Asphalt mow strips are typically used as vegetation barriers around guardrail posts in the design of roadside safety structures. Asphalt mow strips have historically been modeled as a rigid layer in simulations; this assumption results in significant ground level restraint on the guardrail post. However, experiments have shown that asphalt rupture should be considered in the analysis of the response of guardrail posts embedded in mow strips. The present study investigates the effect of asphalt material properties and mow strip geometry on guardrail post performance using finite element simulations. Numerical simulations are performed and correlated with results from static experiments and material testing. The test simulations and experimental results are used to evaluate the response of guardrail posts with various mow strip designs to predict the level of restraint from the asphalt layer. The model is then used to investigate the effects of asphalt material properties and mow strip geometry on the overall performance of the system. The results demonstrate that including asphalt rupture in numerical simulations is essential in accurately predicting the behavior of guardrail posts installed in asphalt mow strips. In addition, mow strip geometry along with asphalt material properties significantly affect the guardrail post response.
Considerable research has been performed with testing and finite element simulation of guardrail posts and systems [
Asphalt mow strips are pavement layers installed around guardrail posts as vegetation barriers. The word asphalt used in this paper refers to asphalt concrete. Without mow strips, regular vegetation control around guardrails such as mowing or herbicide application is required. A common procedure for steel guardrail installation in asphalt mow strips employs a hydraulic machine to drive the posts through a layer of asphalt mow strip. A schematic of an installed post is shown in
Prior research [
・ The extent of the domain meshed was near the zone of influence of the loaded posts, which implies that boundary effects could potentially influence the results.
・ The asphalt mow strip was modeled as a rigid layer; the rupture of the asphalt layer was not modeled.
Asphalt mow strips assumed as a rigid layer cause significant ground level restraint of guardrail posts in simulations. However, experiments have shown that asphalt deforms and ruptures when lateral loads are applied to guardrail posts installed in asphalt mow strips [
In the work presented herein, an experimental program was carried out at an outdoor test site. Guardrail posts were installed in asphalt mow strips subjected to static loading. Results from the tests demonstrated that the performance of the post was affected significantly by mow strip geometry (thickness and rear distance, see
The aim of this paper is to provide a better understanding of the use of numerical simulation to model the behavior of posts restrained by an asphalt layer at the ground line. Static loading is employed in these studies to allow for more extensive evaluation of parameters to design and focus future dynamic tests. Future experiments will be performed to evaluate the performance of individual posts installed in a variety of mow strip configurations under dynamic loading. In addition, pertinent properties will also be evaluated via dynamic material testing. The dynamic material test results will be compared to applicable nondestructive assessments of dynamic properties (such as dynamic modulus). These results from the dynamic subcomponent and material tests will be used to refine the finite element models developed for more detailed parametric analysis of the influence of geometric and material properties of the mow strip on the expected performance of the mow strip. The final phase of the research effort will be MASH compliant full-scale crash testing on selected guardrail-mow strip installations to determine whether systems installed without leave-outs can perform satisfactorily.
The outdoor test site for the experimental program was constructed in accordance with American Association of State Highway and Transportation Officials Manual for Assessing Safety Hardware (MASH) criteria [
A schematic illustration of the experimental setup including the loading fixture and instrumentation is given in
The interactions between the soil, asphalt, and post play a vital role in the response of the system during loading. These interactions can be investigated by first considering the post to be a specialized form of a laterally loaded pile. There are various techniques for solving laterally loaded pile problems. These approaches include: (1) the finite element approach, in which the post is embedded in a soil continuum of solid finite elements, and (2) the subgrade reaction approach, in which the post is supported by a series of uncoupled springs. The
subgrade reaction method has been used widely in the past because of the high computational cost associated with 3D finite element modeling of the soil around the guardrail post. Although the subgrade reaction approach can be used to analyze post-soil interaction, this method only provides an overall performance assessment and does not provide insight into the failure and deformation mechanisms of the soil and possible asphalt layers. With recent advances in computing speeds, researchers have made efforts to model the post-soil interaction using the finite element method. With this approach, models are constructed of the post embedded in a continuum of soil modeled using three-dimensional solid elements. Simulations of physical responses using 3D finite element analysis (FEA) can be readily produced, and the availability of sophisticated FEA tools provides substantial promise for detailed numerical studies to address outstanding questions of the post-soil behavior. However, the quality of the results from simulations depends on several factors including:
・ Accurate representation of geometry details, boundary conditions, and assumed initial conditions.
・ The constitutive relationships for the various materials such as loss of strength in the soil and asphalt under large deformations, asphalt material properties, and the rupture of asphalt.
