CO FLAP US50(1) FINAL GEOTECHNICAL Report- Appendicies only.pdf
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- CO FLAP US50(1) Little Blue Creek Canyon
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- 6982AF20B000008
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This federal contract opportunity notice is for reconstruction and improvements to CO FLAP US50(1) Little Blue Creek Canyon in Montrose, Colorado. The project includes reconstructing 4.17 miles of roadway to provide a consistent 12-foot travel way with 4 to 8-foot shoulders and adding 1.5 miles of climbing lanes. Major work items include large scale rock excavation and embankment, roadway realignment and widening, MSE retaining walls, drainage culvert installation, guardrail, aggregate base, asphalt concrete pavement, minor bridge and bridge railing work, pavement markings, and traffic control. Significant quantities listed are 180,000 cubic yards of roadway excavation, 38,500 cubic yards of waste, 580 cubic yards of grouted riprap, 60,000 square feet of mechanically stabilized earth wall, 2,500 linear feet of rock bolt, and 70,000 tons of aggregate base. The opportunity notice provides project details but plans and specifications are not yet available. The Department of Transportation Federal Highway Administration is the issuing agency.
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APPENDIX A
GRS Wall Analysis Preliminarily Internal and External MathCAD
GRS Retaining Wall Design
PROJECT INFORMATION
Project Name: CO US50 Designer: DM
Project No.: CO US50 Checker: JMA
Location: Gunnison County, CO Date: 06/19/2019
WALL GEOMETRY STATION 647+10 LT
70% Reinforcement Length 8-Inch Reinf Spacing
See Figure 1 (page 2) for wall geometry and loading definitions.
Exposed Wall Height ≔H' 34 ft Slope Above Wall ≔βtop 14 deg
Embedment ≔Hemb 6 ft Distance to crest ≔Lcrest 4.0 ft
Embedment Ignored ≔Hig 6 ft
Design Wall Height ≔H =+H' Hemb 40.0 ft Slope Rise ≔Hslope =⋅Lcrest tan ⎛⎝βtop⎞⎠ 0.997 ft
Reinforcement Length ≔L 28 ft Slope Below Wall ≔βbottom 45 deg
Back Batter ≔α 90 deg
L
H %70
Facing Elements Traffic Loading
Assumed Height ≔Hface 8 in
Assumed Depth ≔bface 8 in Traffic Live Load ≔qt 250 ―― lb ft2
Unit Weight ≔γface 140 ―― lb ft3 Offset to Traffic Load ≔d 4 ft check offset
Width of Traffic Load ≔bf 26 ft
Friction Angle ≔ϕface 45 deg Offset to CL ≔dt =+d ⋅0.5 bf 17 ft
Face Batter ≔ω 14 deg
Reinforcement Spacing Guardrail (y/n)? ≔Rail 1
Normal Reinforcement Spacing ≔sv 8 in y=1, n=0
Facing Reinforcement Spacing ≔svf 8 in Guardrail load in reinforcement
≔Thb =| if else
＝Rail 1
5 ft sv lb ft2
0 ―― lb ft2
40 ―― lb ft2
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Figure 1 - Schematic GRS Wall based on AASHTO LRFD Bridge Design Specifications, Chapter 11.
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 2 of 17
Load and Resistance Factors (AAHSTO LRFD, 2015, Strength I)
Dead Load Max ≔γDCmax 1.25 Earth Surcharge Max ≔γESmax 1.5
Dead Load Min ≔γDCmin 0.9 Earth Surcharge Min ≔γESmin 1.0
Hor. Active Earth Pres. Max ≔γEHmax 1.5 Vert. Active Earth Pres. Max ≔γEVmax 1.35
Hor. Active Earth Pres. Min ≔γEHmin 0.9 Vert. Active Earth Pres. Min ≔γEVmin 1.0
Live Load Surcharge ≔γLS 1.75
GRS Capacity ≔Φcap 0.45 Soil-Sliding Resistance ≔Φτ 1.00
