Prediction method of lateral displacement of modular reinforced soil retaining wall face plate considering tendon creep

Abstract

This invention discloses a method for predicting the lateral displacement of a modular reinforced soil retaining wall panel considering the creep of the reinforcement. First, the interior of the retaining wall is divided into an active zone and a stable zone, and the length L of the reinforcement in the active zone is calculated separately. ai and the length L of the reinforcement in the stable zone ei Next, determine the tensile force of the reinforcing bars in the active and stable zones; then, under the tensile force of the i-th layer of reinforcing bars, determine the elastic deformation δ of the i-th layer of reinforcing bars when the retaining wall is completed. ei Then determine the creep deformation δ of the i-th layer of reinforcement in the retaining wall at different operating times. ci Finally, the δ of each layer ei and δ ci Summing these values ​​yields the total deformation δ of the i-th layer of reinforcement. i This refers to the lateral displacement of the retaining wall panel considering the creep effect of the reinforcement. This invention fully considers the elastic deformation of the reinforcement at the time of construction and the creep deformation of the reinforcement under long-term tension. By establishing the relationship between the total strain of the reinforcement and the operating time, the magnitude of the lateral displacement of the reinforced soil retaining wall panel during normal service is obtained, thereby ensuring the long-term stability of the reinforced soil retaining wall.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering technology, specifically a method for predicting the lateral displacement of a modular reinforced soil retaining wall panel that takes into account the creep of the reinforcing material. Background Technology

[0002] Reinforced soil retaining walls are widely used in geotechnical engineering projects such as roadbeds, bridge abutments, wharves, and dams due to their advantages of light weight, small footprint, low cost, fast construction, and aesthetic appeal. A reinforced soil retaining wall generally consists of three parts: backfill soil, reinforcement, and a panel. The reinforcement is embedded within the fill material at specific intervals and lengths to form reinforced areas, and its front ends are usually fixedly connected to the panel. During service, the lateral displacement of the panel is a crucial criterion for determining whether the reinforced soil retaining wall is operating normally. Especially for projects with strict displacement control requirements, predicting the lateral displacement of the reinforced soil retaining wall panel at different operational stages is a critical issue that urgently needs to be addressed.

[0003] Currently, some research has proposed methods for predicting the lateral displacement of reinforced soil retaining wall panels. For example, the literature "Reinforced soil structures. Vol. 1: Design and construction guidelines" establishes an empirical relationship between the maximum lateral deformation of the retaining wall panel and the length of the reinforcement and the height of the wall. The literature "Vegas mini pier experiment and postulate of zero volume change" predicts the lateral displacement of the panel by determining the settlement at the top of the wall based on the principle of equal volume of the retaining wall. Patent application number 202010519300.6 discloses a method for determining the horizontal displacement of the wall surface in the ultimate state of a modular reinforced soil retaining wall. This method is based on the static equilibrium analysis of the wall panel of the modular reinforced soil retaining wall in the ultimate state, and further determines the horizontal displacement of the wall surface in the ultimate state of the modular reinforced soil retaining wall by obtaining the connection force between the wall panel and the reinforcement. However, the creep of the reinforcement often causes lateral deformation of the retaining wall panel during the long service life. When the amount of deformation exceeds the allowable value of the retaining wall design, it will lead to the instability and collapse of the wall structure, posing a huge threat to personal and property safety. The prediction methods proposed in the aforementioned studies focus primarily on the lateral displacement of the panel upon completion of construction, neglecting the creep effect of the reinforcement under long-term tensile conditions. This leads to significant discrepancies between the predicted results and the actual situation. Therefore, it is essential to establish a method for predicting the lateral displacement of modular reinforced soil retaining wall panels that considers reinforcement creep. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is to provide a method for predicting the lateral displacement of modular reinforced soil retaining wall panels that takes into account the creep of reinforcing materials.

