Design of Roadside Barrier Systems Placed on MSE Retaining Walls (2010)

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Design guidelines were developed as part of this project for three components: • The barrier–moment slab system • The MSE wall reinforcement • The wall panel The guidelines are set in terms of AASHTO LRFD practice. The AASHTO LRFD format version of the design guidelines is shown in Appendix I. An example of the application of the design guidelines for the TL-3 crash test MSE wall is presented in Appendix J. Depending on the design, two points of rotation are possi- ble as shown in Figure 7.1. The point of rotation should be determined based on the interaction between the barrier cop- ing and top of the wall panel. With reference to Figure 7.1, the point of rotation should be taken as Point A if the top of the wall panel is isolated from contact with the coping by pres- ence of an air gap or sufficiently compressible material. The point of rotation should be taken as Point B if there is direct bearing between the bottom of the coping and the top of the wall panel or level-up concrete. 7.1 Guidelines for the Barrier The barrier, coping, and moment slab should be safe against structural failure. A barrier should be designed according to AASHTO LRFD Chapter 13 (2). Any section along the coping and moment slab should not fail in bending when the barrier is subjected to a design impact load. Two modes of stability failure are possible in addition to structural failure of the bar- rier system. They are sliding and overturning of the barrier– moment slab system. 7.1.1 Sliding of the Barrier The factored static resistance (φ P) to sliding of the barrier– moment slab system along its base should be greater than or equal to the factored equivalent static load (γ Ls) due to the dynamic impact force (Figure 7.2). [For the load level TL-3, Ls is 44.48 kN (10 kips), φ resistance factor is 0.8 (AASHTO Table 10.5.5-1), and γ load factor is 1.0 (extreme event).] The static force (P) should be calculated as: where W = weight of the monolithic section of barrier and moment slab plus any material laying on top of the moment slab φr = friction angle of the soil–moment slab interface. The factored equivalent static load should be applied to the length of the moment slab between joints. Any coupling between adjacent moment slabs or friction that may exist between free edges of the moment slab and the surrounding soil should be neglected. If the soil–moment slab interface is rough, φr is equal to the friction angle of the soil φs (cast in place). If the soil–moment slab interface is smooth, φr should be reduced accordingly (precast). 7.1.2 Overturning of the Barrier The factored static moment resistance (φM) to overturn- ing of the barrier–moment slab system should be greater than or equal to the factored static load (γLs) due to the impact force times the moment arm (hA or hB) taken as the vertical distance from the point of impact due to the dynamic force to the point of rotation A or B (Figure 7.2). φ γM L or -≥ ( )s A Bh h ( )7 3 2 3 tanφs⎛⎝⎜ ⎞⎠⎟ P W -= tan ( )φr 7 2 φ γP L -s≥ ( )7 1 C H A P T E R 7 Design Guidelines 152

153 or friction that may exist between the backside of the moment slab and the surrounding soil should be neglected. 7.1.3 Rupture of the Coping in Bending The critical section of the coping must be designed to resist the applicable impact load conditions for the appropriate test level as defined in AASHTO LRFD Bridge Design Specifications (Figure 7.3). 7.2 Guidelines for the Wall Reinforcement The reinforcement guidelines should ensure that the rein- forcement does not pull out or break during a barrier impact with the chosen design vehicle. The connection between the reinforcement and the wall panel should be able to resist the pullout load or breaking load, whichever controls. 