Reinforcement resistance ≔Φreinf 0.40 Bearing Resistance ≔Φbc 0.65
Other Constants
Unit Weight of Water ≔γwater 62.4 ―― lb ft3 Wall Friction ≔δ 0 deg
Equivalent Slope Calculations
≔βint if else
≤Lcrest L return atan
Hslope
L
‖‖ return βtop
≔βext if else
≤Lcrest +L H return atan
Hslope
+L H
‖‖ return βtop
=βint 2.04 deg =βext 0.84 deg
SOIL PARAMETERS Assumed angular rock everywhere, need testing to verify properties (MDD)
Foundation Soil Properties
Friction Angle ≔ϕf' 38 deg Cohesion ≔cf' 100 ―― lb ft2 Unit Weight ≔γf 125 ―― lb ft3
Bearing Capacity Factors by Friction Angle AASHTO 2015 Table 10.6.3.1.2a-1
≔BC 0 5.14 1.0 0.0
≔ϕf =⋅ϕf' ―― π
≔Nc =BC ,ϕf 1
61.4 ≔Nq =BC ,ϕf 2
48.9 ≔Nγ =BC ,ϕf 3
Retained Soil Properties
Friction Angle ≔ϕb' 32 deg Cohesion ≔cb' 0 ―― lb ft2 Unit Weight ≔γb 130 ―― lb ft3
Active Coefficient ≔Kab =―――――――――――――――――― sin ⎛⎝ +α ϕb'⎞⎠
⋅⋅sin ((α)) sin (( -α δ))
+1
⋅sin ⎛⎝ +ϕb' δ⎞⎠ sin ⎛⎝ -ϕb' βext⎞⎠ ⋅sin (( -α δ)) sin ⎛⎝ +α βext⎞⎠
0.31
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Reinforced Soil Properties
Friction Angle ≔ϕr' 38 deg Cohesion ≔cr' 0 ―― lb ft2 Unit Weight ≔γr 125 ―― lb ft3
Assumed d=1.5 vs previous 1.0,(MDD)
Maximum diameter of fill ≔dmax 1.5 in Fill Type: Well-graded
≔Kar =―――――――――――――――――― sin ⎛⎝ +α ϕr'⎞⎠
⋅⋅sin ((α)) sin (( -α δ))
+1
⋅sin ⎛⎝ +ϕr' δ⎞⎠ sin ⎛⎝ -ϕr' βint⎞⎠ ⋅sin (( -α δ)) sin ⎛⎝ +α βint⎞⎠
0.242
Active Coefficient
Passive Coefficient ≔Kpr =―――― +1 sin ⎛⎝ϕr'⎞⎠ -1 sin ⎛⎝ϕr'⎞⎠
4.204
Geosynthetic Reinforcement Properties
Ultimate Reinforcement Strength ≔Tult 4800 ― lb ft Strength at 2% Strain ≔T2 2400 ― lb ft
Factored Reinforcement Strength ≔Tf =⋅Tult Φreinf 1920 ― lb ft
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EXTERNAL STABILITY
Calculated Weights
Reinforced Zone ≔WGRS =⋅⋅H L γr 140000 ― lb ft Slope ≔Wslope =⋅⋅⋅0.5 L2 tan ⎛⎝βint⎞⎠ γr 1745.296 ― lb ft
Facing ≔Wface =⋅⋅H bface γface 3733.333 ― lb ft Facing assumed to have a rectangular cross section.
Calculated Lateral Forces
Retained Soil ≔PA =⋅⋅⋅0.5 Kab γb H2 32217.824 ― lb ft Angle of Action ≔ρ =+(( -90 deg α)) βext 0.84 deg
≔PAH =⋅PA cos ((ρ)) 32214.36 ― lb ft ≔PAV =⋅PA sin ((ρ)) 472.467 ― lb ft
Traffic ≔PTH =⋅⋅qt Kab H 3097.868 ― lb ft
Factored Vertical Forces
GRS ≔WGRSmax =⋅WGRS γEVmax 189000 ― lb ft ≔WGRSmin =⋅WGRS γEVmin 140000 ― lb ft
Facing ≔Wfacemax =⋅Wface γEVmax 5040 ― lb ft ≔Wfacemin =⋅Wface γEVmin 3733.333 ― lb ft
Slope ≔Wslopemax =⋅Wslope γEVmax 2356.15 ― lb ft ≔Wslopemin =⋅Wslope γEVmin 1745.296 ― lb ft
Traffic ≔PTVmax =⋅⋅qt γLS ⎛⎝ -L Lcrest⎞⎠ 10500 ― lb ft
Earth Pressure ≔PAVmax =⋅PAV γEVmax 637.831 ― lb ft ≔PAVmin =⋅PAV γEVmin 472.467 ― lb ft
Factored Lateral Forces
Earth Pressure ≔PAHmax =⋅PAH γEHmax 48321.539 ― lb ft ≔PAHmin =⋅PAH γEHmin 28992.924 ― lb ft
Traffic ≔PTHmax =⋅PTH γLS 5421.268 ― lb ft
Sliding Stability
Total Vertical Force ≔Wmin =++WGRSmin Wfacemin PAVmin 144205.801 ― lb ft
Sliding Friction Factor ≔μf min ⎛⎝ ,tan ⎛⎝ϕf'⎞⎠ tan ⎛⎝ϕr'⎞⎠⎞⎠
Sliding Resistance ≔Rsliding =⋅⋅Wmin μf Φτ 112665.919 ― lb ft
Total Horizontal Force ≔Ptotal =+PAHmax PTHmax 53742.808 ― lb ft
Sliding CDR ≔CDRsliding =――― Rsliding
Ptotal
2.096 =if ⎛⎝ ,,<CDRsliding 1.0 “NO” “OK”⎞⎠ “OK”
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Overturning
Facing Moments ≔d1 =⋅H tan ((ω)) 9.973 ft ≔d3 =⋅H tan (( -90 deg α)) 0 ft ≔d2 =-bface ⎛⎝ +d1 d3⎞⎠ -9.306 ft