[0005] The technical solution of this invention to solve the aforementioned technical problem is to provide a method for predicting the lateral displacement of a modular reinforced soil retaining wall panel considering the creep of the reinforcing material, characterized in that the method includes the following steps:

[0006] Step 1: Assume that the lateral displacement of the modular reinforced soil retaining wall panel is caused by the deformation of the reinforcement, and that the potential failure surface of the retaining wall follows the Rankine failure surface pattern; then, using the Rankine failure surface, divide the interior of the retaining wall into an active zone and a stable zone, with the length L of the reinforcement under tension. i Equal to the length L of the reinforcing bar located in the active zone ai and the length L of the reinforcing bar located in the stable region ei The sum; according to geometric relationships and the principle of static equilibrium, L ai and L ei Calculated using equations (1) and (2) respectively:

[0007]

[0008]

[0009] In equations (1) and (2), H is the total height of the retaining wall; i Depth of reinforcement material embedment; FS is the internal friction angle of the fill soil. p P is the pull-out safety factor; rmi R is the maximum tensile force per unit width of the i-th layer of reinforcing bars; C is the surface geometric coefficient; R c F* is the coverage ratio of the reinforcing bars in the horizontal section of the retaining wall; α is the pull-out resistance coefficient; σ is the dimensional correction factor; vi Let be the vertical earth pressure between the i-th layer of reinforced soil interface;

[0010] Step 2: Determine the tensile force of the reinforcing bars in the active and stable zones;

[0011] Step 3, the tensile force P of the i-th layer of reinforcement ri Under the action of (x), the elastic deformation δ of the i-th layer of reinforcement when the retaining wall is completed. ei ;

[0012]

[0013] In equation (5), ε 0i K represents the elastic deformation of the i-th layer of reinforcement; reinf For the stiffness of the reinforcing material;

[0014] For dδ ei Integrating, we can obtain the elastic deformation of the i-th layer of reinforcement as:

[0015]

[0016] Step 4: Determine the creep deformation δ of the i-th layer of reinforcement in the retaining wall at different operating times during the long-term service phase. ci ;

[0017] Step 4.1: Conduct indoor creep tests to determine the tensile force P of different reinforcing materials. r The creep deformation of the reinforcing bar was measured by fitting the actual creep deformation data using a hyperbolic creep model to obtain the results under different reinforcing bar tensile forces P. r The corresponding hyperbolic creep model parameters a and b are then used to establish aP based on the least squares method. r and bP r The relationship; the formula for the hyperbolic creep model is shown in equation (7):

[0018]

[0019] In equation (7), ε(t) is the total strain of the reinforcing bar at time t; ε0 is the initial strain of the reinforcing bar; t is time; a and b are the hyperbolic creep model parameters, which are related to the tensile force P of the reinforcing bar. r related;

[0020] Step 4.2, using the measured aP r and bP r The relationship is used to determine the creep deformation δ of the i-th layer of reinforcement in the retaining wall at different operating times. ci As shown in equation (10):

[0021]

[0022] Step 5: Calculate the δ value of each layer. ei and δ ci Summing these values ​​yields the total deformation δ of the i-th layer of reinforcement. i Total deformation δ i This refers to the lateral displacement of the retaining wall panel considering the creep effect of the reinforcement:

[0023]

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] (1) This invention fully considers the elastic deformation of the reinforcing steel upon completion of construction and the creep deformation of the reinforcing steel under long-term tension. By establishing the relationship between the parameters of the hyperbolic creep model and the tensile force of the reinforcing steel, the creep deformation of the reinforcing steel at different times is calculated, thereby obtaining the total strain of the reinforcing steel, which is equivalent to the lateral displacement of the panel. Furthermore, the relationship between the lateral displacement of the panel and the operating time is established to obtain the calculated value of the lateral displacement of the reinforced soil retaining wall panel during normal service, thus ensuring the long-term stability of the reinforced soil retaining wall. The lateral displacement value of the retaining wall panel calculated by this invention is closer to the actual value, which is beneficial for the structural design and internal stability analysis of reinforced soil retaining walls.

[0026] (2) The present invention uses the Rankine failure surface to divide the retaining wall into an active zone and a stable zone. The calculated reinforcement laying length is the minimum, which can greatly reduce the amount of reinforcement used in the design of the retaining wall structure and has significant economic benefits.

