Design Guidelines for Test Level 3 through Test Level 5 Roadside Barrier Systems Placed on Mechanically Stabilized Earth Retaining Walls (2022)

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72 4 MOMENT SLAB WIDTH FE models of TL-4 and TL-5 BMS systems were developed to evaluate the dynamic response of the systems when subjected to vehicle impact loading. The analyses were performed using the commercially available FE software LS-DYNA (6). The results of these analyses were used to determine required moment slab widths and study the dynamic behavior of the selected system on top of an MSE wall. A permanent displacement less than 1 in. (25.4 mm) at the coping section was used as the selection criterion for establishing an acceptable moment slab width for a given test level. 4.1 Dynamic Finite Element Analyses Model The objective of these analyses was to determine the optimum BMS system for TL-4 and TL-5 impacts subject to a limiting permanent displacement of 1.0 in. (25.4 mm) at the barrier-coping section. The study includes quantification of barrier capacity, minimum width of the moment slab, and movement of the barrier and the coping system. 4.1.1 Modeling Methodology The methodology followed to model the BMS system and then simulate its performance under vehicle impact consisted of the following steps: - Design a BMS system capable of withstanding an impact corresponding to a specified MASH test level (TL-4 and TL-5). - Develop a FE model of the selected BMS system. - Initialize the BMS system model to account for gravitational loading. - Simulate the vehicle impact into the BMS system. The prescribed impact conditions were based on the nominal conditions specified in MASH for TL-4 and TL-5. - Quantify the displacement of the barrier and the magnitude of the impact forces. The optimum system should have a maximum permanent displacement of approximately 1 in. (25.4 mm) at the coping section of the barrier. An iterative process was followed until the displacement criterion was met. a) Overview of the BMS Model The FE representation of the BMS system model consists of the following components: - Precast concrete barrier and coping section, and cast-in-place moment slab with steel reinforcement, - Backfill soil and overburden soil material, - Steel reinforcement connecting the precast barrier section to the moment slab, - Steel reinforcement shear dowels connecting adjacent moment slab sections to each other, and - Concrete leveling pad on which the precast barrier sections rest.

73 The components of the BMS model (precast barrier, leveling pad, cast-in-place moment slab and soil) were modeled using solid elements. The steel reinforcement (rebars and shear dowels) was modeled using beam elements with six degrees of freedom at each end. The elements of the barrier sections in the impact region were meshed with an element size of 1.5 in. (38.1 mm) to capture the barrier deformation with improved accuracy. The rest of the barriers were more coarsely meshed to reduce computational cost of the simulations. The soil elements located beneath the barrier and moment slab and at the shear interface were finely meshed using an element size ranging from 1.5 in. (38.1 mm) to 4 in. (101.4 mm). This helped to increase the robustness of the contact between the coping, the moment slab and the soil. Figure 4-1 shows the components of a typical BMS model used for these analyses. a) Three-dimensional view b) Rebar connection detail and shear dowels c) Shear dowels details and leveling pad Figure 4-1 Details of a typical section of a BMS model.

74 b) Contact Algorithm The modeling of this large deformation problem required the implementation of advanced contact algorithms to successfully capture the interaction between all free surfaces. The LS-DYNA FE code offers some of the most advanced features for modeling contacts in crash analyses involving full-scale vehicles with different material properties and complex geometry. There are two ways of modeling the interaction between the beam elements and the solid elements (e.g., rebar and concrete). One method requires a model geometry that assigns common nodes between the rebar and the concrete. This often results in the creation of unnecessary small elements and poor element aspect ratios, which decreases the analysis time step and consequently increases computational time. The other method involves coupling the rebar to the concrete using a coupling algorithm. This mitigates the problem of having excessively small elements and poor element aspect ratio (42). This latter methodology was used to model the contact between the rebar and the concrete as well as the metallic soil reinforcement strips and the soil. The steel reinforcing bars were coupled to the concrete using the LS-DYNA feature *CONSTRAINED_LAGRANGE_IN_SOLID. This coupling algorithm permits the reinforcement bars (treated as a slave) to be placed anywhere inside the concrete (treated as a master) without any mesh accommodation (1,43,44). The interface between the soil and the structural slab was modeled using surface contact definitions. The contact friction was based on the angle of internal friction of the backfill material, which was 35 degrees (ϕ=35º) measured using the Direct Shear Test (46). c) Material Model and Model Parameters The LS-DYNA FE code has several material models that can be implemented to model the response of concrete structures. These material models range from a very simple elastic model to a nonlinear damage material model that includes rate effects (2). The elastic material model was used to study the dynamic response of the concrete barriers and moment slabs (LS-DYNA *MAT_001). However, the tensile capacity of the concrete was checked to make sure that the stresses remained within the specified strength of the concrete. The steel rebar was modeled using a piecewise linear isotropic plasticity model that is representative of an actual stress-strain relationship of a grade 60 steel (LS-DYNA *MAT_24). This is an elastic plastic material model that uses the Young’s modulus if stresses are below the yield stress and the measured stress-strain-curve if the stresses are above the yield stress (47). After yielding, the steel rebar exhibits yield in a ductile manner until it breaks at a specified ultimate strain (2). The backfill soil and the overburden soil material were modeled using a two invariant geologic cap model (6) (LS-DYNA *MAT_25). This soil cap constitutive model is defined by a convex yield surface consisting of a failure envelope (f1), an elliptic cap (f2), and a tension cutoff region (f3) as shown in Figure 4-2. The three yield surfaces are defined as follows (6):