≔Mf1 =⋅⋅⋅⎛⎝ ⋅⋅⋅0.5 d1 H γface⎞⎠ d1 γEVmin 1 ft 185664.5 ⋅lb ft
≔Mf2 =⋅⋅⋅⎛⎝ ⋅⋅d2 H γface⎞⎠ d2 d1 γEVmin 1 ft -277252.305 ⋅lb ft
≔Mf3 =⋅⋅⋅⎛⎝ ⋅⋅⋅0.5 d3 H γface⎞⎠ d3 d1 d2 γEVmin 1 ft 0 ⋅lb ft
GRS Moment ≔MGRS =⋅⋅⋅⎛⎝ ⋅⋅L H γr⎞⎠
L bface γEVmin 1 ft 2053333.333 ⋅lb ft Assumes equal front and back batter
Slope ≔Mslope =⋅⋅⎛⎝Wslopemin⎞⎠
L bface
1 ft 33742.39 ⋅lb ft
Vert. Earth Pressure ≔MAV =⋅⋅PAVmin
+bface L
1 ft 6772.029 ⋅lb ft
Resisting Moments ≔MR =+++++Mf1 Mf2 Mf3 MGRS Mslope MAV 2002259.947 ⋅lb ft
Hor. Earth Pressure ≔MAH =⋅⋅PAHmax H
1 ft 644287.191 ⋅lb ft
Traffic ≔MTH =⋅⋅PTHmax H
1 ft 108425.369 ⋅lb ft
Driving Moments ≔MD =+MAH MTH 752712.561 ⋅lb ft
Overturning CDR ≔CDRoverturn =――
MR
MD
2.66 =if ⎛⎝ ,,<CDRoverturn 1.0 “NO” “OK”⎞⎠ “OK”
Total Vertical Force ≔Wmax =++++WGRSmax Wfacemax Wslopemax PAVmax PTHmax 202455.249 ― lb ft
Eccentricity ≔e =――――
-MD MR
⋅Wmax 1 ft -6.172 ft ≔emax =―――
+L bface
7.167 ft
=if ⎛⎝ ,,>e emax “NO” “OK”⎞⎠ “OK”
≔ebearing =if (( ,,≤e 0 0 ft e)) 0 ft ≔B' =-⎛⎝ +L bface⎞⎠ ⋅2 ebearing 28.667 ft
Bearing Resistance
Factored Vertical Stress ≔σVF =―― Wmax
B'
7062.392 ―― lb ft2
Nominal Bearing Resistance ≔qn =++⋅cf' Nc ⋅⋅⋅0.5 B' γf Nγ ⋅⋅γf ⎛⎝ -Hemb Hig⎞⎠ Nq 145890 ―― lb ft2
Factored Bearing Resistance ≔qR =⋅qn Φbc 94828.5 ―― lb ft2
Bearing CDR ≔CDRbearing =―― qR σVF
13.427 =if ⎛⎝ ,,<CDRbearing 1.0 “NO” “OK”⎞⎠ “OK”
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INTERNAL STABILITY
GRS Capacity
Revised with 0.2*eqn per 2016 TF revisions,(MDD)GRS Nominal Capacity ≔qGRSn =⋅0.2
⋅0.7 sv
⋅6 dmax
Tf sv
Kpr 1763.471 ―― lb ft2
GRS Factored Capacity ≔qGRSf =⋅qGRSn Φcap 793.562 ―― lb ft2
Applied Load ≔Vappliedf =+―――― Wslopemax
L PTVmax
L
459.148 ―― lb ft2
Capacity CDR ≔CDRcap =――― qGRSf
Vappliedf
1.728 =if ⎛⎝ ,,<CDRcap 1.0 “NO” “OK”⎞⎠ “OK”
Reinforcement Strength
Matrix calculations, see summary table below. ≔z1 =-⋅2 dt bf 8 ft
Reinforcement Layers ≔z =, ‥sv +sv sv H 0.667 ft
Surcharge Load Angles of Action ≔βb =atan d z
1.406
≔αb =-atan +d bf z βb 0.143
Matrix size setup ≔i ‥0 -rows ((z)) 1
Reinforcement load due to surcharge ≔σhti qt π
+αbi
⋅sin ⎛ αbi cos ⎛
+αbi ⋅2 βbi
Kar 0.057 lb ft2
Factored reinforcement load due to earth pressure ≔σhwf =⋅⋅⋅γEHmax γr z Kar 30.265 lb ft2
Factored reinforcement load due to traffic ≔σhtf =⋅γLS σht 0.1 lb ft2
Factored reinforcement load due to vehicle impact ≔σhbi =if ⎛
,,≤z i 5 ft Thb 0⎞ lb ft2
Total factored reinforcement load ≔σhf =++σhwf σhtf σhb 70.365 lb ft2
Required factored reinforcement strength ≔Treqf =⋅―――― σhf
0.7 sv
⋅6 dmax sv 64.411 lb ft
Factored Reinforcement CDR ≔CDRreff =―― Tf
Treqf
29.809
Nominal reinforcement load due to earth pressure ≔σhw =⋅⋅γr z Kar 20.177 lb ft2
Total nominal reinforcement load ≔σh =+σhw σht 20.234 lb
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Required nominal reinforcement strength ≔Treq =⋅―――― σh
0.7 sv
⋅6 dmax sv 18.522 lb ft
Nominal Reinforcement CDR ≔CDRref =―― T2
Treq
129.577
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FACING STABILITY
Connection
Earth Force at Face ≔Fface =+⋅⋅⋅⋅⋅0.72 γr Kar sv svf γEHmax ⋅⋅σht svf γLS 14.594 lb ft
Assumes that traffic railings are setback to AASHTO minimums and do not impart load directly on the wall face. Other scenarios may require additional loading.