・ The contact conditions between various components such as the contact between the soil and the post as well as the asphalt layer and the soil.
LS-DYNA V971 R8.0.0 [
The soil domain considered in the model is a rectangular prism. The bottom boundary of the prism is fixed at depth (z-direction) of 2 m―approximately twice the embedment depth. For the lateral boundaries, there are three options to use: free, rigid, or non-reflecting boundary conditions. The lateral boundaries are placed far enough from the post that the displacements and change in stresses at the boundaries are negligible. Therefore, the response is insensitive to the lateral boundary assumptions. For the pseudo-static loading employed in this study, the non-reflecting boundary conditions are effectively the same as the free boundary conditions. Therefore, using any of these three boundary conditions gives similar results. However, because explicit integration is employed, using a non-reflecting boundary decreases noise in the system response and thus the lateral soil boundary is modelled using non-reflecting boundary conditions. Three different criteria are used to determine the size of the prism within the plan of the problem to avoid boundary effects:
1) The size of the prism in plan is increased, and the force-displacement curve for the post is monitored. The results show that the boundary effects on the post’s response vanish when the planar size of the soil is larger than 4 m, and the force-displacement curve is effectively unchanged when using greater than this size.
2) The nodes on the lateral boundary are initially set free. The size of the prism in plan is increased until the displacements of the nodes at the boundaries are less than one percent of the ground level displacement of the steel post. The dimension of the prism in plan is obtained as 5 m by this approach. Then the lateral boundaries are modelled using non-reflecting boundary conditions.
3) The width of the model (perpendicular to the post lateral movement) has to be large enough to capture asphalt rupture. The width is increased until the boundaries are far from the end of asphalt rupture and shear stress at the boundaries is less than 1 percent of shear stress close to the post. The size of the model in this direction is determined equal to 10 m.
Therefore, the dimensions of the prism are set as 5 m in the y-direction (parallel to the post lateral movement) and 10 m in the x-direction (perpendicular to the post lateral movement). The steel post is a W150x13 member with a total length of 1.83 m and an embedded depth of 1 m [
Various approaches exist for modeling the interface between the soil and post using a Lagrangian mesh:
1) Nodes from the soil elements are tied to the nodes of the post elements. No contact definition between the post and the soil is necessary when this approach
is used. This method assumes infinite friction between the soil and the post, which is not a correct physical representation. This approach yields a stiffer behavior than reality and is not recommended.
2) Nodes from the soil elements are not tied to the nodes of the post elements, and eroding contact is used to simulate the soil failure. When elements are eroded based on specific failure criteria, they are removed from calculations in the model and do not have resistance anymore. This model demands a very dense mesh and can yield incorrect results. The failed elements are removed from the analysis, and a gap is created between the soil and the post. Therefore, application of a relatively small force in the axial direction can pull out the post. This behavior is observed even using a friction coefficient larger than one [
3) Nodes from the soil elements are not tied to the nodes of the post elements. Automatic surface-to-surface contact which is explained further below is defined between the post and the soil. In this method, the friction between the post and soil has an influence on the behavior [
The contact search algorithms utilized by automatic contacts in LS-DYNA make them better-suited than older contact types. Moreover, subroutines that check the slave nodes for penetration are utilized a second time to check the master nodes for penetration through the slave segments in this approach. The definition of the slave surface and master surface is arbitrary. Therefore, in this study, the contacts between soil and steel post are modeled using the automatic surface-to-surface contact model. Static and dynamic friction coefficients are set equal to 0.6, which is typical for an interface between the soil (a mixture of gravel, sand, and clay) and a driven smooth steel pile [
In addition to the contact between the post and the soil, the contact between the asphalt and the soil and the asphalt and the steel is also modeled using the automatic surface-to-surface contact model. The static coefficient of friction is set to a relatively high value of 1.0 to account for the bitumen in the asphalt that is bonded to the soil surface. However, after this connection breaks and the asphalt layer starts to slip over the soil, friction substantially decreases. The kinetic coefficient of friction is assumed to be negligible and is set equal to zero to avoid large forces at the free edge of the asphalt behind the post. This allows the asphalt to move easily on the soil, as observed in the experiments and avoids mesh distortions at the edge of the asphalt layer where there is no confining pressure. Segment based (SOFT 2) contact also is used in this part of the model.