75 Figure 4-2 Yield surface of the cap model (6). 1. Failure envelope region: 1 2 1( ) ( ) 0D ef J F Iσ = − = , for 1 ( )T I Lκ≤ < (4-1) 1 1 1( ) I eF I e I βα γ θ−= − + (4-2) 2. Cap region: ( )2 2 1( , ) , 0D cf J F Iσ κ κ= − = , for 1( ) ( )L I Xκ κ≤ < (4-3) ( ) [ ] [ ]2 21 1 1, ( ) ( ) ( )cF I X L I LR κ κ κ κ= − − − (4-4) ( ) ( )eX RFκ κ κ= + (4-5) 0 ( ) 0 0 if L if κ κ κ κ > =  ≤ (4-6) 3. Tension cutoff region: 3 1( ) 0f T Iσ = − = , for 1I T= (4-7) The above equations shows that the failure surface of the cap model is defined in terms of the first stress invariant (I1) and the second deviatoric stress invariant (J2D=1/2SijSji), where σ = stress tensor. The parameter T is the maximum hydrostatic tension sustainable by the material (value of I1 at the tension cutoff location), and L(κ) is the intersection point between the shear failure surface and the ellipsoidal cap. The parameters α, θ, γ, α and β are used to evaluate the

76 yield surface at the elastic range. They are usually evaluated by fitting a curve through failure data taken from a set of triaxial compression tests (6). The value of R is the ratio of the major to minor axes of the elliptical cap. The parameter X(κ) defines the intersection of the cap with I1, and κ is the hardening parameter which is equal to the plastic volumetric strain (κ=εvp). The plastic volumetric strain is evaluated using the hardening law function, as follows: [ ]{ }01 exp ( ( )pv W D X Xε κ= − − − (4-8) The parameters W, D and Xo, shown in Eq. (4-8), are material constants. The value of W represents the maximum plastic volumetric strain that the material can developed, D is the initial slope of loading in hydrostatic compression, and Xo in the hardening law coefficient (defines the initial location of the cap). The implementation of the cap model exhibits two major advantages over other classical models such as Drucker-Prager and Mohr-Coulomb. The first advantage is the ability to control dilatancy produced under shear loading and the second advantage is the ability to model plastic compaction (6). These properties make this model suitable to study the dynamic behavior of the backfill and overburden soil material during impact and shear loading. The soil material properties implemented in the cap model in this study are described in Table 4-1. The values of the parameters were successfully implemented during the previous study as documented in NCHRP Report 663. Table 4-1 Soil cap material properties used in the simulation (2) Elasticity K (MPa) 22.219 G (MPa) 7.407 Plasticity α (MPa) 4.154 β (MPa-1) 0.0647 γ (MPa) 4.055 θ (radian) 0.0 Hardening Law W 0.08266 D (MPa-1) 0.239 R 28 X0 (MPa) -2.819 Tension Cut T (MPa) 0.0

77 4.1.2 Analyses for Test Level 4 Impact A nonlinear FE analysis was performed to investigate the dynamic behavior of a BMS system subjected to a MASH TL-4 impact. The principal objective was to obtain the optimum width of moment slab required to contain a MASH TL-4 test vehicle with a limiting permanent displacement of 1.0 in. (25.4 mm). The study was conducted using a 42-in. (1.07 m) tall vertical wall because the vertical shape will limit any potential climb associated with other shapes and develop the largest impact load. a) Description of the Barrier and the Moment Slab The design load for a MASH TL-4 impact is 80 kips (356 kN), as recommended in section 3. This load was estimated based on a 42-in. (1.07 m) tall rigid barrier study using full-scale impact simulation. Therefore, the barrier section used in this study was a 42-in. (1.07 m) tall concrete vertical wall barrier, as shown in Figure 4-3. TL-4 9" 4' 6" 9" 2 5/8" 5" 5 1/2" 5 3/4" 2'-6" 3'-6" 2' 3 4" 1' #6 @ 8" A-A B-B 63° a) Concrete barrier detail b) Modeled concrete barrier detail c) Barrier and moment slab sections Figure 4-3 BMS system details for TL-4 analyses.

78 d) Three-dimensional view Figure 4-3 BMS system details for TL-4 analyses (Continued). The end section ultimate capacity of this barrier was computed to be 89.8 kips (399.6 kN) using the yield line failure mechanism described in AASHTO LRFD (3). The length of the failure surface (in end failure) calculated for the 42-in. (1.07-m) tall barrier section analyzed was 4.2 ft (1.3 m). The moment and shear capacity at the coping section (section B-B) was computed to be 424 kip-ft (575 kN-m) and 133 kips (591.8 kN), respectively. Since the coping provides enough capacity to resist the impact load, this indicates that the 10 ft (3.05 m) section length selected for evaluation of the TL-4 impact is sufficient to develop the primary failure mechanism for the barrier. The TL-4 BMS system model was composed of three 30-ft (9.15-m) long moment slab sections. Each section was attached to three 10 ft (3.05 m) long barrier segments (Figure 4-3). The width of the moment slab was 4.5 ft (1.37 m) measured from the inner traffic face of the panels. The width of the moment slab was estimated using equilibrium analyses, simulated and re- designed, if necessary, until it met the displacement criterion. Two #9 shear dowel bars were used to connect the joints between the moment slabs to replicate standard construction practice. The shear dowels were embedded 18 in. (457 mm) into each side of the moment slab. b) Loads and Displacements of the Barrier-Moment Slab System The simulated SUT vehicle impacted barrier 5 (B-5) (Figure 4-3) at a speed of 56 mph (90 km/hr) and an angle of 15 degrees. Sequential images for the simulation truck are shown in Figure 4-4. Figure 4-4(b) corresponds to the time of peak load due to the front impact, Figure 4-4(c) corresponds to the time of maximum load in the barrier, and Figure 4-4(d) corresponds to the time of maximum longitudinal load.