Frictional Resistance ≔Rface =⋅⋅⋅⋅γface bface z ― tan ⎛⎝ϕface⎞⎠
41.481 lb ft
≔CDRface =―― Rface
Fface
2.842
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Seismic Stability
NO SEISMIC ASSUMED (MDD)
Seismic Design Parameters Site Class: Lat Long.:
Peak Ground Acceleration ≔PGA 0 Seismic parameters obtained from USGS Sesimic Design Maps online tool:
https://earthquake.usgs.gov/designmaps/us/ application.php? Spectral Acceleration at 1 sec ≔S1 0
Site Factors ≔FPGA 0
≔Fv 0.0 Seismic Load Factor ≔γEQ 1.0
Extreme Event I
Maximum Acceleration ≔kmax =⋅FPGA PGA 0
Peak Ground Velocity ≔PGV =⋅⋅38 Fv S1 0
Site Reduction Factor ≔αsite =+1 ⋅⋅0.01 ―― H
1 ft
-⋅0.5
⋅Fv S1 kmax
Average Ground Acceleration ≔kav =⋅αsite kmax ?
Kv is typically assumed as 0, unless PGA >0.6. More critical for bridge structure than walls. CalTrans Report CA/UCD- SESM-08-01 and Memo "Seismic Design and Selection of Standard Retaining Walls" 06/16/2013
Vertical Ground Acceleration ≔kv 0
Angle of Seismic Action ≔θ =atan kav -1 kv
Forces on GRS
Weight of GRS ≔W =⋅⋅⋅γr H ((L)) γEVmin 140000 ― lb ft
For wall with no bridge abutment, qb, qrb, b, ab, H2, g1 = 0
≔qb 0 ≔b 0 ≔qrb 0 ≔ab 0 ≔H2 0 ≔γ1 0
Bridge Deadload ≔Wb =⋅⋅qb b γDCmin 0
Road Base ≔Wrb =⋅⋅qrb ⎛⎝ --L b ab⎞⎠ γESmin 0 ft
Effective GRS Weight ≔Weff =⋅⋅⋅0.5 ((H)) H γr 100000 ― lb ft
Effective Roadbase Weight ≔Wrbeff =⋅⋅
H b ab
H2 γ1 0 ft
Average Maximum Acceleration ≔Am =⋅⎛⎝ -1.45 kav⎞⎠ kav ?
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Direct Sliding
Thrust Forces on GRS Wall
Retained Backfill ≔Fb =⋅⋅⋅0.5 γb Kab H2 32217.824 ― lb ft ≔qrb 0 ―― lb ft2
Road Base ≔Frb =⋅⋅qrb Kab H 0 ― lb ft
Traffic ≔Ft =⋅⋅qt Kab H 3097.868 ― lb ft
Inertia of GRS ≔Pir =⋅⋅γEQ Weff Am ?
Inertia of Roadbase ≔Pirb =⋅⋅γEQ Wrbeff Am ?
Inertia of Sill ≔Pis 0 For wall with no bridge, Pis = 0
Dynamic Earth Pressure Coefficient
≔KAE ⋅――――――――――
cos ⎛⎝ --ϕr' θ ω⎞⎠
⋅⋅cos ((θ)) cos ((ω)) cos (( ++δ ω θ))
+1 ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾2
⋅sin ⎛⎝ +ϕr' δ⎞⎠ sin ⎛⎝ --ϕr' θ βtop⎞⎠ ⋅cos (( ++δ ω θ)) cos ⎛⎝ -βtop ω⎞⎠
-2
=KAE ?
Dynamic Earth Force ≔PAE =⋅⋅⋅⋅0.5 γr H2 ⎛⎝ -KAE Kar⎞⎠ γEQ ?
Factored Driving Forces ≔FR =+++⋅γEHmax Fb ⋅γLS Ft Pir ⋅0.5 PAE ?
Total Vertical Forces ≔V =W 140000 ― lb ft
Factored Resisting Force ≔RR =⋅⋅Φτ V μf 109379.988 ― lb ft
Sliding CDR ≔CDRslidings =――
RR
FR
? =if ⎛⎝ ,,≥CDRslidings 1.0 “OK” “NO”⎞⎠ ?
Overturning Stability
Reinforced Soil Moment ≔Mb =⋅⋅γEHmax Fb ― H
644356.481 lb
Roadbase surcharge Moment ≔Mrb =0 0
Inertial Moments ≔Mi ⋅⋅γEQ Pir ― H
Dynamic Moment ≔MAE ⋅⋅⋅0.5 γEQ PAE (( ⋅0.6 H))
Total Factored Driving Moments ≔MD =++Mb Mi MAE ?
Total Factored Resisting Moments ≔MR =⋅W ― L
1960000 lb
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 13 of 17
Overturning CDR ≔CDRoverturnings =――
MR
MD
? =if ⎛⎝ ,,≥CDRoverturnings 1.0 “OK” “NO”⎞⎠ ?
Eccentricity
Eccentricity ≔eseismic =――――
-MD MR
V ? ≔ebear =if ⎛⎝ ,,≤eseismic 0 0 ft eseismic⎞⎠ ?
=if
,,≤eseismic ― L
“OK” “NO”
Effective Width ≔B' =-⎛⎝ +L bface⎞⎠ ⋅2 ebear ?
Bearing Stability
Bearing Capacity Factors =Nc 61.4 =Nq 48.9 =Nγ 78
Factored Vertical Stress ≔σVF =― V
B'
Nominal Bearing Resistance =qn 145890 ―― lb ft2
Factored Bearing Resistance ≔qR =⋅qn Φbc 94828.5 ―― lb ft2
Bearing CDR ≔CDRbearings =―― qR σVF
? =if ⎛⎝ ,,≥CDRbearings 1.0 “OK” “NO”⎞⎠ ?