7.2.1 Pullout of the Wall Reinforcement Pressure Distribution Approach The capacity of the reinforcement calculated by common static methods should be compared to the dynamic impact loads because no significant difference was found between the static capacity and the dynamic capacity of the reinforcement. The factored static resistance (φ P) to pullout of the rein- forcement should be greater than or equal to the sum of the factored static load (γs Fs) due to the earth pressure and the fac- tored dynamic load (γd Fd) due to the impact. The static load (Fs) should be obtained from the static earth pressure (ps) times the tributary area (At) of the reinforcement unit. The dynamic load (Fd) should be obtained from the pressure (pd) of the pressure distribution (Figure 7.4) times the tributary area (At) of the reinforcement unit. Figure 7.1. Barrier–moment slab system for design guideline. Rotation Point, A C.G. Rotation Point, B Panel Leveling pad Traffic Barrier Overburden Soil Moment Slab Coping Figure 7.2. Barrier–moment slab system for barrier design guideline (sliding and overturning). Rotatio n Point, A C.G. h A l A F s L s W Rotation Point, B l B h B H e Panel Levelin g pad Traffi c Barrier Overburden Soi l Moment Sla b Coping He = effective height of the impact force (AASHTO LRFD Bridge Design Specifications, Figure A13.2-1). [For the load level TL-3, Ls is 44.48 kN (10 kips), φ resistance factor is 0.9, and γ load factor is 1.0 (extreme event).] M should be calculated as: where W = weight of the monolithic section of barrier and moment slab plus any material laying on top of the moment slab lA or lB = horizontal distance from the center of gravity of the weight (W) to the point of rotation A or B. The moment contribution due to any coupling between adjacent moment slabs, shear strength of the overburden soil, M W or -= ( )l lA B ( )7 4 Figure 7.3. Coping and possible weakest section. Rotation Point, A C.G. Rotation Point, B Panel Leveling pad Traffic Barrier Overburden Soil Moment Slab Coping Critical section

154 (For the load level TL-3, pd is given by the pressure distribution shown in Figure 7.4, φ resistance factor is 1.0, γd load factor is 1.0, and γs load factor is 1.0.) The reinforcement resistance (P) for strips should be cal- culated as (AASHTO LRFD Equation 11.10.6.3.2-1): where F* = resistance factor (sliding plus bearing) σv = vertical effective stress on the reinforcement b = width of the strip L = full length of the reinforcement The value of F* should be obtained from the current AASHTO guidelines (Figure 7.5). The reinforcement resistance (P) for bar mats should be calculated as: where D = diameter of the bar mats N = number of longitudinal bars Line Load Approach The factored static resistance (φ P) to pullout of the rein- forcement should be greater than or equal to the sum of the factored static load (γs Fs) due to the earth pressure and the P F D n L -v= * ( )σ π 7 8 P F b L -v= * ( )σ 2 7 7 φ γ γP p A p A -s s t d d t≥ + ( )7 6 φ γ γP F F -s d d≥ +s ( )7 5 Figure 7.4. Pressure distribution (pd) for reinforcement pullout. pd = 230 psf Top Row of Reinforcement Second Row of Reinforcement pd = 315 psf1.8 ft 2.5 ft ps Traffic Barrier Moment Slab Coping Figure 7.5. Default values for the pullout friction factor (F*). Source: AASHTO LRFD Figure 11.10.6.3.2-1 Figure 7.6. Line load (Qd) for reinforcement pullout. Top Row of Reinforcement Second Row of Reinforcement Qd=575 lb/ft Qd=575 lb/ft < 2.7 ft < 1 ft Traffic Barrier Moment Slab Coping ps factored dynamic load (γd Fd) due to the impact. The static load (Fs) should be obtained from the static earth pressure (ps) times the tributary area (At) of the reinforcement unit. The dynamic impact load (Fd) should be obtained from the line load (Qd) (Figure 7.6) times the longitudinal spacing (SL) of the reinforcement. φ γ γP p A Q S -s s t d d L≥ + ( )7 10 φ γ γP F F -s s d d≥ + ( )7 9

155 (For the load level TL-3, Qd is given by the line load shown in Figure 7.6, φ resistance factor is 1.0, γd load factor is 1.0, and γs load factor is 1.0.) The reinforcement resistance (P) for strips should be calcu- lated as (based on AASHTO LRFD Equation 11.10.6.3.2-1): where F* = resistance factor (sliding plus bearing) σv = vertical effective stress on the reinforcement b = width of the strip L = full length of the reinforcement The value of F* should be obtained from the current AASHTO guidelines (Figure 7.5). The reinforcement resistance (P) for bar mats should be calculated as: where D = diameter of the bar mats n = number of longitudinal bars. 7.2.2 Rupture of the Wall Reinforcement Pressure Distribution Approach The factored resistance (φ R) to rupture of the reinforcement should be greater than or equal to the sum of factored static load (γs Fs) due to the earth pressure and the factored dynamic load (γd Fd) due to the