79 a) t=0.0 sec. b) t=0.11 sec. c) t=0.235 sec. d) t=0.365 sec. Figure 4-4 TL-4 SUT vehicle position at each significant moment. The calculated maximum 50-msec. average impact force Ft was 74.2 kips (330.1 kN) at 0.235 sec and was associated with the back slap impact (Figure 4-5). The reduction in impact force from the rigid barrier estimate is likely due to barrier displacement, which helps dissipate kinetic energy of the impacting SUT vehicle. In the longitudinal and vertical direction, the maximum 50- msec. average impact loads were 38.8 kips (172.7 kN) at 0.365 sec and 20.5 kips (91.2 kN) at 0.30 sec, respectively. The simulation results indicate that the concrete barrier did not exceed the tensile capacity threshold of the concrete (approximately 400 psi (2.76 MPa)). The maximum displacement at the top of the barrier occurred close to the impact point (IP) (barrier section “B-5”) and was 1.6 in. (40.6 mm). The displacement–time history at the IP is shown in Figure 4-6(a). Figure 4-6(b) shows that about 2/3 of this displacement is associated with rotation of the barrier while approximately 1/3 is associated with sliding. The total permanent displacement at the coping section was 0.75 in. (19 mm).

80 a) Lateral impact force (Ft) b) Longitudinal impact force (FL) c) Vertical impact force (FV) c) Longitudinal impact force (FL) e) Vertical impact force (FV) Figure 4-5 TL-4 time history load in the barrier and load distribution. 0 10 20 30 40 0.0 0.1 0.2 0.3 0.4 0.5 Lo ng itu di na l F or ce , k ip s Time, sec. Raw Data 50-msec Ave 0 10 20 30 40 0.0 0.1 0.2 0.3 0.4 0.5 Ve rti ca l F or ce , k ip s Time, sec. Raw Data 50-msec Ave. 0 5 10 15 20 0 5 10 15 20 25 30 Av e. F or ce , k ip s/f t Distance along the barrier, ft Impact Point Downstream 0 7 14 21 28 35 42 0 15 30 45 60 Ba rri er H ei gh t, in . Ave. Force, kips/ft Resultant Location Approx. Force Dist. 74.2 kips at 31 in.

81 Figure 4-6(c) through Figure 4-6(e) show the relative displacement between two adjacent barriers at the joint “B3-B4” and joint “B5-B6” located upstream of the IP, and joint “B6-B7” located downstream of the IP. The relative displacement is obtained by subtracting the displacements at the downstream barriers from those at the upstream barriers at the specified joints between two adjacent barriers. a) Displacement at IP b) Sliding and rotational comp. c) Relative displacement at B3-B4 d) Relative displacement at B5-B6 e) Relative displacement at B6-B7 f) Vertical displacement of moment slab Figure 4-6 Displacement of the barriers and the moment slab for TL-4 impact. 0.0 0.5 1.0 1.5 2.0 0.0 0.1 0.2 0.3 0.4 0.5 D isp la ce m en t a t I P, in . Time, sec. B-5 Bottom B-5 Top 0.0 0.5 1.0 1.5 0.0 0.1 0.2 0.3 0.4 0.5 D isp la ce m en t a t I P, in . Time, sec. Sliding Comp. Rotational Comp. -1.00 -0.75 -0.50 -0.25 0.00 0.0 0.1 0.2 0.3 0.4 0.5 Re la tiv e D isp l., in . Time, sec. B3-B4 Top B3-B4 Bottom -0.50 -0.25 0.00 0.25 0.50 0.0 0.1 0.2 0.3 0.4 0.5 Re la tiv e D isp l., in . Time, sec. B5-B6 Top B5-B6 Bottom -0.25 0.00 0.25 0.50 0.75 0.0 0.1 0.2 0.3 0.4 0.5 D isp la ce m en t a t I P, in . Time, sec. B6-B7 Top B6-B7 Bottom 0.0 0.2 0.4 0.6 0.8 0.0 0.1 0.2 0.3 0.4 0.5 M om en t S la b D isp l., in . Time, sec. Downstream IP Upstream IP

