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This paper reports results of laboratory and 3D numerical modeled Pull Out Boxes-out tests with steel ladders and polymeric strip reinforcements. These types of reinforcement are commonly used in reinforced soil walls constructed with concrete facing elements. Laboratory pull-out tests are required to determine accurate and realistic pull-out strength values considering the interaction of specific reinforcement and backfill materials under different confining pressures (i.e., trying to simulate the different reinforcement layer arrangements and load conditions in actual reinforced soil walls). International design Codes for reinforced soil walls provide default values for pull-out strength. However, in many cases, default values are too conservative and/or are not strictly specified for particular reinforcement types. Pull-out tests can be difficult and expensive to perform, thus not being common nor worth for the vast majority of reinforced soil wall projects. Consequently, calibrated numerical models can be useful to predict pull-out response under site-specific conditions, and provide further understanding of the mechanisms involved in the soil-reinforcement interaction. Details of the numerical approach, including relevant aspects of the soil-reinforcement interfaces, are described. Examples of calibrated numerical predictions for pull-out loads, displacements, and soil-dilatancy effects are presented. The influence of reinforcement, soil and interface stiffnesses is shown. Numerical results provide useful insight for future modelling works of the complex interaction between type-specific backfill materials and reinforcement element, relevant for investigation and/or practical design of reinforced soil walls.
Design of reinforced soil walls (RSWs) typically considers working stress conditions (i.e., far away from failure), meaning strains are not enough to fully develop the soil-reinforcement interface strength, even for extensible reinforcements, in which maximum strains are not expected to surpass a 1% threshold1. Accurate designing of RSWs requires a proper characterization of the interface shear behaviour between the embedded reinforcement elements and surrounding soil material. Pullout tests are particularly useful to study the shear response between soil and reinforcement materials, allowing to quantify interface strength and stiffness parameters required for an optimized reinforcement design while ensuring safety conditions.
Ample research of pullout test data for steel and polymeric reinforcements with varied geometries (i.e., ladders, grids, mats, strips, among others) is available in the literature. Pullout failure can be troublesome depending on the reinforcement geometry and surcharge conditions2 as well as backfill material characteristics3,4,5. The pullout response between metallic and polymeric reinforcement has proven to be drastically different6. Metallic (i.e. inextensible) reinforcement presents an instantaneous stress–strain response throughout the material, while in polymeric (i.e., extensible) reinforcement, the stress-stress response is gradual and varies from the head to rear. Latest research still includes experimental work (e.g., Gergiou et al.7), as well as a special focus on model accuracy and reliability assessments of current design methods (e.g.,8,9,10,11,12), where it has been stated that the pullout limit state can have practical variations depending on the chosen load model.
Numerical methods have been used to replicate the pullout behaviour in reinforced soil structures, either by discrete element (e.g.,13,14) or finite element (e.g.,15,16) methods. Reported results have shownproper adjustments between simulated and measured values, providing evidence of the accuracy of numerical tools.
The present study focuses, first, in laboratory measured data from pullout tests using steel ladder and polymeric strip reinforcements following the requirements of ASTM D6706-0117 and EN 1373818 and lessons learned from previous cases in the literature (e.g.,19,20, among others). Measured results were compared with past measured and theorical data available in the literature as well as international codes. Second, a 3D finite element model was implemented to simulate and analyze pullout response. A base case was defined with typical properties considering frequently used backfill soils in RSWs. Sensitivity analyses were carried out over model parameters, followed by a calibration process which took into account the measured steel ladder and polymeric strip pullout test data.
The stress-transfer mechanism of soil-reinforcement pullout interactions depend on reinforcement type and configuration, soil properties, and applied stress. For strips and sheet reinforcement, the pullout resistance is equal to the frictional shear stresses over the whole contact area between soil and reinforcement. For bar-mat, ladder, grid, or ribbed strip reinforcements, a complementary passive strength or bearing resistance is developed due to the transversal member surfaces, in which dilatancy, reinforcement roughness and soil stress state come into play21. The pullout resistance (Pr) can be expressed as follows (Eq. 1):
Here, f’ is the friction interaction factor between the soil and the reinforcement, C is the overall reinforcement surface area geometry factor (i.e., equal to 2 for strips and ladder as in two contact faced-reinforcement configuration systems), w is the width of the reinforcement, and \({{\text{L}}}_{{\text{e}}}^{\mathrm{^{\prime}}}\) is the effective reinforcement length in the resisting zone.