impact. The static load (Fs) should be obtained from the static earth pressure (ps) times the tributary area (At) of the reinforcement unit. The dynamic load (Fd) should be obtained from the dynamic pressure (pd) of the pressure dis- tribution (Figure 7.7) times the tributary area (At) of the rein- forcement unit. (For the load level TL-3, pd is given by the pressure distribution shown in Figure 7.7, φ resistance factor is 1.0, γd load factor is 1.0, and γs load factor is 1.0.) The reinforcement resistance (R) for strips or bar mats should be calculated as: where σt = tensile strength of the reinforcement As = cross-section area of the reinforcement. R A -t s= σ ( )7 15 φ γ γR p A p A -s s t d d t≥ + ( )7 14 φ γ γR F F -s s d d≥ + ( )7 13 P F D n L -v= * ( )σ π 7 12 P F b L -v= * ( )σ 2 7 11 where Ec is the strip thickness corrected for corrosion loss. (AASHTO LRFD Figure 11.10.6.4.1-1) where D* is the diameter of bar or wire corrected for corro- sion loss. (AASHTO LRFD Figure 11.10.6.4.1-1) Line Load Approach The factored resistance (φ R) to rupture of the reinforce- ment should be greater than or equal to the sum of factored static load (γs Fs) due to the earth pressure and the factored dynamic load (γd Fd) due to the impact. The static load (Fs) should be obtained from the static earth pressure (ps) times the tributary area (At) of the reinforcement unit. The dynamic load (Fd) should be obtained from the line load (Qd) (Figure 7.8) times the longitudinal spacing (SL) of the reinforcement. (For the load level TL-3, Qd is given by the line load shown in Figure 7.8, φ resistance factor is 1.0, γd load factor is 1.0, and γs load factor is 1.0.) The reinforcement resistance (R) for strips or bar mats should be calculated as: R A -t s= σ ( )7 20 φ γ γR p A Q S -s s t d d L≥ + ( )7 19 φ γ γR F F -s s d d≥ + ( )7 18 A D s = π * ( ) 2 4 7 17for bar mats - A b E for strip -s c= × ( )7 16 Figure 7.7. Pressure distribution (pd) for reinforcement rupture. ps Traffic Barrier Moment Slab Coping pd = 230 psf Top Row of Reinforcement Second Row of Reinforcement pd = 1200 psf1.8 ft 2.5 ft

156 where σt = tensile strength of the reinforcement As = cross-section area of the reinforcement. where Ec is the strip thickness corrected for corrosion loss. (AASHTO LRFD Figure 11.10.6.4.1-1) where D* is the diameter of bar or wire corrected for corro- sion loss. (AASHTO LRFD Figure 11.10.6.4.1-1) 7.3 Guidelines for the Wall Panel The wall panels must be designed to resist the dynamic pres- sure distributions defined in Figure 7.7. The wall panel should have sufficient structural capacity to resist the maximum design rupture load for the wall reinforcement. The static load is not included because it is not located at panel connection. 7.4 Data to Back Up Guidelines 7.4.1 Barrier The guidelines were developed based on analysis and test- ing of N.J. profile and vertical-wall concrete barriers. How- ever, the results should apply to other common barrier types. Note that the calculations indicate that a 1.37 m (4.5 ft) wide, 9.14 m (30 ft) long moment slab without the shear strength A D s = π * ( ) 2 4 7 22for bar mats - A b E for strip -cs = × ( )7 21 of soil on top of it is the minimum required to satisfy the above requirements. The researchers also found that the overturn- ing mode occurs before the sliding mode and is, therefore, the controlling mechanism. The proposed design guidelines are based on the evidence presented below. Note that a decision was made to aim for a barrier–moment slab design that would generate 25.4 mm (1 in.) movement during impact. This 25.4 mm (1 in.) move- ment was considered acceptable as it would likely require lit- tle or no repair of the underlying MSE wall and should not affect the impact performance of the barrier system. The static analysis for sliding and overturning is conducted using equilibrium equations as described in Section 3.2.1. Two points of rotation were considered for sliding and over- turning as shown in Figures 7.9 and 7.10. Also the coefficient Figure 7.8. Line load (Qd) for reinforcement rupture. Top Row of Reinforcement Second Row of Reinforcement Qd=2160 lb/ft Qd=575 lb/ft < 2.7 ft < 1 ft Traffic Barrier Moment Slab Coping ps Figure 7.9. Static load by analytical solution (point of rotation A). Figure 7.10. Static load by analytical solution (point of rotation B).