82 In all cases, the relative displacement at the coping is very small which indicates that the shear dowels and the connection between the barrier and the moment slab are adequate to withstand this impact level. At the top of the barrier, the relative displacement is more appreciable. However, this relative displacement is associated with the rotation of the barrier and therefore most of it is recoverable. The vertical displacement of the middle moment slab was also captured from the simulation. Figure 4-6(f) shows that the maximum vertical movement of the upstream joint edge and the downstream joint edge of the moment slab are 0.69 in. (17.3 mm) and 0.6 in. (15.2 mm), respectively. This indicates that the 30 ft (9.15 m) long BMS section is behaving mostly as a rigid body and that the connection between the moment slab and the barrier is also adequate. 4.1.3 Analyses for Test Level 5 Impact with 42-in. (1.07 m) tall barrier (TL-5-1) In Chapter 3, it was found that the impact load associated with a fully loaded tractor-trailer is highly influenced by the height of the barrier. Consequently, the analysis conducted in this section for MASH TL-5 was divided into a TL-5-1 (MASH TL-5 test vehicle impacting a 42-in. (1.07-m) tall barrier) with 7-ft (2.13 m) wide moment slab, and a TL-5-2 (MASH TL-5 test vehicle impacting a 48-in. (1.22 m) tall barrier) with a 9-ft (2.74 m) wide moment slab. The rotation in these BMS systems occurred around point A (Figure 4-7(a)). The overturning capacity around point A is generally less than that around point B (Figure 4-7(a)). For this reason, it was believed that if these systems have limited deformation based on this analysis, the BMS system adopted herein would perform well when placed over an MSE wall. Nonlinear FE impact simulations were performed to investigate the performance of selected BMS systems subjected to MASH TL-5 impacts. The principal objective was to obtain the optimum width of moment slab and the length of the barrier sections required to contain a MASH TL-5 test vehicle with a limiting permanent displacement of 1.0 in. (25.4 mm). The TL-5- 1 study was conducted using a 42-in. (1.07-m) tall vertical wall barrier. a) Description of the Barrier and the Moment Slab Figure 4-7 shows the cross section of the 42-in. (1.07 m) tall BMS system used to withstand a MASH TL-5-1 impact. The barrier section was designed to contain a dynamic load of 160 kips (712 kN), as recommended in Chapter 3. The ultimate capacity of the end section of the barrier was computed to be 161.1 kips (716.9 kN) using the yield line failure methodology described in AASHTO LRFD (3). The length of the failure surface calculated for the end section of this barrier was 10.3 ft (3.14 m). Therefore, 15 ft (4.57 m) long barrier segments were selected for evaluation under a TL-5-1 impact in order to have sufficient length to develop the primary failure mechanism of the barrier rather than have the controlling failure mechanism of the barrier be at the coping section. The moment and shear capacity at the coping section (section B-B) was 1175 kip-ft (1593.3 kN-m) and 255 kips (1134.8 kN), respectively. The results indicate that the coping section provides sufficient capacity to resist the impact load.

83 TL-5 2'-10"3'-6" 3' 1' #7 @ 8" 512" 1'-4" 8" 1' 7' 112" 1' A-A B-B 35° B A a) Concrete barrier detail b) Concrete barrier detail in the model c) Alphanumeric designator for the barriers d) Three-dimensional view Figure 4-7 BMS system details for TL-5-1 analyses. The TL-5-1 BMS system model was composed of three 30-ft (9.15-m) long moment slab sections. Each section was attached to two 15 ft (4.57 m) long barrier segments (Figure 4-7). The width of the moment slab was 7 ft (2.13 m) measured from the inside traffic face of the panels. The procedure used to estimate the optimum width of the moment slab was an iterative procedure similar to the procedure described for MASH TL-4 impact.

84 Since the impact load applied by a fully loaded tractor-trailer is significantly larger than a MASH TL-4 impact, the number of shear dowels was increased from two #9 steel bars to three #11 steel bars. The shear dowels were embedded 18 in. (457 mm) into each of the adjacent moment slabs. These shear dowels help ensure a good connection between the impacted moment slab and its neighbors. The vertical wall barrier was extended beyond the BMS model (Figure 4-7(d)) to ensure full redirection of the tractor-trailer vehicle model. b) Loads and Displacements of the Barrier-Moment Slab System The simulated tractor-trailer vehicle model impacted the joint between barrier segment 3 (B-3) and barrier segment 4 (B-4) at a speed of 50 mph (80 km/hr.) and an angle of 15 degrees. Sequential images from the simulation are shown in Figure 4-8. Figure 4-8(b) corresponds to the time of peak load due to the front impact of the tractor, Figure 4-8(c) corresponds to the time of peak load due to the impact of the rear tandem axles of the tractor and the front of the trailer, and Figure 4-8(d) corresponds to the time of peak load associated with the impact of the rear tandem axles of the trailer. a) t=0.0 sec. b) t=0.07 sec. c) t=0.261 sec. d) t=0.809 sec. Figure 4-8 TL-5-1 tractor-trailer vehicle position at each significant moment.

85 The time history of the impact load shows that the maximum 50-msec. average force (Ft) was 168.8 kips (751.2 kN) at 0.808 sec. and it was associated with the impact of the rear tandem axles of the trailer (Figure 4-9). It should be noted that this force also includes the lateral component of the friction load imposed while it is riding on top of the barrier. The friction load on top of the barrier might not have a significant effect for designing the strength capacity of a concrete barrier but it has a significant influence on the overall stability of the BMS system. a) Lateral impact force (Ft) b) Longitudinal impact force (FL) c) Vertical impact force (FV) d) Longitudinal distribution (LL) of Ft e) Vertical distribution of Ft Figure 4-9 TL-5 time history load in the barrier and load distribution on the 42 in. (1.07 m) BMS system. 0 25 50 75 100 0.0 0.3 0.6 0.9 1.2 Lo ng itu di na l F or ce , k ip s Time, sec. Raw Data 50-msec. Ave. 0 50 100 150 0.0 0.3 0.6 0.9 1.2 Ve rti ca l F or ce , k ip s Time, sec. Raw Data 50-msec. Ave. 0 10 20 30 0 10 20 30 Av e. F or ce , k ip s/f t Distance along the barrier, ft Impact Point Downstream