The friction interaction factor f’ will vary depending on the refenced code. In the case of AASHTO22, a scale effect correction factor (α), and a pullout friction factor (F*) are proposed. Factor α is assume to be 1 for inextensible reinforcement, and less than 1 for extensible reinforcements. Factor F* is a reduction of soil strength via an interaction coefficient, Ri, and the soil friction angle, ϕ (Eq. 2). For geosynthetic materials (i.e., geogrids, geotextiles, and geostrips), Ri has a proposed value of 0.6722. In the case of polymeric strips, values of Ri = 0.8 can be conservatively assumed in the absence of test data23,24. By means of statistical analysis, Miyata et al.12 showed that the accuracy of linear pullout models for polymeric strips will depend on the magnitude of predicted pullout capacity and vertical stress acting over the reinforcement, which is generally not desired in design methodologies. For bar-mat or steel ladders, the value of F* can be obtained as a relationship between thickness of the transversal bar members, t, and separation between transversal bar members, St, as follows (Eq. 3):
Here, nq is a bearing capacity factor that varies linearly with depth from nq = 20 at surface level (z = 0) to nq = 10 at depths of 6 m or more. Values of nq mean F* will be a linearly decreasing function from 0 to 6 m of depth, and constant for greater depths. Pullout models based on grid geometry and containing empirical parameters have shown to perform better than purely theoretical bearing capacity and soil friction angle models1,25
In the case of NF P 94-27026, f´ is related to an apparent soil-reinforcement interaction coefficient, μ*(z), which varies with soil gradation, transversal bar diameter and separation for steel ladders, and soil gradation and soil friction angle ϕ for polymeric strips. As with F* (from AASHTO22, the value of μ*(z) decreases linearly until 6 m of depth, after which it remains constant.
Figure 1 compares the values of f´ obtained through AASHTO22 and NF26 guidelines. For steel ladder reinforcements (Fig. 1a), a transversal bar separation of 300 mm with 10 mm-diameter bars is assumed. For polymeric strips (Fig. 1b) a soil friction angle ϕ = 36° and a coefficient of uniformity Cu > 2 is assumed. Clear variations between design codes evidence the need for laboratory pullout tests to obtain valuable data concerning the combined response of project specific type of reinforcement, loading conditions, and fill material characteristics.
Friction-interaction factor (f’) according to AASHTO22 and NF26 codes adapted to (a) steel strips and (b) polymeric reinforcements under backfill soil types 1 (draining) and 2 (granular). In steel ladder case transversal bar thickness and separation assumed as 10 and 300 mm, respectively; backfill friction angle assumed as 36° with soil Cu > 2 for polymeric strip case.
If required, using on Eq. (1) and AASHTO22 guidelines, a simple modification can be carried out to incorporate cohesion in the pullout resistance using a frictional (f’) and cohesion (fc’) friction interaction factors, as follows (Eq. 4):
Here, ci is the soil-reinforcement interface cohesion, understood as soil-reinforcement adherence, reduced from the fill-soil cohesion using the frictional interaction coefficient (i.e., Ri). Test apparatus and methodology
Design of reinforced soil walls (RSWs) typically considers working stress conditions (i.e., far away from failure), meaning strains are not enough to fully develop the soil-reinforcement interface strength, even for extensible reinforcements, in which maximum strains are not expected to surpass a 1% threshold1. Accurate designing of RSWs requires a proper characterization of the interface shear behaviour between the embedded reinforcement elements and surrounding soil material. Pullout tests are particularly useful to study the shear response between soil and reinforcement materials, allowing to quantify interface strength and stiffness parameters required for an optimized reinforcement design while ensuring safety conditions.
Ample research of pullout test data for steel and polymeric reinforcements with varied geometries (i.e., ladders, grids, mats, strips, among others) is available in the literature. Pullout failure can be troublesome depending on the reinforcement geometry and surcharge conditions2 as well as backfill material characteristics3,4,5. The pullout response between metallic and polymeric reinforcement has proven to be drastically different6. Metallic (i.e. inextensible) reinforcement presents an instantaneous stress–strain response throughout the material, while in polymeric (i.e., extensible) reinforcement, the stress-stress response is gradual and varies from the head to rear. Latest research still includes experimental work (e.g., Gergiou et al.7), as well as a special focus on model accuracy and reliability assessments of current design methods (e.g.,8,9,10,11,12), where it has been stated that the pullout limit state can have practical variations depending on the chosen load model.
Numerical methods have been used to replicate the pullout behaviour in reinforced soil structures, either by discrete element (e.g.,13,14) or finite element (e.g.,15,16) methods. Reported results have shownproper adjustments between simulated and measured values, providing evidence of the accuracy of numerical tools.