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 14 of 17
GRS Wall Design Summary
Project Name: Designer:
Project No.: Checker:
Location: Date:
WALL GEOMETRY
See Figure 1 (page 2) for wall geometry and loading definitions.
Exposed Wall Height =H' 34.0 ft Slope Above Wall =βtop 14 ° Slope Rise =Hslope 1.0 ft
Embedment =Hemb 6.0 ft Distance to crest =Lcrest 4.0 ft Slope Below Wall =βbottom 45 °
Design Wall Height =H 40.0 ft
Reinforcement Length =L 28.0 ft =― L
H %70
Back Batter =α 90 °
Facing Elements
Assumed Height =Hface 8 in Unit Weight =γface 140 ―― lb ft3 Friction Angle =ϕface 45 °
Assumed Depth =bface 8 in Face Batter =ω 14 °
Traffic Loading
Traffic Live Load =qt 250 ―― lb ft2 Width of Traffic Load =bf 26.0 ft Offset to Traffic Load =d 4.0 ft
Offset to CL =dt 17.0 ft
Reinforcement Spacing
Normal Reinforcement Spacing =sv 8 in Facing Reinforcement Spacing =svf 8 in
Strength I Limit State
External Stability
=CDRsliding 2.096 =if ⎛⎝ ,,<CDRsliding 1.0 “NO” “OK”⎞⎠ “OK”
=CDRoverturn 2.66 =if ⎛⎝ ,,<CDRoverturn 1.0 “NO” “OK”⎞⎠ “OK”
Eccentricity =e -6.172 ft
=emax 7.167 ft
=if ⎛⎝ ,,>e emax “NO” “OK”⎞⎠ “OK”
=CDRbearing 13.427 =if ⎛⎝ ,,<CDRbearing 1.0 “NO” “OK”⎞⎠ “OK”
=CDRcap 1.728 =if ⎛⎝ ,,<CDRcap 1.0 “NO” “OK”⎞⎠ “OK”
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Extreme Event I Limit State
=CDRslidings ? =if ⎛⎝ ,,≥CDRslidings 1.0 “OK” “NO”⎞⎠ ?
=CDRoverturnings ? =if ⎛⎝ ,,≥CDRoverturnings 1.0 “OK” “NO”⎞⎠ ?
=eseismic ? =if
,,≤eseismic ― L
“OK” “NO”
=CDRbearings ? =if ⎛⎝ ,,≥CDRbearings 1.0 “OK” “NO”⎞⎠ ?
Internal Stability
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Project Name: CO US50 Designer: DM
Project No.: CO US50 Checker: JMA
Location: Gunnison County, CO Date: 06/19/2019
WALL GEOMETRY STATION 647+10 LT
70% Reinforcement Length 12-Inch Reinf Spacing
See Figure 1 (page 2) for wall geometry and loading definitions.
Exposed Wall Height ≔H' 34 ft Slope Above Wall ≔βtop 14 deg
Embedment ≔Hemb 6 ft Distance to crest ≔Lcrest 4.0 ft
Embedment Ignored ≔Hig 6 ft
Design Wall Height ≔H =+H' Hemb 40.0 ft Slope Rise ≔Hslope =⋅Lcrest tan ⎛⎝βtop⎞⎠ 0.997 ft
Reinforcement Length ≔L 28 ft Slope Below Wall ≔βbottom 45 deg
Back Batter ≔α 90 deg
L
H %70
Facing Elements Traffic Loading
Assumed Height ≔Hface 8 in
Assumed Depth ≔bface 8 in Traffic Live Load ≔qt 250 ―― lb ft2
Unit Weight ≔γface 140 ―― lb ft3 Offset to Traffic Load ≔d 4 ft check offset
Width of Traffic Load ≔bf 26 ft
Friction Angle ≔ϕface 45 deg Offset to CL ≔dt =+d ⋅0.5 bf 17 ft
Face Batter ≔ω 14 deg
Reinforcement Spacing Guardrail (y/n)? ≔Rail 1
Normal Reinforcement Spacing ≔sv 12 in y=1, n=0
Facing Reinforcement Spacing ≔svf 12 in Guardrail load in reinforcement
≔Thb =| if else
＝Rail 1
5 ft sv lb ft2
0 ―― lb ft2
60 ―― lb
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Dead Load Min ≔γDCmin 0.9 Earth Surcharge Min ≔γESmin 1.0
Hor. Active Earth Pres. Max ≔γEHmax 1.5 Vert. Active Earth Pres. Max ≔γEVmax 1.35
Hor. Active Earth Pres. Min ≔γEHmin 0.9 Vert. Active Earth Pres. Min ≔γEVmin 1.0
Live Load Surcharge ≔γLS 1.75
GRS Capacity ≔Φcap 0.45 Soil-Sliding Resistance ≔Φτ 1.00
Reinforcement resistance ≔Φreinf 0.40 Bearing Resistance ≔Φbc 0.65