When the rupture failure pattern propagates in the asphalt, the tip of the rupture moves from the edges of the post toward the sides of the asphalt layer (
Hourglass control number 9 is an enhanced assumed strain stiffness formulation for three-dimensional hexahedral elements. To prevent high hourglass energy during simulations, this hourglass control is used for the soil elements and the hexahedral mesh part of the asphalt. The steel post and tetrahedral mesh portion of the asphalt are modeled as fully integrated elements and do not require an hourglass control. For each analysis, the hourglass energy is monitored and compared to the internal energy. The hourglass energy in the soil and the hexahedral mesh portion of the asphalt is limited to approximately 3 percent of the internal energy, which was deemed acceptable. Kinetic energy is less than 0.5 percent of the total energy in the current simulations, which indicates that the rate of loading is a good representation of quasi-static loading.
Soil is often a pressure dependent material. Therefore, the soil behavior changes at different depths because of the change in the pressure as the depth increases. To capture this important aspect, gravity loading must be applied, and stresses must be initialized before the start of the main simulation. This is accomplished in this research by applying a “load body” in the z direction to all parts of the model. Because applying gravity loading during real-time simulation causes dynamic waves that can contaminate the results, the gravity load is applied in the pseudo-time before the main simulation. Gravity loading is applied using a ramp load to minimize dynamic waves, and dynamic relaxation is utilized in the pseudo-time to dampen the waves caused by applying gravity. After the waves are damped, and the material reaches a static equilibrium, the main simulation is conducted in real-time. Applying the gravity load also ensures the proper representation of friction forces on the surfaces that are in contact with each other. As can be seen in
load is applied without a dynamic relaxation phase, large dynamic waves contaminate the result. Moreover, if the gravity loading is not applied in the model, the soil material shows significantly lower strength and the contact between the soil, the asphalt, and the post does not perform correctly.
Ignoring gravity leads to a lower peak force which requires lower stresses and strains to reach. This causes the peak force to occur at a lower displacement equal to 45 mm which is less than the displacement at peak force for the experiment equal to 70 mm.
A piecewise linear metal plasticity model is used for the steel post. The yield strength of the steel, modulus of elasticity, and Poisson’s ratio are given as inputs using a representative steel stress-strain curve. The common steel parameters presented in
Different material models are available in LS-DYNA for modeling of the soil; these were examined to find the most appropriate one to use for modeling of these components. Lewis [
Material | Constitutive Parameter | Value | Determined from |
---|---|---|---|
Steel | Density, ρ | 7930 kg/m3 | Material test |
Young modulus, E | 200 GPa | [ | |
Poisson’s ratio, ν | 0.3 | [ | |
Yield Strength, σy | 348 MPa | Material test | |
Soil | Density, ρ | 2300 kg/m3 | Material test |
Cohesion, C | 13 kPa | Material test and via system test calibrationa | |
Peak friction angle, | 45˚ | Material test and via system test calibrationa | |
Critical friction angle, | 15˚ | [ | |
Shear modulus, G | 50 MPa | [ | |
Poisson’s ratio, ν | 0.25 | [ | |
Density, ρ | 2300 kg/m3 | Material test | |
Cohesion, C | 500 kPa | Material test | |
Friction angle, f' | 35˚ | [ | |
Asphalt | Shear modulus, G | 50 MPa | Via system test calibrationa |
Poisson’s ratio, ν | 0.35 | [ | |
Maximum principal stress, σmax | 680 kPa | ||
Maximum principal strain, εmax | 0.07 | Via system test calibrationa |
a. The term “system test calibration” refers to the selection of particular material constants based on one selected system test as described above.
(material number 173), Drucker-Prager (material number 193), and FHWA (material number 147) soil material models were selected to be evaluated in this research. The FHWA material model manual [
After performing the simulations with the various relevant material models, the soil and foam model and Mohr-Coulomb model both proved to be stable under the desired displacement for the current problem. An extensive investigation was conducted to determine the most appropriate of these two for this application. In general, the soil and foam material model is easier to work with; it only has three constitutive parameters for the yield surface and one for pressure cut off. It is also possible to give a volumetric strain versus stress curve as an input. This model is stable for large displacements and low confining pressures. However, the yield surface is smooth, and the material model does not capture the difference in the soil behavior under extension and compression. Many experiments in the past have proven that soil behaves differently under extension and compression [
where
To identify the soil type used in the experiment and determine the range of acceptable soil material properties in the literature, the grain size distribution was obtained using sieve analysis. Two processes were used to classify the soil type in this study: Unified Soil Classification System (USCS [
The USCS uses symbols for the particle size groups. These symbols and their representations are G for gravel, S for sand, M for silt, and C for clay. These are combined with other symbols expressing gradation characteristics, W for well graded and P for poorly graded. USCS was used to classify the compacted soil that is deposited around the guardrail post in the experimental program. Grain size distribution was obtained using laboratory sieve testing in accordance with AASHTO T 27 [
A model without an asphalt mow strip was created to calibrate the soil material properties based on a system level static experiment without an asphalt layer. The soil was modeled using structured hexahedral constant stress solid elements. The mesh was refined until the results did not change noticeably. The final mesh size for soil changes from 25 mm close to the post to 200 mm at locations far from the post. Using a mesh in the soil finer than approximately 25 mm caused instability in the model. Lateral loading in the static test program was simulated as follows. A transverse displacement was applied to the post at 625 mm above the ground level. Mass scaling was not used, and the rate of displacement of the post was varied between 5000 mm/s and 25 mm/s. Analysis of the results demonstrates that rates slower than 50 mm/s give results within 1 percent for all the primary response quantities. Therefore, 50 mm/s was used as the displacement rate of the post to represent quasi-static loading. The kinetic energy of the system was checked and determined to be less than 0.5 percent of the total energy. The contact forces between the post and the soil in the y-direction were calculated to determine the applied force versus displacement curve for the post.
