group of interfaces was 8°. The operation method of the inclined plate test is to stack two concrete slabs horizontally, and then lift the lower concrete slab from one side to slowly tilt it. During the tilting process, the tilt angle corresponding to the upper concrete slab starting to slide along the interface between the two slabs is the interface friction angle.

[0037] The above three groups of concrete slabs were subjected to direct shear tests on the interface in turn: the shear box size of the direct shear apparatus is 600mm×400mm×100mm (length×width×height), and the maximum normal loading force is 100kN. Before starting the test, a group of concrete slabs were placed in the upper and lower boxes of the shear box, and then the upper and lower boxes were aligned and pressed. Then, direct shear tests were carried out on the interface at a horizontal speed of 1mm / min under normal stresses of 40kPa, 80kPa, 120kPa and 160kPa, respectively, and the shear stress and shear displacement data were obtained on the computer end of the direct shear apparatus.

[0038] Analysis of test results:

[0039] Group 1 interface

[0040] According to the shear stress and shear displacement data directly read by the direct shear tester, the shear stress-shear displacement relationship curve of the interface is drawn, such as Figure 1.1 The ratio of shear stress to shear displacement when the shear displacement is 2 mm is taken as the shear stiffness value, which is obtained from Figure 1.1 It can be seen that the shear stiffness of the interface under 40kPa, 80kPa, 120kPa and 160kPa normal stresses are 15.7MPa / m, 17.5MPa / m, 22.4MPa / m and 28.3MPa / m respectively. Figure 1.1 The peak shear stress and corresponding normal stress of each curve in the figure are plotted to draw the shear strength-normal stress relationship curve of the interface, as shown in Figure 1.2 As shown. Figure 1.2 The relationship curve shown can be obtained from the function τ=1+σ n tan(39°); where τ is the shear strength, σ n is the normal stress and 39° is the friction angle of the interface.

[0041] Group 2 interface

[0042] According to the shear stress and shear displacement data directly read by the direct shear tester, the shear stress-shear displacement relationship curve of the interface is drawn, such as Figure 2.1 The ratio of shear stress to shear displacement when the shear displacement is 2 mm is taken as the shear stiffness value, which is obtained from Figure 2.1 It can be seen that the shear stiffness of the interface under normal stresses of 40 kPa, 80 kPa, 120 kPa and 160 kPa is 4.3 MPa / m, 8.5 MPa / m, 12.3 MPa / m and 16.0 MPa / m respectively. Figure 2.1 The peak shear stress and corresponding normal stress of each curve in the figure are plotted to draw the shear strength-normal stress relationship curve of the interface, as shown in Figure 2.2 As shown. Figure 2.2 The relationship curve shown can be obtained as the function τ=0.5+σ n tan(13°), where τ is the shear strength, σ n is the normal stress and 13° is the friction angle of the interface.

[0043] Group 3 interface

[0044] According to the shear stress and shear displacement data directly read by the direct shear tester, the shear stress-shear displacement relationship curve of the interface is drawn, such as Figure 3.1 The ratio of shear stress to shear displacement when the shear displacement is 2 mm is taken as the shear stiffness value, which is obtained from Figure 3.1It can be seen that the shear stiffness of the interface under normal stresses of 40 kPa, 80 kPa, 120 kPa and 160 kPa is 2.6 MPa / m, 5.0 MPa / m, 7.5 MPa / m and 8.8 MPa / m respectively. Figure 3.1 The peak shear stress and corresponding normal stress of each curve in the figure are plotted to draw the shear strength-normal stress relationship curve of the interface, as shown in Figure 3.2 As shown. Figure 3.2 The relationship curve shown can be obtained as the function τ=0.2+σ n tan(8°), where τ is the shear strength, σ n is the normal stress and 8° is the friction angle of the interface.

[0045] Comparison of shear stiffness of different interfaces:

[0046] according to Figure 1.1 , 2.1 , 3.1 can be used to obtain the shear stiffness of the above three concrete interfaces under different normal stress conditions, and then the shear stiffness and normal stress relationship curves of the above three interfaces can be drawn, such as Figure 4 As shown. Figure 4 It can be seen that the shear stiffness of each interface increases with the increase of interface normal stress. Under the same normal stress, the interface shear stiffness increases with the increase of interface friction angle or shear strength.