Other Constants
Unit Weight of Water ≔γwater 62.4 ―― lb ft3 Wall Friction ≔δ 0 deg
Equivalent Slope Calculations
≔βint if else
≤Lcrest L return atan
Hslope
L
‖‖ return βtop
≔βext if else
≤Lcrest +L H return atan
Hslope
+L H
‖‖ return βtop
=βint 2.04 deg =βext 0.84 deg
SOIL PARAMETERS Assumed angular rock everywhere, need testing to verify properties (MDD)
Foundation Soil Properties
Friction Angle ≔ϕf' 38 deg Cohesion ≔cf' 100 ―― lb ft2 Unit Weight ≔γf 125 ―― lb ft3
Bearing Capacity Factors by Friction Angle AASHTO 2015 Table 10.6.3.1.2a-1
≔BC 0 5.14 1.0 0.0
≔ϕf =⋅ϕf' ―― π
≔Nc =BC ,ϕf 1
61.4 ≔Nq =BC ,ϕf 2
48.9 ≔Nγ =BC ,ϕf 3
Retained Soil Properties
Friction Angle ≔ϕb' 32 deg Cohesion ≔cb' 0 ―― lb ft2 Unit Weight ≔γb 130 ―― lb ft3
Active Coefficient ≔Kab =―――――――――――――――――― sin ⎛⎝ +α ϕb'⎞⎠
⋅⋅sin ((α)) sin (( -α δ))
+1
⋅sin ⎛⎝ +ϕb' δ⎞⎠ sin ⎛⎝ -ϕb' βext⎞⎠ ⋅sin (( -α δ)) sin ⎛⎝ +α βext⎞⎠
0.31
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 3 of 16 lb ft2 Unit Weight ≔γr 125 ―― lb ft3
Assumed d=1.5 vs previous 1.0,(MDD)
Maximum diameter of fill ≔dmax 1.5 in Fill Type: Well-graded
≔Kar =―――――――――――――――――― sin ⎛⎝ +α ϕr'⎞⎠
⋅⋅sin ((α)) sin (( -α δ))
+1
⋅sin ⎛⎝ +ϕr' δ⎞⎠ sin ⎛⎝ -ϕr' βint⎞⎠ ⋅sin (( -α δ)) sin ⎛⎝ +α βint⎞⎠
0.242
Active Coefficient
Passive Coefficient ≔Kpr =―――― +1 sin ⎛⎝ϕr'⎞⎠ -1 sin ⎛⎝ϕr'⎞⎠
4.204
Geosynthetic Reinforcement Properties
Ultimate Reinforcement Strength ≔Tult 8000 ― lb ft Strength at 2% Strain ≔T2 2400 ― lb ft
Factored Reinforcement Strength ≔Tf =⋅Tult Φreinf 3200 ― lb
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 4 of 16
Reinforced Zone ≔WGRS =⋅⋅H L γr 140000 ― lb ft Slope ≔Wslope =⋅⋅⋅0.5 L2 tan ⎛⎝βint⎞⎠ γr 1745.296 ― lb ft
Facing ≔Wface =⋅⋅H bface γface 3733.333 ― lb ft Facing assumed to have a rectangular cross section.
Calculated Lateral Forces
Retained Soil ≔PA =⋅⋅⋅0.5 Kab γb H2 32217.824 ― lb ft Angle of Action ≔ρ =+(( -90 deg α)) βext 0.84 deg
≔PAH =⋅PA cos ((ρ)) 32214.36 ― lb ft ≔PAV =⋅PA sin ((ρ)) 472.467 ― lb ft
Traffic ≔PTH =⋅⋅qt Kab H 3097.868 ― lb ft
Factored Vertical Forces
GRS ≔WGRSmax =⋅WGRS γEVmax 189000 ― lb ft ≔WGRSmin =⋅WGRS γEVmin 140000 ― lb ft
Facing ≔Wfacemax =⋅Wface γEVmax 5040 ― lb ft ≔Wfacemin =⋅Wface γEVmin 3733.333 ― lb ft
Slope ≔Wslopemax =⋅Wslope γEVmax 2356.15 ― lb ft ≔Wslopemin =⋅Wslope γEVmin 1745.296 ― lb ft
Traffic ≔PTVmax =⋅⋅qt γLS ⎛⎝ -L Lcrest⎞⎠ 10500 ― lb ft
Earth Pressure ≔PAVmax =⋅PAV γEVmax 637.831 ― lb ft ≔PAVmin =⋅PAV γEVmin 472.467 ― lb ft
Factored Lateral Forces
Earth Pressure ≔PAHmax =⋅PAH γEHmax 48321.539 ― lb ft ≔PAHmin =⋅PAH γEHmin 28992.924 ― lb ft
Traffic ≔PTHmax =⋅PTH γLS 5421.268 ― lb ft
Sliding Stability
Total Vertical Force ≔Wmin =++WGRSmin Wfacemin PAVmin 144205.801 ― lb ft
Sliding Friction Factor ≔μf min ⎛⎝ ,tan ⎛⎝ϕf'⎞⎠ tan ⎛⎝ϕr'⎞⎠⎞⎠
Sliding Resistance ≔Rsliding =⋅⋅Wmin μf Φτ 112665.919 ― lb ft
Total Horizontal Force ≔Ptotal =+PAHmax PTHmax 53742.808 ― lb ft
Sliding CDR ≔CDRsliding =――― Rsliding
Ptotal
2.096 =if ⎛⎝ ,,<CDRsliding 1.0 “NO” “OK”⎞⎠ “OK”
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 5 of 16
Facing Moments ≔d1 =⋅H tan ((ω)) 9.973 ft ≔d3 =⋅H tan (( -90 deg α)) 0 ft ≔d2 =-bface ⎛⎝ +d1 d3⎞⎠ -9.306 ft