The density of the soil was determined as 2,300 kg/m3 using a laboratory test on a soil sample. This value was used as the soil density in the model. Experimental direct shear tests in accordance with ASTM D3080 [
When the asphalt is loaded, part of its deformation comes from viscous behavior. To account for this, the shear modulus of the material was lowered to consider viscous deformation effects under quasi-static loading. The Mohr-Coulomb material model is widely used to model asphalt, and this material model was chosen to model the shear strength of the asphalt. In this study, the density of the asphalt was estimated to be equal 2,300 kg/m3 by laboratory tests. The Poisson’s ratio and friction angle of the asphalt were specified as 0.35 and 35 degrees, respectively, which are typical values for asphalt [
The tensile rupture in the asphalt observed in the experimental tests is modeled using element erosion. Element erosion is implemented in this research using the general erosion criteria for solid elements in LS-DYNA. Each criterion is applied independently, and satisfaction of one or more criteria causes deletion of an element from the calculation. The erosion criteria that must be satisfied before an element is removed can be specified by the user. The maximum principal stress criterion was initially used in this research to eliminate the elements when the tensile failure criterion is met. However, the rupture in the asphalt was abrupt when this sole criterion was used, and the strength decreased dramatically, similar to what is commonly observed in very brittle materials. To account for the fact that asphalt can accommodate larger strains before failing under tensile stress, a maximum principal strain failure criterion was added to the material model. Therefore, an element is removed when both the maximum principal stress criterion and the principal strain criteria are satisfied as follows:
・
・
The maximum principal stress at failure can be obtained using Mohr-Coulomb yield criterion as 0.95C/
Five experiments with an asphalt layer were conducted and compared to finite element simulations. System behavior after loading from one static experiment (90-mm asphalt layer), FEA with asphalt modeled as discussed above, and FEA with asphalt modeled as rigid are shown in
Design Number | Peak Force (kN) |
---|---|
1 | 29.58 |
2 | 35.63 |
3 | 36.61 |
4 | 28.20 |
5 | 27.58 |
6 | 28.02 |
No pre-cut | 37.50 |
and finite element simulations with the calibrated Mohr-Coulomb asphalt model are summarized in
The above model was used to evaluate the relative performance of guardrail posts with various designs including pre-cutting of the asphalt layer. The following sections discuss the effects of the asphalt material and geometric properties on overall performance. The effects of asphalt material constants on the system response are studied because these constants change by aging of the asphalt layer and temperature change. Therefore, it is important to investigate the relationship between the system and these constants.
The numerical simulations indicate that rear distance of the mow strip behind
Test | Thickness | Rear Distance | Peak Force | Max Ground Displacement | ||||
---|---|---|---|---|---|---|---|---|
No. | (mm) | (mm) | (kN) | (kN) | Var. | (mm) | (mm) | Var. |
Exp. | FEA | % | Exp. | FEA | % | |||
1 | 50 | 600 | 38.6 | 37.5 | 2.8 | 110 | 117 | 6.4 |
2 | 90 | 600 | 42.5 | 41.7 | 1.9 | 97 | 90 | 7.2 |
3 | 50 | 150 | 28.9 | 26.3 | 8.9 | 150 | 155 | 3.3 |
4 | 50 | 300 | 33.1 | 29.9 | 9.6 | 129 | 149 | 15.5 |
5 | 90 | 300 | 40.7 | 34.5 | 15.2 | -a | 146 | - |
aNot available due to gage malfunction.