[0047] The shear stiffness of concrete interfaces with three kinds of roughness under different normal stresses is plotted on Figure 5 In order to obtain the relationship curve between interface shear stiffness and friction angle, Figure 5 It can be seen that the relationship curves between the interface friction angle and shear stiffness under different normal stresses can be expressed by logarithmic functions. The logarithmic functions under different normal stresses are normalized to obtain the formula In formula 1, K st is the concrete interface shear stiffness, using H and P a The shear stiffness is treated as dimensionless; H is the wall height; P a is one standard atmospheric pressure; is the interface friction angle; under different normal stress conditions, χ(σ n ),η(σ n ) varies with σ n increases with the increase of .

[0048] Different σ n The corresponding χ(σ n ),η(σ n ) is plotted on Figure 6 In the above equation, we obtain χ(σ n ),η(σ n ) and σ n According to the relationship curve. Figure 6 The χ(σ n ),η(σ n ) and σ n The relationship curve of χ(σ n ),η(σ n ) About σ n The fitting function formulas are polynomial functions shown in formulas 2 and 3 respectively;

[0049]

[0050]

[0051] In formulas 2 and 3, a standard atmospheric pressure P is used. a σ n Dimensionless; a1, a2, b1, b2, c1, c2 are all fitting parameters, and their values ​​are shown in Table 1.

[0052] Table 1

[0053] Fitting parameters Value <![CDATA[a1]]> 336.4 <![CDATA[a2]]> 824.4 <![CDATA[b1]]> -114.0 <![CDATA[b2]]> 7.5 <![CDATA[c1]]> 141.4 <![CDATA[c2]]> 187.5

[0054] Formulas 1, 2, and 3 determine the interface shear stiffness K st On the interface normal stress σ n and interface friction angle The interface normal stress σ n Determined by the wall height H, σ n The relationship with H is σ n =H·γ b , where γ b is the weight of the concrete module. Therefore, we only need to know the wall height H and the weight of the concrete module γ b and interface friction angle According to σ n =H·γ b Calculate σ n Then, the interface shear stiffness K is calculated by using the formulas 2, 3, and 1 provided by the present invention. st .

[0055] Since the density of concrete modules is generally 2200kg / m 3 , that is, the weight of the concrete module γ b Generally 21.6kN / m 3 ; In order to more conveniently obtain the interface shear stiffness K in the modular reinforced soil retaining wall st , the different interface friction angles can be plotted Wall height H and interface shear stiffness K under the condition st The relationship curve is used as the standard curve. When using, only the interface friction angle and wall height H, then read the interface shear stiffness K through the standard curve st Specifically, the interface shear stiffness K can be established st With wall height H, interface friction angle One-to-one correspondence, such as Figure 7 shown. Figure 7 It is given in K is within the range of 5° to 45°, H is within the range of 3m to 10m st If the wall height H is known, we can use Figure 7 Directly obtain K st .

[0056] The test values ​​of the interface shear stiffness and the calculated values ​​of the interface shear stiffness (a small number of values ​​are listed in Table 2) are compared and analyzed. The results show that the absolute error between the calculated value and the test value obtained by the method of the present invention does not exceed 0.4MPa / m, and the relative error does not exceed 5%. It can be seen that the method for obtaining the interface shear stiffness provided by the present invention has high accuracy.

[0057] Table 2

[0058]

[0059] Example 1

[0060] A 7.4m high modular reinforced earth retaining wall constructed of 600mm×400mm×100mm (length×width×height) concrete modules was selected for the inclined plate test to measure the interface friction angle between the concrete modules. 34°, and then four measuring points are selected at different heights of the retaining wall, and the distances between each measuring point and the top surface of the wall are 1.8m, 3.7m, 5.6m, and 7.4m, respectively. The method of the present invention is used to calculate the interface shear stiffness K at these four measuring points st .

[0061] Step S1: Use formula σ n =H·γ b Calculate the normal stress σ at 1.8m, 3.7m, 5.6m, and 7.4m from the top of the wall (H) n ; The calculated results are 38.9kPa, 79.9kPa, 121.0kPa, and 159.8kPa respectively.