157 the barrier does not slide during impact. It did slide slightly during both the static and the dynamic test, but the majority of the movement was due to rotation. Evaluation of sliding should be part of the design process. Figure 7.11 shows part of the results of the static test on the 1.37 m (4.5 ft) wide, 3.05 m (10 ft) long barrier–moment slab. As can be seen, a maximum load of 9 kips was reached. Further- more at 22.24 kN (5 kips), the load–displacement relationship becomes nonlinear, typical of soil behavior. This behavior indi- cates that the load resisted by the barrier due only to the dead weight is 22.24 kN (5 kips) leaving 17.8 kN (4 kips) of soil resis- tance along the moment slab perimeter. Figure 7.12 shows the distribution of the soil resistance along the perimeter for the 1.37 m (4.5 ft) wide, 3.05 m (10 ft) long moment slab that was used in static test. By extrapolation, a 1.37 m (4.5 ft) wide, 6.1 m (20 ft) long moment slab–barrier assembly would resist 44.48 kN (10 kips) without soil on its periphery and 71.17 kN (16 kips) with peripheral soil. As the length of moment slab increases, the friction associated with the side soil would be neglected. There- fore, by further extrapolation, a 1.37 m (4.5 ft) wide and n × 3.05 m (10 ft) long moment slab barrier assembly would resist n × 22.24 kN (5 kips) without soil on its periphery and n × 31.14 kN (7 kips) with peripheral soil. Table 7.1 shows the values of the static resistance developed by a barrier with a 1.37 m (4.5 ft) wide moment slab of varying length. The Figure 7.11. Static test data at the top of barrier. Figure 7.12. Soil resistance along the perimeter of the barrier–moment slab system. Overburden Soil and Moment Slab Barrier 1 kips for 5' 1 kips for 5' 2 kips for 10' Table 7.1. Total static load with respect to the length of the barrier. Length of Moment Slab (ft) (1) Resistance from Moment Slab and Overburden (kips) (2) Soil Resistance (kips) (3) = (1)+(2) Total Static Load (kips) (3) / (1) Ratio 10 5 2 7 1.4 : : : : : 10 × n 5 × n 2 × n 7 × n 1.4 of friction for the soil–moment slab interface was taken as equal to the coefficient of friction of the soil. These figures show the barrier force that a 1.37 m (4.5 ft) wide moment slab of varying length can resist when discounting the shear strength of the soil on top of it. As can be seen, the overturning mode develops less resistance than the sliding mode for both points of rotation. Thus, in this case, the overturning mode controls design. This is not to say that sliding could not control and that

158 Figure 7.13. Finite element model for dynamic analysis. Table 7.2. Impact loads with various velocities of bogie on 10 ft barrier system. Velocity of Bogie (mph) Maximum Displacement of Barrier (in.) Impact Force (kips) 2 0.14 6.79 5 0.97 23.33 8 1.73 34.35 10 2.35 39.95 13 3.56 46.00 resistance is split in two parts: the load due to dead weight and the load due to soil friction along the back edge of the moment slab (i.e., resistance contributed by the soil on the sides of the moment slab is neglected). A dynamic impact test was performed with a bogie on the same 1.37 m (4.5 ft) wide, 3.05 m (10 ft) long barrier–moment slab system. At 20.9 km/h (13 mph), the bogie generated a max- imum 50 msec average impact force of 193.05 kN (43.4 kips), and moved the top of the barrier 89 mm (3.5 in.). The numer- ical simulation was used to predict and compare the dynamic test as shown in Figure 7.13. The numerical simulation gave 204.62 kN (46 kips) and 89 mm (3.5 in.). Table 7.2 shows the maximum 50 msec average impact load and the correspon- ding displacement at the top of the barrier according to the numerical simulations of bogie vehicle impacts into a 3.05 m (10 ft) long barrier–moment slab system at different speeds. Figure 7.14 is a comparison between the static load test results (load–deflection curve), the numerical simulations (peak impact force and corresponding displacement), and the result of the two dynamic bogie tests [20.9 km/h (13 mph) and 28.97 km/h (18 mph)]. This comparison shows the amplifi- cation due to the inertia force with the increase in velocity at impact. This comparison gave credibility to the numerical simulations. Numerical simulation was then used to find what