86 In the longitudinal and vertical direction, the maximum 50-msec. average impact loads were 94.4 kips (420.1 kN) at 0.807 sec and 131.4 kips (584.7 kN) at 0.816 sec, respectively. The simulation results indicate that the concrete barrier did not exceed the tensile capacity threshold of the concrete (approximately 400 psi (2.76 MPa)). The maximum displacement of the barriers occurred close to the IP and was 1.73 in. (43.9 mm) at the top of the barrier and 0.55 in. (14 mm) at the coping section. The displacement–time history at the IP is shown in Figure 4-10(a). Figure 4-10(b) shows that the impact associated with the rear tandem axles of the tractor displaces the barrier about 0.75 in. (19.1 mm) in rotation and 0.25 in. (6.4 mm) in sliding. Then, the barrier rebounds back and is subsequently impacted by the rear tandem axles of the trailer, which displaces it about 1.25 in. (31.8 mm) in rotation and induces 0.3 in. (7.6 mm) more of sliding of the system. a) Displacement at IP b) Sliding and rotational comp. c) Relative displacement at B2-B3 d) Relative displacement at B3-B4 Figure 4-10 Displacement of the barriers and the moment slab for TL-5-1 impact. 0.0 0.5 1.0 1.5 2.0 0.0 0.3 0.6 0.9 1.2 D isp la ce m en t a t I P, in . Time, sec. IP Bottom IP Top -0.5 0.0 0.5 1.0 1.5 0.0 0.3 0.6 0.9 1.2 D isp la ce m en t a t I P, in . Time, sec. Sliding Comp. Rotational Comp. -0.6 -0.3 0.0 0.3 0.0 0.3 0.6 0.9 1.2 Re la tiv e D isp l., in . Time, sec. B2-B3 Top B2-B3 Bottom -0.3 -0.2 0.0 0.2 0.3 0.0 0.3 0.6 0.9 1.2 Re la tiv e D isp l., in . Time, sec. B3-B4 Top B3-B4 Bottom

87 e) Relative displacement at B4-B5 f) Vertical displacement of moment slab Figure 4-10 Displacement of the barriers and the moment slab for TL-5-1 impact (Continued). The relative displacements at the upstream joint (“B2-B3”), barrier section “B3-B4” and downstream joint (“B4-B5”) are very small as shown in Figure 4-10(c), Figure 4-10(d) and Figure 4-10(e), respectively. These displacements were calculated by subtracting the downstream displacements from the upstream displacements at a joint location between two adjacent barriers. This small movement at the coping indicates that the shear dowels and the connection between the barrier and the moment slab are appropriate to withstand this impact level. At the top of the barriers, the relative displacement is more appreciable. However, this displacement is associated with the rotation of the barriers and much of it is recoverable. Figure 4- 10(f) shows the vertical displacement of the middle moment slab section. The motion of the moment slab when impacted by the tractor-van-trailer model was similar to the behavior observed in the MASH TL-4 impact simulation analysis. The rotational displacement at the top of the barrier and the vertical movement of the moment slab are similar, indicating rigid body motion of the BMS system. 4.1.4 Analyses for Test Level 5 Impact with 48-in. (1.22 m) tall barrier (TL-5-2) The impact performance of a 48-in. (1.22-m) tall vertical barrier impacted by a fully loaded tractor- trailer was studied in a manner similar to the 42-in. (1.07-m) tall barrier system. As previously discussed, the impact loads associated with a 48-in. (1.22-m) tall barrier are greater than for a 42- in. (1.07-m) tall barrier due to the impact of the trailer floor with the barrier. The objectives of this analysis are similar to those described in the previous section but using a prescribed barrier height of 48 in. (1219 mm). The objective of this analysis effort was to obtain the optimum width of moment slab and the length of barrier sections required for a 48-in. (1.22-m) tall barrier to contain a MASH TL-5 test vehicle with a limiting permanent displacement of 1.0 in. (25.4 mm) at the barrier coping. -0.4 -0.2 0.0 0.2 0.4 0.6 0.0 0.3 0.6 0.9 1.2 Re la tiv e D isp l., in . Time, sec. B4-B5 Top B4-B5 Bottom 0.0 0.3 0.6 0.9 1.2 0.0 0.3 0.6 0.9 1.2 M om en t S la b D isp l., in . Time, sec. Downstream IP Upstream IP

88 a) Description of the Barrier and the Moment Slab The cross section of the 48-in. (1.22-m) tall BMS system used in this analysis is presented in Figure 4-11. To study the response of this system, a 90 ft (27.4 m) long FE model was developed for use in LS-DYNA (Figure 4-11(b)). The model consisted of three 30-ft (9.15-m) long moment slab sections each mounted with two 15 ft (4.57 m) long barriers. The moment slab was 9 ft (2.74 m) wide. The moment slabs sections were connected using three #11 shear dowels embedded 18 in. (0.46 m) on each side of the adjacent moment slab sections. TL-5 3'-7" 4' 3'-4" 1'-2" #7 @ 8" 512" 1'-812" 1' 9' 112" 10" A-A B-B 712" 32° a) Concrete barrier detail b) Concrete barrier detail in the model c) Alphanumeric designator for the barriers d) Three-dimensional view Figure 4-11 BMS system details for TL-5-2 analyses.