[0027] (3) The application of this invention requires specific design parameters for reinforced soil retaining walls, as follows: ① Geometric dimensions, such as the total height of the retaining wall; ② Reinforcement arrangement, such as reinforcement length, reinforcement embedment depth, horizontal and vertical spacing between adjacent reinforcement units; ③ Backfill material properties, such as backfill unit weight and internal friction angle; ④ Reinforcement material properties, such as reinforcement stiffness, the relationship between hyperbolic creep model parameters and reinforcement tension; ⑤ Top overburden load originates from traffic dynamic load, which can be equivalent to a uniformly distributed load, such as traffic load that can be equivalent to a uniformly distributed load; ⑥ Other parameters, such as pull-out safety factor, pull-out resistance factor, size correction factor, surface geometric coefficient, reinforcement coverage rate in the horizontal section of the retaining wall, and time.

[0028] In contrast, this invention overcomes the shortcomings of existing methods, which involve numerous and difficult-to-determine model parameters. It establishes the relationship between the creep characteristics of the reinforcement and the lateral displacement of the retaining wall panel by employing basic parameters used by engineers in designing reinforced soil retaining wall structures. Furthermore, this method involves simple principles and convenient calculations, making it beneficial for practical engineering applications.

[0029] (4) This invention provides a prediction method for the lateral displacement of the panel of a modular reinforced soil retaining wall during long-term service, which can reasonably predict whether the service performance of the modular reinforced soil retaining wall is good throughout the entire operation cycle: by comparing the theoretical value calculated by this invention with the measured value detected in actual engineering, it can be determined in advance whether the retaining wall is in good service condition at different operating times, and thus take effective disaster prevention and control measures in advance. If the two can match well, it can be used to predict the lateral displacement of the panel of the retaining wall during the entire service cycle of 15 to 25 years. When the maximum predicted value is close to the existing relevant specifications, such as the upper limit of the maximum horizontal displacement of 0.9%H to 4.0%H specified in Reference 3, an alarm can be issued to the maintenance and repair unit in a timely manner so that effective disaster prevention and control measures can be taken.

[0030] (5) This invention is applicable to reinforced soil retaining walls built on rigid foundations with vertical panels, and reinforcements distributed at equal intervals with a laying length that meets the internal stability requirements of the retaining wall. Attached Figure Description

[0031] Figure 1 This is a structural schematic diagram of the modular reinforced soil retaining wall of the present invention;

[0032] Figure 2 This is a diagram showing the division of the tensile stress zone of the internal reinforcing bars in the retaining wall according to the present invention;

[0033] Figure 3This is a comparison diagram of the minimum reinforcement laying length specified by the method of the present invention and existing methods;

[0034] Figure 4 This is a comparison diagram of the deformation of the retaining wall panel calculated by the method of the present invention and existing methods. Detailed Implementation

[0035] Specific embodiments of the present invention are given below. These specific embodiments are only used to further illustrate the present invention in detail and do not limit the scope of protection of the claims of the present invention.

[0036] This invention provides a method for predicting the lateral displacement of a modular reinforced soil retaining wall panel considering the creep of the reinforcing steel (hereinafter referred to as the method), characterized in that the method includes the following steps:

[0037] Step 1: Assume that the lateral displacement of the panel of the modular reinforced soil retaining wall (hereinafter referred to as the retaining wall) is caused by the deformation of the reinforcement (including elastic deformation and creep deformation), and that the potential failure surface of the retaining wall follows the Rankine failure surface form; then, using the Rankine failure surface, the interior of the retaining wall is divided into an active zone and a stable zone, and the length L of the reinforcement with tensile force is... i Equal to the length L of the reinforcing bar located in the active zone ai and the length L of the reinforcing bar located in the stable region ei The sum of, i.e., L i =L ai +L ei (like Figure 2 (as shown); based on geometric relationships and the principle of static equilibrium, L ai and L ei Calculated using equations (1) and (2) respectively:

[0038]

[0039]

[0040] In equations (1) and (2), H is the total height of the retaining wall, in meters; i The embedment depth of the reinforcing bars is expressed in meters (m). FS is the internal friction angle of the backfill, in degrees. p P is the pull-out safety factor; rmi R represents the maximum tensile force per unit width of the i-th layer of reinforcing bars, in kN / m; C is the surface geometry coefficient, which can be taken as 2.0 for strip and grid-type reinforcing bars; c The coverage ratio of the reinforcing bars within the horizontal section of the retaining wall is 1.0 for continuously laid reinforcing bars; F* is the pull-out resistance coefficient, which can be taken as [value missing]. α is a size correction factor, which is 0.8 for geogrids and 0.6 for geotextiles; σ vi is the vertical earth pressure between the i-th layer of reinforced soil interface, in kPa;