The present study focuses, first, in laboratory measured data from pullout tests using steel ladder and polymeric strip reinforcements following the requirements of ASTM D6706-0117 and EN 1373818 and lessons learned from previous cases in the literature (e.g.,19,20, among others). Measured results were compared with past measured and theorical data available in the literature as well as international codes. Second, a 3D finite element model was implemented to simulate and analyze pullout response. A base case was defined with typical properties considering frequently used backfill soils in RSWs. Sensitivity analyses were carried out over model parameters, followed by a calibration process which took into account the measured steel ladder and polymeric strip pullout test data.
The stress-transfer mechanism of soil-reinforcement pullout interactions depend on reinforcement type and configuration, soil properties, and applied stress. For strips and sheet reinforcement, the pullout resistance is equal to the frictional shear stresses over the whole contact area between soil and reinforcement. For bar-mat, ladder, grid, or ribbed strip reinforcements, a complementary passive strength or bearing resistance is developed due to the transversal member surfaces, in which dilatancy, reinforcement roughness and soil stress state come into play21. The pullout resistance (Pr) can be expressed as follows (Eq. 1):
Here, f’ is the friction interaction factor between the soil and the reinforcement, C is the overall reinforcement surface area geometry factor (i.e., equal to 2 for strips and ladder as in two contact faced-reinforcement configuration systems), w is the width of the reinforcement, and \({{\text{L}}}_{{\text{e}}}^{\mathrm{^{\prime}}}\) is the effective reinforcement length in the resisting zone.
The friction interaction factor f’ will vary depending on the refenced code. In the case of AASHTO22, a scale effect correction factor (α), and a pullout friction factor (F*) are proposed. Factor α is assume to be 1 for inextensible reinforcement, and less than 1 for extensible reinforcements. Factor F* is a reduction of soil strength via an interaction coefficient, Ri, and the soil friction angle, ϕ (Eq. 2). For geosynthetic materials (i.e., geogrids, geotextiles, and geostrips), Ri has a proposed value of 0.6722. In the case of polymeric strips, values of Ri = 0.8 can be conservatively assumed in the absence of test data23,24. By means of statistical analysis, Miyata et al.12 showed that the accuracy of linear pullout models for polymeric strips will depend on the magnitude of predicted pullout capacity and vertical stress acting over the reinforcement, which is generally not desired in design methodologies. For bar-mat or steel ladders, the value of F* can be obtained as a relationship between thickness of the transversal bar members, t, and separation between transversal bar members, St, as follows (Eq. 3):
Here, nq is a bearing capacity factor that varies linearly with depth from nq = 20 at surface level (z = 0) to nq = 10 at depths of 6 m or more. Values of nq mean F* will be a linearly decreasing function from 0 to 6 m of depth, and constant for greater depths. Pullout models based on grid geometry and containing empirical parameters have shown to perform better than purely theoretical bearing capacity and soil friction angle models1,25
In the case of NF P 94-27026, f´ is related to an apparent soil-reinforcement interaction coefficient, μ*(z), which varies with soil gradation, transversal bar diameter and separation for steel ladders, and soil gradation and soil friction angle ϕ for polymeric strips. As with F* (from AASHTO22, the value of μ*(z) decreases linearly until 6 m of depth, after which it remains constant.
Figure 1 compares the values of f´ obtained through AASHTO22 and NF26 guidelines. For steel ladder reinforcements (Fig. 1a), a transversal bar separation of 300 mm with 10 mm-diameter bars is assumed. For polymeric strips (Fig. 1b) a soil friction angle ϕ = 36° and a coefficient of uniformity Cu > 2 is assumed. Clear variations between design codes evidence the need for laboratory pullout tests to obtain valuable data concerning the combined response of project specific type of reinforcement, loading conditions, and fill material characteristics.
Friction-interaction factor (f’) according to AASHTO22 and NF26 codes adapted to (a) steel strips and (b) polymeric reinforcements under backfill soil types 1 (draining) and 2 (granular). In steel ladder case transversal bar thickness and separation assumed as 10 and 300 mm, respectively; backfill friction angle assumed as 36° with soil Cu > 2 for polymeric strip case.
If required, using on Eq. (1) and AASHTO22 guidelines, a simple modification can be carried out to incorporate cohesion in the pullout resistance using a frictional (f’) and cohesion (fc’) friction interaction factors, as follows (Eq. 4):
Here, ci is the soil-reinforcement interface cohesion, understood as soil-reinforcement adherence, reduced from the fill-soil cohesion using the frictional interaction coefficient (i.e., Ri). Test apparatus and methodology