peak dynamic load would generate a peak displacement of the top of the barrier of 25.4 mm (1 in.) for different lengths of the 1.37 m (4.5 ft) wide moment slab. It was found that a bogie impact at 20.9 km/h (13 mph) on a 6.1 m (20 ft) long moment slab would generate a dynamic force of 227.75 kN (51.2 kips) at 25 mm (0.98 in.) of move- ment, and that the same 6.1 m (20 ft) long moment slab would resist 43.59 kN (9.8 kips) statically without counting on the shear strength of the soil on top of it as shown in Figure 7.15. Another numerical simulation indicated that a bogie impact at 28.97 km/h (18 mph) on a 9.14 m (30 ft) long moment slab would generate a dynamic force of 384.74 kN (78.4 kips) at 24 mm (0.96 in.) of movement, and that the same 9.14 m (30 ft) long moment slab would resist 65.39 kN (14.7 kips) statically without counting on the shear strength of the soil on top of it. These data indicate that a 240 kN (54 kips) dynamic load associated with 25.4 mm (1 in.) movement is approximately equivalent to a 44.48 kN (10 kips) static load when the shear strength of the soil above the moment slab is discounted. These data further indicate that a 9.14 m (30 ft) moment slab gives a

159 Figure 7.14. Comparison of static test and dynamic test and finite element model of 10 ft barrier–moment slab system. 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 8 9 10 Max_displacement (in.) St at ic o r I m pa ct F or ce (k ips ) Simulation(Dynamic)_Hyperbolic Simulation(Dynamic) Static_HyperbolicStatic Test 54 2 mph 5 mph 8 mph 10 mph 13 mph Dynamic Bogie Test (3.54-in, 43.42-kips, 13-mph) (SAE 60hz, 50ms average) Dynamic Bogie Test (7.52-in, 54.11-kips, 18-mph) (50ms average, SAE 60hz) 18 mph 5 Ratio=4.96 Figure 7.15. Comparison of static and dynamic impact force in 1 in. maximum displacement. 78.39 14.2 4.7 9.5 23.33(0.97-in/5-mph) 51.21(0.98-in/13-mph) 0 10 20 30 40 50 60 70 80 90 0 5 10 15 20 25 30 35 Length of Moment Slab (ft) St at ic o r D yn am ic Im pa ct F or ce (k ips ) Static no soil contribution Dynamic (0.96-in/ 18-mph) 54 10.31 factor of safety of 1.5 against the 240 kN (54 kips) dynamic design load for a 25.4 mm (1 in.) movement and a 1.5 factor of safety against a 44.48 kN (10 kips) static design load. Figure 7.16 shows the ratio of the dynamic force over the static force (with shear resistance) as a function of the length of the 1.37 m (4.5 ft) wide moment slab. Note that for the 9.14 m (30 ft) barrier, the ratio is very close to 5.4, which is equal to 240.2 kN/44.48 kN (54 kips/10 kips). 7.4.2 Wall Reinforcement Four bogie tests were conducted to develop the design guidelines for a barrier system on top of an MSE wall. The impact speeds varied from 32.5 km/h (20.19 mph) to 35.1 km/h (21.8 mph). The maximum load on the barrier (50 msec aver- age) varied from 286.47 kN (64.4 kips) to 326.5 kN (73.4 kips). To capture the tensile forces transmitted into the reinforcement

160 during the dynamic impact, strain gages were installed. The placement of these strain gages was selected to measure the maximum tensile load in each layer of reinforcement as well as give an indication of the distribution of forces in the lat- eral, longitudinal, and vertical directions. The maximum dynamic loads in the reinforcement in excess of the static load measured during the impact varied from 9.47 kN (2.13 kips) to 33.18 kN (7.46 kips) in the upper- most layer. The load used is the one corresponding to the loca- tion where two strain gages (top and bottom of the strip) were available to get an average value. Higher loads were registered at locations where only one gage was available. However, it appears that significant bending occurred, which made the single–strain gage readings doubtful and unreliable. The maximum load in the strip closest to the impact (upper- most layer) in excess of the static load was 33.18 kN (7.46 kips) for the 4.88 m (16 ft) long strips under the vertical wall (Test 4) and 31.98 kN (7.19 kips) for the 4.88 m (16 ft) long strips under the N.J. barrier (Test 1). Assuming the increase in strip load is proportional to the barrier impact load, the design strip loads corresponding to a design impact load of 240 kN (54 kips) can be estimated to be 27.8 kN (6.25 kips) and 23.53 kN (5.29 kips), respectively. For