89 The methodology followed to design and model the 48 in. (1219 mm) BMS system, and evaluate its performance under TL-5 impact conditions is similar to that used for the 42-in. (1.07- m) tall barrier system. However, the barriers used in this analysis were designed to withstand an impact load of 260 kips (1157 kN). The ultimate capacity of the barrier end section was 323 kips (1437.4 kN) with a calculated length of failure mechanism equal to 10.2 ft (3.12 m). Therefore, 15 ft (4.57 m) long barrier sections were used to ensure that the length of barrier was sufficient to develop the primary failure mechanism. The moment and shear capacity at the coping section (section B-B) were 1728 kip-ft (2343.2 kN-m) and 364 kips (1620 kN), respectively. The results indicate that the coping section provides enough capacity to resist the impact load and develop the primary failure barrier failure mechanism. b) Loads and Displacements of the Barrier-Moment Slab System The tractor-trailer impacted the 48-in. (1.22 m) tall barrier system at the joint between barrier segments B-3 and B-4 at a speed of 50 mph (80 km/hr.) and an angle of 15 degrees. Sequential images from the simulation are shown in Figure 4-12. Figure 4-12(a) corresponds to the time before impact. Figure 4-12(b) corresponds to the time of peak load due to the front impact of the tractor, Figure 4-12(c) corresponds to the time of peak load due to the impact of the rear tandem axles of the tractor and the front of the trailer, and Figure 4-12(d) corresponds to the time of peak load associated with the impact of the trailer and trailer tandem axles. a) t=0.0 sec. b) t=0.082 sec. c) t=0.212 sec. d) t=0.813 sec. Figure 4-12 TL-5-2 tractor-trailer vehicle position at each significant moment.

90 The time history of the impact force indicates that the maximum 50-msec. average force (Ft) is 251 kips (1117 kN) at 0.813 sec as shown in Figure 4-13. This load is associated with the impact of the trailer and rear tandem axles. In the longitudinal and vertical direction, the maximum 50-msec. average impact force were 69.1 kips (307.5 kN) at 0.811 sec and 79.1 kips (351.9 kN) at 0.796 sec, respectively. The simulation results indicated that the concrete barrier did not exceed the tensile capacity threshold of the concrete. a) Lateral impact force (Ft) b) Longitudinal impact force (FL) c) Vertical impact force (FV) d) Longitudinal distribution (LL) of Ft e) Vertical distribution of Ft Figure 4-13 TL-5 time history load in the barrier and load distribution on the 48-in. (1.22 m) tall BMS system. 0 30 60 90 120 0.0 0.3 0.6 0.9 1.2 Lo ng itu di na l F or ce , k ip s Time, sec. Raw Data 50-msec. Ave. 0 30 60 90 120 0.0 0.3 0.6 0.9 1.2 Ve rti ca l F or ce , k ip s Time, sec. Raw Data 50-msec. Ave. 0 20 40 60 0 5 10 15 20 25 30 Av e. F or ce , k ip s/f t Distance along the barrier, ft Impact Point Downstream

91 The maximum displacement of the barriers occurred close to the IP and was 2.12 in. (53.8 mm) at the top of the barrier and 0.7 in. (17.8 mm) at the coping section. The displacement– time history at the IP is shown in Figure 4-14(a). The dynamic behavior of the 48-in. (1.22 m) tall barrier is different from the behavior of the 42.in. (1.07-m) tall barrier. Figure 4-14(b) shows that the impact associated with the rear tandem axles of the tractor and the front of the trailer generates the largest displacement at the top of the barrier, whereas the largest displacement for the 42-in. (1.07 m) tall barrier is associated with the impact of the rear tandem axles of the trailer. This is because of the location of the impact load. While in the case of the 42-in. (1.07-m) tall barrier the floor of the trailer travels over the top of the barrier, in the case of the 48-in. (1.22m) tall barrier, the trailer impacts the top edge face of the barrier. This generates a larger rotational displacement than the load transmitted through the tractor axles. Figure 4-14(b) shows that the impact associated with the rear tandem axles of the tractor displaces the barrier about 1.7 in. (43.2 mm) in rotation and 0.5 in. (12.7 mm) in sliding. Then, the barrier rebounds back and is subsequently impacted by the rear tandem axles of the trailer, which displaces it about 1.2 in. (30.5 mm) in rotation and induces a total of 0.65 in. (16.5 mm) of sliding in the system. The maximum permanent displacement associated with the barrier top is about 0.83 in. (21 mm), and that at the barrier bottom is around 0.59 in. (15 mm). The relative displacements were calculated by subtracting the downstream displacements from the upstream displacements at a joint location between two adjacent barriers. This displacement between the barriers is more significant for this test level as shown in Figure 4-14(c) through Figure 4-14(e) than other test levels. However, the barriers rebound back to their vertical position with little residual displacement between them. The relative displacement at the coping section is also negligible. Figure 4-14(f) shows the vertical displacement of the central moment slab section. A comparison between the rotational displacement at the top of the barrier and the vertical movement of the moment slab indicates that the 30 ft (9.15 m) long BMS section behaves rigidly.

92 a) Displacement at IP b) Sliding and rotational comp. c) Relative displacement at B2-B3 d) Relative displacement at B3-B4 e) Relative displacement at B4-B5 f) Vertical displacement of moment slab Figure 4-14 Displacement of the barriers and the moment slab for TL-5-2 impact. 4.2 Static Analysis of the BMS System The static capacity of the BMS systems that met the dynamic displacement threshold was determined using static equilibrium analyses and quasi-static FE analyses. The purpose of these studies was to quantify the equivalent static load (Ls) associated with MASH TL-4 and TL-5 impacts. This is the static load equivalent to the lateral dynamic load perpendicular to the barrier height, and that is used in the proportioning of the moment slab. The analyses were conducted for a 30 ft (9.15 m) long BMS section. The shear dowels were removed from the model in order to isolate the capacity of a single BMS section. 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.3 0.6 0.9 1.2 D isp la ce m en t a t I P, in . Time, sec. IP Bottom IP Top -0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.3 0.6 0.9 1.2 D isp la ce m en t a t I P, in . Time, sec. Sliding Comp. Rotational Comp. -1.2 -0.9 -0.6 -0.3 0.0 0.0 0.3 0.6 0.9 1.2 Re la tiv e D isp l., in . Time, sec. B2-B3 Top B2-B3 Bottom -0.6 -0.3 0.0 0.3 0.6 0.0 0.3 0.6 0.9 1.2 Re la tiv e D isp l., in . Time, sec. B3-B4 Top B3-B4 Bottom 0.0 0.5 1.0 1.5 0.0 0.3 0.6 0.9 1.2 Re la tiv e D isp l., in . Time, sec. B4-B5 Top B4-B5 Bottom 0.0 0.6 1.2 1.8 0.0 0.3 0.6 0.9 1.2 M om en t S la b D isp l., in . Time, sec. Downstream IP Upstream IP