[0041] Step 2: Determine the tensile force of the reinforcing bars in the active and stable zones;

[0042] Step 2.1: Determine the horizontal earth pressure σ at the i-th layer of reinforcement-soil interface behind the retaining wall panel. hi :

[0043]

[0044] In equation (3), K a γ is the Rankine active earth pressure coefficient; γ is the unit weight of the fill, in kN / m³. 3 ;q represents the equivalent uniformly distributed load caused by the overlying load, in kN / m;

[0045] Step 2.2: Assume that the tensile force of the reinforcement in the active zone is uniformly distributed, and its value is equal to the horizontal earth pressure σ at the buried depth. hi Meanwhile, the tensile force of the reinforcing bars in the stable region decreases linearly along the length of the reinforcing bars (e.g., ...). Figure 2 As shown), therefore, the tensile force P of the i-th layer of reinforcement is determined. ri (x):

[0046]

[0047] In equation (4), P ri (x) represents the tensile force of the i-th layer of reinforcement at position x, in kN / m; x is the horizontal distance from the back of the retaining wall panel, in meters, when 0 ≤ x ≤ L. ai When located at L ai Within the region, when L ai <x≤L i When located at L ei Within the area; S v and S h These represent the vertical and horizontal spacing between adjacent reinforcing bar units, respectively, in meters (m).

[0048] Step 3, the tensile force P of the i-th layer of reinforcement ri Under the action of (x), determine the elastic deformation δ of the i-th layer of reinforcement when the retaining wall is completed. ei ;

[0049]

[0050] In equation (5), ε 0i K represents the elastic deformation of the i-th layer of reinforcement; reinf This refers to the stiffness of the reinforcing bar, expressed in kN / m.

[0051] For dδ ei Integrating, we can obtain the elastic deformation of the i-th layer of reinforcement as:

[0052]

[0053] Step 4: Determine the creep deformation δ of the i-th layer of reinforcement in the retaining wall at different operating times during the long-term service phase. ci ;

[0054] Step 4.1: Conduct indoor creep tests to determine the tensile force P of different reinforcing materials. r The creep deformation of the reinforcing bar was measured by fitting the actual creep deformation data using a hyperbolic creep model to obtain the results under different reinforcing bar tensile forces P. r The corresponding hyperbolic creep model parameters a and b are then used to establish aP based on the least squares method. r and bP r The relationship; the formula for the hyperbolic creep model is shown in equation (7):

[0055]

[0056] In equation (7), ε(t) is the total strain of the reinforcing bar at time t; ε0 is the initial strain of the reinforcing bar, i.e., the elastic strain; t is time, in hours; a and b are the hyperbolic creep model parameters, which are related to the tensile force P of the reinforcing bar. r Related; numerous existing indoor reinforcement creep tests show that: a is related to tensile force P. r It exhibits an exponential relationship, while b and P r It exhibits a negative linear relationship.

[0057] Step 4.2, using the measured aP r and bP r The relationship is used to determine the creep deformation δ of the i-th layer of reinforcement in the retaining wall at different operating times. ci As shown in equation (10):

[0058]

[0059] Preferably, step 4.2 specifically involves: the creep of the reinforcing steel is time-dependent and a function of time. The creep deformation of the reinforcing steel within a unit time dt is dε. c (t), the creep deformation dδ of the i-th layer of reinforcement within a unit length dx. ci for:

[0060] dδ ci =dε ci (t)dx (8)

[0061] Then, ε in equation (7) c Substituting (t) into equation (8) yields the following equation:

[0062]

[0063] Integrating equation (9) again, we obtain the creep deformation δ of the i-th layer of reinforcement.ci for:

[0064]

[0065] Step 5: Calculate the δ value of each layer. ei and δ ci Summing these values ​​yields the total deformation δ of the i-th layer of reinforcement. i Total deformation δ i This refers to the lateral displacement of the retaining wall panel considering the creep effect of the reinforcement:

[0066]

[0067] Preferably, the method further includes: step 6, drawing the lateral displacement δ of the retaining wall panel. i By comparing the relationship curves between the wall height h or the normalized wall height (h / H) and the panel lateral displacement at different service periods, the variation law of the maximum lateral displacement in terms of both value and location can be clarified, thereby quantifying the influence of the reinforcement creep effect on the panel lateral displacement.