the 2.44 m (8 ft) long strips case, the maximum load in the strip closest to the impact (top layer) in excess of the static load was 9.47 kN (2.13 kips) under the vertical wall (Test 3). The design strip load in excess of static corresponding to a design impact load of 240 kN (54 kips) can be estimated to be 7.3 kN (1.64 kips). The maximum load in excess of static in the single bar clos- est to the impact load (uppermost layer) in the bar mat, which was 2.44 m (8 ft) long, was 6.85 kN (1.54 kips) (Test 2). The design strip load in excess of static corresponding to a design impact load of 240 kN (54 kips) can be estimated to be 5.6 kN (1.26 kips). Even though the reinforcement appears to have reached its maximum pullout resistance during impact, the overall performance of the wall was very satisfactory in all four tests. Therefore it was decided that having the reinforcement work- ing at maximum pullout resistance would be acceptable. The design recommendations were based on a pressure diagram approach to be resisted by the reinforcement while using the design loads in excess of static recorded in the tests. Pullout of the Wall Reinforcement The pullout tests in the laboratory were performed at rates varying from quasi-static rates all the way to rates approach- ing impact loading rates. Because no consistent rate effect was found, the recommended design guidelines require the pull- out resistance of the reinforcement to be calculated according to common static methods and sized to resist the full dynamic loads. The design strip load in excess of static in Test 3, which is for a 2.44 m (8 ft) long strip, was used to develop the design guide- line for pullout of the reinforcement. This test was selected because the wall performed well during that impact. During Test 4 with strips that were 4.88 m (16 ft) long, the strips devel- oped a higher load because the system was stiffer. As a result, the wall panel developed a crack during impact. Therefore the stiffer 16 ft long strips are not acceptable in this case. The resistance (P) for the 8 ft long strips was calculated to be 6.58 kN (1.48 kips) for the uppermost layer and 12.02 kN (2.7 kips) for the second layer using Equation 2-1 in Chapter 2. The pullout friction factor (F*) was 1.837 for the uppermost layer and 1.674 for the second layer. The dynamic maximum design load (50 msec average) in excess of static in the strip at the uppermost layer was mea- sured and then interpolated back to the 240 kN (54 kips) impact load to be 7.295 kN (1.64 kips). The static load at the uppermost layer was calculated to be 2.53 kN (0.569 kips) by AASHTO LRFD. The total design load was thus calculated to be 9.799 kN (2.203 kips) at the uppermost layer. Because this measured total design load [9.799 kN (2.203 kips)] in the strip was higher than the resistance [6.595 kN (1.483 kips)], the resistance was used to obtain the dynamic design load in excess of static at the uppermost layer. The controlling design load in excess of the static due to static earth pressures was calcu- lated to be 4.066 kN (0.914 kips). This represents a static load, equivalent to a dynamic load, which would indicate that an 8 ft long strip would perform well in the case of a TL-3 impact. The value of 4.066 kN (0.914 kips) was found by cal- culating the total resistance of the 8 ft strip at the depth of the Figure 7.16. Ratio of static load and dynamic impact load. 4.96 5.39 5.52 0 1 2 3 4 5 6 0 5 10 15 20 25 30 35 R at io Length of Moment Slab (ft)

161 first layer [6.595 kN (1.483 kips)] minus the calculated load due to static earth pressures from AASHTO LRFD [2.53 kN (0.569 kips)]. At the second layer, the same process was followed. The measured dynamic load in excess of static was 4.092 kN (0.92 kips). The static earth pressure load for the second layer was calculated to be 4.87 kN (1.095 kips) by AASHTO LRFD. The total load was therefore calculated to be 8.963 kN (2.015 kips), which is less than the calculated pullout load at that depth [12.019 kN (2.702 kips)]. Therefore, the measured dynamic load in excess of static was used as the controlling dynamic load in excess of static for pullout design. Table 7.3 shows the measured dynamic load, calculated static load, total load, resistance, and