93 4.2.1 Static Analytical Solution The static analyses for sliding and overturning were conducted using equilibrium equations. The static force (Fs) required to initiate sliding motion of the system is: tans r r sF W f Aφ= + (4-9) where W= weight of the barrier, moment slab and soil of the section ϕ= angle of the internal friction of the soil tanϕr= interface friction between the soil and the moment slab (ϕr is taken as ϕ if the interface is rough (cast in place) and 2/3ϕ if the interface is smooth (precast concrete)). fr= shear strength resistance of the soil As= interface area of the soil in contact with the side of the moment slab For this analysis, it is assumed that the moment slab interface is rough (cast-in-place concrete). The strength resistance of the soil (fr) was back calculated using the results of the static test presented in Chapter 2 of NCHRP Report 663(2). The results of the test indicated that the average shear strength resistance of the concrete–soil interface (fr) was 126 psf (6.3 kPa) (2). The static force (Fo) required to initiate rotation of the system is: 𝐹 = (4-10) where W= weight of the barrier, moment slab and soil of the section l= moment arm of the weight of the system h= moment arm of the equivalent static load applied to the system to the rotation point. xs= moment arm of the force associated with the shear strength of the soil A’s= interface area of the soil in contact with side and front edge of the moment slab The static analysis was conducted using two different points of rotation as shown in Figure 4-15. Rotation point A assumes the barrier is isolated from the wall panels and rotates about the bottom of the coping. Rotation point B assumes the barrier is in contact with and rotates about the back of the wall panel. Table 4-2 summarizes the results of the static equilibrium analyses for sliding and overturning of the BMS system for TL-4, TL-5-1, and TL-5-2. According to the results, rotation point B offers more resistance to overturning than rotation point A. This increase in rotation resistance is associated with the reduction of the moment arm of the overturning load and the increase of the moment arm associated with the resisting force.

94 Equivalent Static Load, L hh Rotation Point B Rotation Point A Overburden Soil BA W lA lB Moment Slab Traffic Barrier C.G. Panels s Finished Grade Figure 4-15 Detail of the rotation points on the BMS system. Table 4-2 Summary of the static forces using equilibrium equation. Test Level W (kips) Moment Arms Sliding Analyses Overturning Analyses Rotation Point A Rotation Point B Rotation Point A Rotation Point B lA (in) hA (in) lB (in) hB (in) FS (kips) Fs+soil (kips) (1) Fo (kips) Fo+soil (kips) Fo (kips) Fo+soil (kips) TL-4 59.8 13.6 54.0 20.3 48.8 40.3 42.4 15.1 23.4 24.9 35.6 TL5-1 112.4 29.5 70.0 36.8 60.0 75.8 78.4 47.4 62.6 69.0 88.3 TL5-2 149.5 42.0 83.0 47.0 73.0 100.8 104.7 75.6 94.7 96.2 119.9 (1) Strength of the soil was only considered at the side faces of the moment slab and not at the front. 4.2.2 Quasi-static FE Analyses In order to conduct the quasi-static FE analyses, the shear dowels were removed from the finite element model of the BMS system to isolate one moment slab section. The analysis was conducted by applying a prescribed displacement to a block that was used as a means of providing distribution of the applied load to the barrier. A constant rate of displacement was applied at a very low rate to eliminate inertia effects. The length of the force block was 4 ft (1.22 m) for TL-4 and 10 ft (3.05

95 m) for TL-5-1 and TL-5-2. The loads were applied at an effective height of 30 in. (762 mm), 34 in. (864 mm) and 43 in. (1092 mm) for TL-4, TL-5-1 and TL-5-2, respectively. These dimensions matched the longitudinal distribution of the lateral force and the height of the resultant lateral impact load associated with TL-4, TL-5-1 and TL-5-2 impacts. The FE model was initialized to account for gravitational loading on the soil mass before application of the quasi-static load. The quasi-static FE models are shown in Figure 4-16. The analyses were conducted using both a point of rotation at the toe of the barrier coping (rotation point A) and the point of contact between the barrier-coping and top of the wall panels (rotation point B). a) TL-4 BMS system model b) TL-5-1 BMS system model c) TL-5-2 BMS system model Figure 4-16 Load distribution and application point of the quasi-static FE models.