[0068] Example 1

[0069] This embodiment presents a method for predicting the lateral displacement of a modular reinforced soil retaining wall panel considering reinforcement creep. The modular reinforced soil retaining wall (hereinafter referred to as the retaining wall) includes backfill, reinforcement, and a panel. The retaining wall is built on a rigid foundation and the panel is vertical. The reinforcement is evenly distributed and its laying length satisfies the internal stability of the retaining wall. Figure 1 As stated above.

[0070] In this embodiment, the modular reinforced soil retaining wall described in reference 1, "Liu H, Wang X, Song E. Long-term behavior of GRS retaining walls with marginal backfill soils. Geotextiles and Geomembranes 2009; 27: 295–307," is selected. The wall has H = 8.0m, L = 5.6m, and 13 layers of reinforcement. i The lengths are 0.6m, 1.2m, 1.8m, 2.4m, 3.0m, 3.6m, 4.2m, 4.8m, 5.4m, 6.0m, 6.6m, 7.2m, and 7.8m respectively. h =0m, S v =0.6m, γ =20kN / m 3 and K reinf =1300kN / m, a=1.689e -0.110Pr b = 0.677 - 0.014P r q = 0 kPa, FS p=1.5, F*=0.38, α=0.8, C=2.0, R c =1.0, t=43800h (i.e., 5 years).

[0071] Substitute the above parameters into equations (1) to (11) to carry out step-by-step calculations. The lengths of the reinforcement in each layer calculated using equations (1) and (2) are compared with the results obtained by the method described in references 2 (Jewell RA, Milligan GW. Deformation calculation for reinforced soil walls. Vol 2 Proc, 12th Int Conf Soil Mech Found Eng 1259–1262 Abingdon, UK Taylor Fr 1989.) and 3 (FHWA-NHI-10-024: Design and construction of mechanically stabilized earth walls and reinforced soilslopes-volume I. Washington, DC Fed Highw Adm US Dep Transp 2009.). Figure 3 As shown, the method proposed in Reference 2 specifies that the distribution of the tensile force of the reinforcement is related to the internal friction angle of the backfill and the embedment depth of the reinforcement. The length of each layer of reinforcement can be taken as [value missing]. In Reference 3, the length of each layer of reinforcing material should not be less than 0.7H. Figure 3 It can be seen that the method of the present invention calculates the minimum length of each layer of reinforcing material, which has significant economic benefits.

[0072] The lateral displacement δ of the modular reinforced soil retaining wall panel is plotted according to equation (11). i The relationship curve between the wall height and the normalized wall height (h / H) is as follows: Figure 4 As shown. Compared with the methods described in References 2 and 4 (Wu JT, Pham TQ, Adams MT. Composite behavior of geosynthetic reinforced soil mass. FHWARep No. FHWA-HRT-10-077, McLean, VA 2013.), the panel lateral displacement obtained by the method of the present invention is in best agreement with the results obtained in Reference 1, proving the effectiveness and accuracy of the method of the present invention.