the controlling load for pullout design. The dynamic pressure per strip was calculated as shown in Table 7.4. For the 2.44 m (8 ft) long strip with a density of 3 strips per panel per layer, the tributary area was 0.27 m2 (2.92 ft2 = 4.87 ft × 1.8 ft/3 strips per panel) for the top layer and the tributary area was 0.37 m2 (3.94 ft2 = 4.87 ft × 2.43 ft/3 strips per panel) for the second layer. The dynamic design pressure was calculated as shown in Table 7.4. The dynamic design pressure in excess of the static earth pressure for pull- out is recommended to be 15.08 kPa (315 psf ) for the upper- most layer and 11.012 kPa (230 psf) for the second layer as shown in Figure 7.4. Rupture of the Wall Reinforcement The Reinforcement resistance to rupture (R) for a strip was calculated as: where σt = tensile strength of the reinforcement [ASTM Grade 60, therefore, 414 MPa (60 ksi)] As = cross-section area of the reinforcement. where Ec is the strip thickness corrected for corrosion loss. (AASHTO LRFD Figure 11.10.6.4.1-1) (Ec = 1.984 mm = 0.078 in. for 100-year design life) The reinforcement resistance to rupture (R) was calcu- lated to be 41.037 kN (9.226 kips). To develop the design guideline against rupture of the rein- forcement, the highest design load on the strip measured in the test was used. The maximum dynamic 50 msec average load on the strip located in the uppermost layer for Test 1 was 23.531 kN (5.29 kips). In the second layer, the measured maximum dynamic load was 4.092 kN (0.92 kips). Therefore, the controlling design strip load for rupture of the reinforce- ment was 23.531 kN (5.29 kips) for the uppermost layer and 4.092 kN (0.92 kips) for the second layer. The dynamic pressure per strip for rupture of the reinforce- ment was calculated as shown in Table 7.5. For 2.44 m (8 ft) A mm mm mm in -s = × = =50 1 984 99 2 0 154 7 252 2. . . ( ) A b E -s c= × ( )7 24 R A -t s= σ ( )7 23 Table 7.3. Test results and calculation of design strip load for pullout design. Layer (1) Measured Dynamic Load* (kips) (2) Static** (kips) (3)=(1) + (2) Total (kips) (4) Calculated Resistance** (kips) Controlling Design Dynamic Load (kips) Top 1.64 0.569 2.209 1.483 (4)-(2) = 0.914 Second 0.92 1.095 2.015 2.702 0.92 * Adjusted for 54 kips design impact load ** Calculated from AASHTO LRFD Sections 11.10.6.2–11.10.6.3 Table 7.4. Dynamic design load on the strip for pullout design. Layer Total Design Pressure (psf) Top 0.914 kips / 2.92 ft 2 * = 313 psf Second 0.92 kips / 3.94 ft 2 ** = 234 psf * Tributary area of a panel for the top layer (2.92 ft2 = 4.87 ft × 1.8 ft / 3 strips per panel) ** Tributary area of a panel for the second layer (3.94 ft2 = 4.87 ft × 2.43 ft / 3 strips per panel)

162 long strip with a density of three strips per panel per layer, the tributary area was 0.37 m2 (3.94 ft2 = 4.87 ft × 2.43 ft/3 strips per panel). For 4.88 m (16 ft) long strip with a density of two strips per panel per layer, the tributary area was 0.41 m2 (4.38 ft2 = 4.87 ft × 1.8 ft/2 strips per panel). The dynamic design pressure in excess of static earth pressure to consider in the design against rupture of the reinforcement was calculated as shown in Table 7.6. The dynamic design pressure for rup- ture of the reinforcement is recommended to be 57.456 kPa (1,200 psf) for the uppermost layer and 11.01 kPa (230 psf) for the second layer as show in Figure 7.7. Table 7.6. Design load on the strip for breaking design. Layer Total Design Pressure, p(psf) Top 5.29 kips / 4.38 ft 2 * = 1,208 psf Second 0.92 kips / 3.94 ft 2 ** = 224 psf * Tributary area of a panel for the top layer (4.38 ft2 = 4.87 ft × 1.8 ft / 2 strips per panel) ** Tributary area of a panel for the second layer (3.94 ft2 = 4.87 ft × 2.43 ft / 3 strips per panel) Table 7.5. Test results and calculation of design strip load for breaking design. (1) Measured Dynamic Load* (kips) (2) Static** (kips) (1)+(2)=(3) Total (kips) (4) Calculated Resistance** (kips)Layer 8 ft 16 ft 8 ft 16 ft 8 ft 16 ft 8 ft 16 ft Controlling Design Dynamic Load (kips) Top 1.64 5.29 0.569 0.853 2.209 6.143 9.23† 9.23 5.29 Second 0.92 0.06 1.095 1.642 2.015 1.702 9.23 9.23 0.92 * Adjusted for 54 kips design impact load ** Calculated from AASHTO Section 11.10.6.4.3 † Reinforcing steel is ASTM Grade 60.