≔Mf1 =⋅⋅⋅⎛⎝ ⋅⋅⋅0.5 d1 H γface⎞⎠ d1 γEVmin 1 ft 185664.5 ⋅lb ft
≔Mf2 =⋅⋅⋅⎛⎝ ⋅⋅d2 H γface⎞⎠ d2 d1 γEVmin 1 ft -277252.305 ⋅lb ft
≔Mf3 =⋅⋅⋅⎛⎝ ⋅⋅⋅0.5 d3 H γface⎞⎠ d3 d1 d2 γEVmin 1 ft 0 ⋅lb ft
GRS Moment ≔MGRS =⋅⋅⋅⎛⎝ ⋅⋅L H γr⎞⎠
L bface γEVmin 1 ft 2053333.333 ⋅lb ft Assumes equal front and back batter
Slope ≔Mslope =⋅⋅⎛⎝Wslopemin⎞⎠
L bface
1 ft 33742.39 ⋅lb ft
Vert. Earth Pressure ≔MAV =⋅⋅PAVmin
+bface L
1 ft 6772.029 ⋅lb ft
Resisting Moments ≔MR =+++++Mf1 Mf2 Mf3 MGRS Mslope MAV 2002259.947 ⋅lb ft
Hor. Earth Pressure ≔MAH =⋅⋅PAHmax H
1 ft 644287.191 ⋅lb ft
Traffic ≔MTH =⋅⋅PTHmax H
1 ft 108425.369 ⋅lb ft
Driving Moments ≔MD =+MAH MTH 752712.561 ⋅lb ft
Overturning CDR ≔CDRoverturn =――
MR
MD
2.66 =if ⎛⎝ ,,<CDRoverturn 1.0 “NO” “OK”⎞⎠ “OK”
Total Vertical Force ≔Wmax =++++WGRSmax Wfacemax Wslopemax PAVmax PTHmax 202455.249 ― lb ft
Eccentricity ≔e =――――
-MD MR
⋅Wmax 1 ft -6.172 ft ≔emax =―――
+L bface
7.167 ft
=if ⎛⎝ ,,>e emax “NO” “OK”⎞⎠ “OK”
≔ebearing =if (( ,,≤e 0 0 ft e)) 0 ft ≔B' =-⎛⎝ +L bface⎞⎠ ⋅2 ebearing 28.667 ft
Bearing Resistance
Factored Vertical Stress ≔σVF =―― Wmax
B'
7062.392 ―― lb ft2
Nominal Bearing Resistance ≔qn =++⋅cf' Nc ⋅⋅⋅0.5 B' γf Nγ ⋅⋅γf ⎛⎝ -Hemb Hig⎞⎠ Nq 145890 ―― lb ft2
Factored Bearing Resistance ≔qR =⋅qn Φbc 94828.5 ―― lb ft2
Bearing CDR ≔CDRbearing =―― qR σVF
13.427 =if ⎛⎝ ,,<CDRbearing 1.0 “NO” “OK”⎞⎠ “OK”
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 6 of 16
Revised with 0.2*eqn per 2016 TF revisions,(MDD)GRS Nominal Capacity ≔qGRSn =⋅0.2
⋅0.7 sv
⋅6 dmax
Tf sv
Kpr 1672.17 ―― lb ft2
GRS Factored Capacity ≔qGRSf =⋅qGRSn Φcap 752.477 ―― lb ft2
Applied Load ≔Vappliedf =+―――― Wslopemax
L PTVmax
L
459.148 ―― lb ft2
Capacity CDR ≔CDRcap =――― qGRSf
Vappliedf
1.639 =if ⎛⎝ ,,<CDRcap 1.0 “NO” “OK”⎞⎠ “OK”
Reinforcement Strength
Matrix calculations, see summary table below. ≔z1 =-⋅2 dt bf 8 ft
Reinforcement Layers ≔z =, ‥sv +sv sv H 1 ft
Surcharge Load Angles of Action ≔βb =atan d z
1.326
≔αb =-atan +d bf z βb 0.212
Matrix size setup ≔i ‥0 -rows ((z)) 1
Reinforcement load due to surcharge ≔σhti qt π
+αbi
⋅sin ⎛ αbi cos ⎛
+αbi ⋅2 βbi
Kar 0.186 lb ft2
Factored reinforcement load due to earth pressure ≔σhwf =⋅⋅⋅γEHmax γr z Kar 45.397 lb ft2
Factored reinforcement load due to traffic ≔σhtf =⋅γLS σht 0.326 lb ft2
Factored reinforcement load due to vehicle impact ≔σhbi =if ⎛
,,≤z i 5 ft Thb 0⎞ lb ft2
Total factored reinforcement load ≔σhf =++σhwf σhtf σhb 105.723 lb ft2
Required factored reinforcement strength ≔Treqf =⋅―――― σhf
0.7 sv
⋅6 dmax sv 170.101 lb ft
Factored Reinforcement CDR ≔CDRreff =―― Tf
Treqf
18.812
Nominal reinforcement load due to earth pressure ≔σhw =⋅⋅γr z Kar 30.265 lb ft2
Total nominal reinforcement load ≔σh =+σhw σht 30.451 lb
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 7 of 16
0.7 sv
⋅6 dmax sv 48.994 lb ft
Nominal Reinforcement CDR ≔CDRref =―― T2
Treq
48.986
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 8 of 16
Earth Force at Face ≔Fface =+⋅⋅⋅⋅⋅0.72 γr Kar sv svf γEHmax ⋅⋅σht svf γLS 33.012 lb ft
Assumes that traffic railings are setback to AASHTO minimums and do not impart load directly on the wall face. Other scenarios may require additional loading.