the post significantly affects the post/mow strip system performance. The rear distance was varied using discrete values equal to 0, 150, 300, 600, 1200, 2500 mm and infinity (i.e. infinite medium) with all other system parameters held constant (G = 50 MPa, ν = 0.35, C = 0.5 MPa, f' = 35˚, asphalt thickness = 50 mm, εmax = 0.09, σmax = 0.7 MPa). The peak force applied to the post from the asphalt layer was measured, and the results are presented in
The asphalt thickness was varied using discrete values equal to 0, 25, 50, 90, 125, 175, and 250 mm. The remaining parameters were held constant as in Section 6.1 with the asphalt rear distance equal to 300 mm. The peak force from the asphalt layer applied to the post was measured, and the results are presented in
The asphalt’s cohesion value was varied using discrete values equal to 0.01, 0.1, 0.25, 0.5, 1, and 2 MPa. The principal stress was varied as a function of cohesion using the relationship
The asphalt friction angle was varied using discrete values equal to 1, 5, 10, 15, 20, 30, 40, and 50 degrees. The peak force applied to the post was measured, and the results are presented in
The asphalt’s shear modulus was varied using discrete values equal to 50, 100, 1,000, and 10,000 MPa. The peak force from the asphalt layer applied to the post was measured, and the results are presented in
The asphalt’s Poisson’s ratio was varied using discrete values equal to 0.1, 0.2, 0.3, and 0.4. The peak force applied to the post was measured, and the results are presented in
As discussed in Section 5, if the asphalt is modeled as a rigid material, the asphalt rupture cannot be captured, and the system performance changes significantly. Based on the experimental results, rupture is the primary mechanism of the asphalt failure around the guardrail post. As the rupture propagates, the strength of the asphalt layer decreases up to the point that one portion of the asphalt detaches from the rest of the mow strip. After this occurs, the asphalt has a negligible impact on the system and the soil is the only source of ground restraint. Therefore, one potentially effective way to decrease mow strip restraint would be to introduce predetermined fracture planes (referred to here as “pre-cuts”) in the asphalt layer. A controlled rupture along a predetermined fracture plane in the asphalt avoids uncontrolled crack propagation in a large area and potentially reduces expected maintenance costs. The cuts would be designed based on the experimental and numerical investigation of rupture patterns of the asphalt layer. Two cut patterns were tested experimentally (
along with FEA results in
Given improvements in computational methods and speed that have occurred since the development of early models for guardrail systems, it is now feasible to perform detailed finite element simulations to characterize the responses at a fundamental material level. Prior FEA methods of the performance of guardrail
posts in which the asphalt layer was assumed as a rigid layer are capable of representing the response of cases where the asphalt layer provides excessive levels of restraint; however, such models are not capable of accounting for the influence of the deformability and finite strength of many typical mow strip geometries. As shown in this study, the asphalt finite stiffness and strength of the asphalt layer should be modeled to capture the general non-rigid response of this layer.
The use of a Mohr-Coulomb material model for the soil and asphalt provides an effective representation of the load-deflection response of the guardrail post, soil and asphalt layer system over a broad range of material and geometric parameters. However, erosion based on a combined principal strain and principal stress criterion to capture the rupture of the asphalt layer and the modeling of the contact conditions between the post and the soil are also key attributes of the FE simulation model. To ensure proper performance of the Mohr-Coulomb material model and the contact definition, gravity loading must be applied. Dynamic relaxation should be employed in applying the gravity load to avoid waves caused by the sudden application of the gravity loading to the model.
The finite element models developed in this project were employed to perform parametric studies on pertinent geometric and material variables. The analyses performed indicate that there are definitive combinations of mow strip thickness and rear distance that are more likely to result in higher ground level restraint for guardrail posts. The analyses also indicate that fabricating targeted full-depth cuts in the mow strip significantly reduces the amount of restraint the mow strip provides to a guardrail post.
The effects of asphalt material properties on the system response were studied. The results show that changes in certain material properties significantly affect system response. These properties change by aging of the asphalt layer and temperature change. Therefore, the influence of an asphalt mow strip on the behavior of a guardrail system will change over time in different environmental exposure conditions.
The research was sponsored by the Georgia Department of Transportation (GDOT) through Research Project Number 13-21. Any findings, opinions, recommendations or conclusions expressed herein are those of the authors and do not necessarily reflect the views of GDOT.
Bakhtiary, E., Lee, S.-H., Scott, D.W., Stewart, L.K. and White, D.W. (2017) Evaluation of Guardrail Posts Installed in Asphalt Mow Strips by Static Finite Element Simulation. Open Journal of Civil Engineering, 7, 141-164. https://doi.org/10.4236/ojce.2017.71009