[0073] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for predicting the lateral displacement of a modular reinforced soil retaining wall panel considering the creep of reinforcing materials, characterized in that, The method includes the following steps: Step 1: Assume that the lateral displacement of the modular reinforced soil retaining wall panel is caused by the deformation of the reinforcement, and that the potential failure surface of the retaining wall follows the Rankine failure surface pattern; then, using the Rankine failure surface, divide the interior of the retaining wall into an active zone and a stable zone, with the length L of the reinforcement under tension. i Equal to the length L of the reinforcing bar located in the active zone ai and the length L of the reinforcing bar located in the stable region ei The sum; according to geometric relationships and the principle of static equilibrium, L ai and L ei Calculated using equations (1) and (2) respectively: In equations (1) and (2), H is the total height of the retaining wall; i Depth of reinforcement material embedment; FS is the internal friction angle of the fill soil. p P is the pull-out safety factor; rmi R is the maximum tensile force per unit width of the i-th layer of reinforcing bars; C is the surface geometric coefficient; R c F* is the coverage ratio of the reinforcing bars in the horizontal section of the retaining wall; α is the pull-out resistance coefficient; σ is the dimensional correction factor; vi Let be the vertical earth pressure between the i-th layer of reinforced soil interface; Step 2: Determine the tensile force of the reinforcing bars in the active and stable zones; Step 3, the tensile force P of the i-th layer of reinforcement ri Under the action of (x), determine the elastic deformation δ of the i-th layer of reinforcement when the retaining wall is completed. ei ; In equation (5), ε 0i K represents the elastic deformation of the i-th layer of reinforcement; reinf For the stiffness of the reinforcing material; For dδ ei Integrating, we can obtain the elastic deformation of the i-th layer of reinforcement as: Step 4: Determine the creep deformation δ of the i-th layer of reinforcement in the retaining wall at different operating times during the long-term service phase. ci ; Step 4.1: Conduct indoor creep tests to determine the tensile force P of different reinforcing materials. r The creep deformation of the reinforcing bar was measured by fitting the actual creep deformation data using a hyperbolic creep model to obtain the results under different reinforcing bar tensile forces P. r The corresponding hyperbolic creep model parameters a and b are then used to establish aP based on the least squares method. r and bP r The relationship; the formula for the hyperbolic creep model is shown in equation (7): In equation (7), ε(t) is the total strain of the reinforcing bar at time t; ε0 is the initial strain of the reinforcing bar; t is time; a and b are the hyperbolic creep model parameters, which are related to the tensile force P of the reinforcing bar. r related; Step 4.2, using the measured aP r and bP r The relationship is used to determine the creep deformation δ of the i-th layer of reinforcement in the retaining wall at different operating times. ci As shown in equation (10): Step 5: Calculate the δ value of each layer. ei and δ ci Summing these values ​​yields the total deformation δ of the i-th layer of reinforcement. i Total deformation δ i This refers to the lateral displacement of the retaining wall panel considering the creep effect of the reinforcement:

2. The method for predicting the lateral displacement of a modular reinforced soil retaining wall panel considering the creep of reinforcing materials according to claim 1, characterized in that, Step 2 specifically involves: Step 2.1: Determine the horizontal earth pressure σ at the i-th layer of reinforcement-soil interface behind the retaining wall panel. hi : In equation (3), K a γ is the Rankine active earth pressure coefficient; γ is the unit weight of the fill; q is the equivalent uniformly distributed load caused by the overburden load. Step 2.2: Assume that the tensile force of the reinforcement in the active zone is uniformly distributed, and its value is equal to the horizontal earth pressure σ. hi The tensile force of the reinforcing bars in the stable region decreases linearly along the length of the reinforcing bars. Therefore, the tensile force P of the i-th layer of reinforcing bars is determined. ri (x): In equation (4), P ri (x) represents the tensile force of the i-th layer of reinforcement at position x; x is the horizontal distance from the back of the retaining wall panel, S v and S h These represent the vertical and horizontal spacing between adjacent reinforcing bar units, respectively.

3. The method for predicting the lateral displacement of a modular reinforced soil retaining wall panel considering the creep of reinforcing materials according to claim 1, characterized in that, Step 4.2 specifically refers to: when the creep deformation of the reinforcing steel within a unit time dt is dε c (t), the creep deformation dδ of the i-th layer of reinforcement within a unit length dx. ci for: dδ ci =dε ci (t)dx (8) Then, ε in equation (7) c Substituting (t) into equation (8) yields the following equation: Integrating equation (9) again, we obtain the creep deformation δ of the i-th layer of reinforcement. ci for:

4. The method for predicting the lateral displacement of a modular reinforced soil retaining wall panel considering the creep of reinforcing materials according to claim 1, characterized in that, The method also includes: Step 6, drawing the lateral displacement δ of the retaining wall panel. i By comparing the relationship curves between the wall height h or the normalized wall height h / H, the magnitude of the lateral displacement of the panel at different service periods can be identified, clarifying the variation law of the maximum lateral displacement in terms of both value and location, thereby quantifying the degree of influence of the reinforcement creep effect on the lateral displacement of the panel.

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