[0062] Step S2: According to the normal stress σ at different H points obtained n , using the formula Calculate the fitting function χ(σ n ) values, where a1 = 336.4, b1 = -114.0, c1 = 141.4; P ais a standard atmospheric pressure, i.e. 101.3 kPa; the calculation results are: χ(38.9 kPa) = 147.2, χ(79.9 kPa) = 260.8, χ(121.0 kPa) = 485.2, χ(159.8 kPa) = 798.7; Step S3: According to the normal stress σ at different H points obtained n , using the formula Calculate the fitting function η(σ n ) values, where a2 = 824.4, b2 = 7.5, c2 = 187.5; P a is a standard atmospheric pressure, i.e. 101.3 kPa; the calculation results are: η(38.9 kPa) = 311.9, η(79.9 kPa) = 706.3, η(121.0 kPa) = 1372.7, η(159.8 kPa) = 2250.8;

[0063] Step S4: According to H, And the calculated χ(σ n ) and η(σ n ) Using the formula Calculation of interface shear stiffness K st , where P a is a standard atmospheric pressure, i.e. 101.3 kPa; the interface shear stiffness K at the distances of 1.8 m, 3.7 m, 5.6 m and 7.4 m from the top of the wall is calculated. st They are 14.0MPa / m, 16.5MPa / m, 21.4MPa / m and 26.5MPa / m respectively.

[0064] The wall module of the retaining wall was subjected to direct shear test. The normal stress of the direct shear test was set to 38.9 kPa, 79.9 kPa, 121.0 kPa, and 159.8 kPa, respectively. The interface shear stress-shear displacement curve was obtained as shown in Figure 8 As shown in the curve, the concrete interface shear stiffness K at the distances of 1.8m, 3.7m, 5.6m and 7.4m from the top of the wall can be obtained. st They are 13.3MPa / m, 16.2MPa / m, 21.1MPa / m and 27.0MPa / m respectively.

[0065] The wall toe interface shear stiffness values ​​calculated in this embodiment are compared with the shear stiffness values ​​obtained by the direct shear test. The minimum error is only 0.3 MPa / m, corresponding to a relative error of 1%; the maximum error is 0.7 MPa / m, corresponding to a relative error of 5%.

[0066] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for obtaining the shear stiffness of the concrete interface in a modular reinforced earth retaining wall, characterized in that: The following steps are involved: S1: Get wall height H、 Module Heavy γ b 、Interface friction angle φ t ; S2: Using formula σ n = H•γ b Calculate the interface normal stress σ n ; S3: Obtained by calculation σ n , using the formula Calculate the fitting function χ ( σ n );in a 1=336.4、 b 1=-114.0、 c 1=141.4； S4: obtained by calculation σ n , using the formula Calculate the fitting function η ( σ n ); a 2. b 2. c 2 is the fitting parameter, a 2=824.4, b 2=7.5, c 2=187.5; S5: obtained by calculation σ n , χ ( σ n )and η ( σ n ) Using the formula Calculate the shear stiffness of the wall toe interface K st ; In the above formula P a is a standard atmospheric pressure.

2. The acquisition method according to claim 1, characterized in that: The wall height H It refers to the wall height above the interface where the shear stiffness is required.

3. The acquisition method according to claim 1, characterized in that: The interface friction angle φ t Obtained by means of inclined plate test.

4. The acquisition method according to claim 1, characterized in that: The interface includes the wall toe interface between the wall module and the base and the interface between modules.

5. The acquisition method according to claim 4, characterized in that: The modules of the modular reinforced earth retaining wall are concrete modules.

6. The acquisition method according to claim 4, characterized in that: The base is a horizontal base made of plain concrete.

7. The acquisition method according to claim 4, characterized in that: The wall surface is formed by stacking and dry-laying concrete blocks.

8. The acquisition method according to claim 1, characterized in that: Establishing interface shear stiffness K st With wall height H 、Interface friction angle φ t The one-to-one correspondence curve of the interface shear stiffness can be obtained through this curve. K st .

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