96 The results of the numerical simulation showed that the BMS system was controlled by overturning rather than sliding. Figure 4-17 presents the results as a load versus displacement curve, and compares them with the analytical solution using equilibrium equations. The information is also summarized in Table 4-3. a) TL-4 (Rotation Point A) b) TL-4 (Rotation Point B) c) TL-5-1 (Rotation Point A) d) TL-5-1 (Rotation Point B) e) TL-5-2 (Rotation Point A) f) TL-5-2 (Rotation Point B) Figure 4-17 Result of the quasi-static FE analyses for the BMS system. 0 5 10 15 20 25 0 0.5 1 1.5 2 St at ic F or ce (k ip s) Displacement (in.) FE Analysis Analytical Sol. RP-A (with soil) Analytical Sol. RP-A (without soil) 0 10 20 30 40 0 0.5 1 1.5 2 St at ic F or ce (k ip s) Displacement (in.) FE Analysis Analytical Sol. RP-B (with soil) Analytical Sol. RP-B (without soil) 0 25 50 75 0 0.5 1 1.5 2 St at ic F or ce (k ip s) Displacement (in.) FE Analysis Analytical Sol. RP-A (with soil) Analytical Sol. RP-A (without soil) 0 25 50 75 100 0 0.5 1 1.5 2 St at ic F or ce (k ip s) Displacement (in.) FE Analysis Analytical Sol. RP-B (with soil) Analytical Sol. RP-B (without soil) 0 25 50 75 100 0 0.5 1 1.5 2 St at ic F or ce (k ip s) Displacement (in.) FE Analysis Analytical Sol. RP-A (with soil) Analytical Sol. RP-A (without soil) 0 25 50 75 100 125 0 0.5 1 1.5 2 St at ic F or ce (k ip s) Displacement (in.) FE Analysis Analytical Sol. RP-B (with soil) Analytical Sol. RP-B (without soil)

97 Table 4-3 Comparison between analytical solution and FE analyses Test Level Rotation Point A (RP-A) Rotation Point B (RP-B) Analytical Solution FEA Analytical Solution FEA Fo (kips) Fo+soil (kips) Fo (kips) Fo (kips) Fo+soil (kips) Fo+soil (kips) TL-4 15.1 23.4 15.7 24.9 35.6 37.0 TL-5-1 47.4 62.6 49.2 69.0 88.3 78.0 TL-5-2 75.6 94.7 78.6 96.2 119.9 115.7 In the case of rotation point A, the results indicate that the analytical solution compares reasonably well with the quasi-static FE analyses when the static equilibrium analysis does not include the soil resistance. In the case of rotation point B, the analytical solution compares reasonably well with the quasi-static FE analyses when the static equilibrium analysis includes the soil resistance. This behavior is likely because the location of the rotation point B remains fixed as the barrier moves (Figure 4-18(a)). However, when the barrier system rotates around point A, the toe of the barrier starts punching into the soil, and the actual point of rotation changes as the barrier rotates (Figure 4-18(b)). This behavior decreases the moment arm, d, of the resisting force and reduces the static resistance to overturning. These phenomena cannot be captured using equilibrium analysis. Consequently, the difference between both analyses gets more significant. 4.3 Conclusions The following conclusions are based on and limited to the content of this chapter: 1. A set of full-scale impact simulations were conducted on a BMS system for MASH TL-4 and TL-5 impact conditions. The TL-5 study was performed with two different barrier heights (42 in. (1067 mm) and a 48 in. (1219 mm)) to addresses the effect of barrier height on the impact load. 2. The results of the full-scale impact simulations show that the width of the moment slab required to contain a MASH TL-4 and MASH TL-5 impact with a limiting permanent displacement of 1 in. (25.4 mm) at the coping section are as follows: - 4.5 ft (1.37 m) wide and 30 ft (9.15 m) long for MASH TL-4 impact - 7.0 ft (2.13 m) wide and 30 ft (9.15 m) long for MASH TL-5-1 impact - 9.0 ft (2.74 m) wide and 30 ft (9.15 m) long for MASH TL-5-2 impact These moment slab widths were used in the preparation of the crash tests and to obtain the soil reinforcement loads that are included in Chapter 5. Additional analyses were later carried out to further optimize the adopted BMS systems in light of additional simulations performed in Chapter 5 and data gathered from the 36 in. (914.4 mm) TL-4 (termed TL-4- 1) barrier and the 42 in. (1066.8 mm) TL-5-1 barrier full-scale crash tests. The results of the analyses are presented in Chapter 5 and Chapter 9, respectively.

98 a) Rotation Point B (RP-B) b) Rotation Point A (RP-A) Figure 4-18 Displacement vector during rotation of the barrier system 3. A set of static analytical calculations and quasi-static FE analyses were conducted on the BMS systems that met the permanent displacement threshold of 1in. (25.4 mm) that was specified at this stage to determine static equivalent loads for the static design of the moment slab. The results show that overturning of the barrier system occurs before sliding.

99 However, significant sliding was also observed in the analyses for TL-5. Therefore, both criteria should be checked for the TL-4 and the TL-5 cases. 4. The static loads associated with TL-4 and TL-5 impacts vary significantly between point of rotation A and B. For rotation point B, a quasi-static FE analysis indicates that the quasi- static load capacity (including soil resistance) required to resist overturning due to a TL-4, TL-5-1 and TL-5-2 impact are 37 kips (164.6 kN), 78 kips (347 kN) and 115.7 kips (514.9 kN), respectively. The static analytical solutions indicate that the quasi-static load capacity (without soil resistance) required to resist overturning around rotation point B due to a TL- 4, TL-5-1 and TL-5-2 impact are 23.4 kips (104.1 kN), 62.6 kips (278.6 kN) and 96.2 kips (428.1 kN), respectively. The static capacity required to resist overturning around point A due to a TL-4, TL-5-1 and a TL-5-2 impact, neglecting soil friction, are 15.1 kips (67.2 kN), 47.4 kips (210.8 kN) and 75.6 (336.3 kN), respectively.