Frictional Resistance ≔Rface =⋅⋅⋅⋅γface bface z ― tan ⎛⎝ϕface⎞⎠
62.222 lb ft
≔CDRface =―― Rface
Fface
1.885
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 9 of 16
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 10 of 16
Seismic Design Parameters Site Class: Lat Long.:
Peak Ground Acceleration ≔PGA 0 Seismic parameters obtained from USGS Sesimic Design Maps online tool:
https://earthquake.usgs.gov/designmaps/us/ application.php? Spectral Acceleration at 1 sec ≔S1 0
Site Factors ≔FPGA 0
≔Fv 0.0 Seismic Load Factor ≔γEQ 1.0
Extreme Event I
Maximum Acceleration ≔kmax =⋅FPGA PGA 0
Peak Ground Velocity ≔PGV =⋅⋅38 Fv S1 0
Site Reduction Factor ≔αsite =+1 ⋅⋅0.01 ―― H
1 ft
-⋅0.5
⋅Fv S1 kmax
Average Ground Acceleration ≔kav =⋅αsite kmax ?
Kv is typically assumed as 0, unless PGA >0.6. More critical for bridge structure than walls. CalTrans Report CA/UCD- SESM-08-01 and Memo "Seismic Design and Selection of Standard Retaining Walls" 06/16/2013
Vertical Ground Acceleration ≔kv 0
Angle of Seismic Action ≔θ =atan kav -1 kv
Forces on GRS
Weight of GRS ≔W =⋅⋅⋅γr H ((L)) γEVmin 140000 ― lb ft
For wall with no bridge abutment, qb, qrb, b, ab, H2, g1 = 0
≔qb 0 ≔b 0 ≔qrb 0 ≔ab 0 ≔H2 0 ≔γ1 0
Bridge Deadload ≔Wb =⋅⋅qb b γDCmin 0
Road Base ≔Wrb =⋅⋅qrb ⎛⎝ --L b ab⎞⎠ γESmin 0 ft
Effective GRS Weight ≔Weff =⋅⋅⋅0.5 ((H)) H γr 100000 ― lb ft
Effective Roadbase Weight ≔Wrbeff =⋅⋅
H b ab
H2 γ1 0 ft
Average Maximum Acceleration ≔Am =⋅⎛⎝ -1.45 kav⎞⎠ kav ?
Direct SlidingFHWA-CFL GRS Wall Calculations 03/26/2020 Page 11 of 16
Direct Sliding
Retained Backfill ≔Fb =⋅⋅⋅0.5 γb Kab H2 32217.824 ― lb ft ≔qrb 0 ―― lb ft2
Road Base ≔Frb =⋅⋅qrb Kab H 0 ― lb ft
Traffic ≔Ft =⋅⋅qt Kab H 3097.868 ― lb ft
Inertia of GRS ≔Pir =⋅⋅γEQ Weff Am ?
Inertia of Roadbase ≔Pirb =⋅⋅γEQ Wrbeff Am ?
Inertia of Sill ≔Pis 0 For wall with no bridge, Pis = 0
Dynamic Earth Pressure Coefficient
≔KAE ⋅――――――――――
cos ⎛⎝ --ϕr' θ ω⎞⎠
⋅⋅cos ((θ)) cos ((ω)) cos (( ++δ ω θ))
+1 ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾2
⋅sin ⎛⎝ +ϕr' δ⎞⎠ sin ⎛⎝ --ϕr' θ βtop⎞⎠ ⋅cos (( ++δ ω θ)) cos ⎛⎝ -βtop ω⎞⎠
-2
=KAE ?
Dynamic Earth Force ≔PAE =⋅⋅⋅⋅0.5 γr H2 ⎛⎝ -KAE Kar⎞⎠ γEQ ?
Factored Driving Forces ≔FR =+++⋅γEHmax Fb ⋅γLS Ft Pir ⋅0.5 PAE ?
Total Vertical Forces ≔V =W 140000 ― lb ft
Factored Resisting Force ≔RR =⋅⋅Φτ V μf 109379.988 ― lb ft
Sliding CDR ≔CDRslidings =――
RR
FR
? =if ⎛⎝ ,,≥CDRslidings 1.0 “OK” “NO”⎞⎠ ?
Overturning Stability
Reinforced Soil Moment ≔Mb =⋅⋅γEHmax Fb ― H
644356.481 lb
Roadbase surcharge Moment ≔Mrb =0 0
Inertial Moments ≔Mi ⋅⋅γEQ Pir ― H
Dynamic Moment ≔MAE ⋅⋅⋅0.5 γEQ PAE (( ⋅0.6 H))
Total Factored Driving Moments ≔MD =++Mb Mi MAE ?
Total Factored Resisting Moments ≔MR =⋅W ― L
1960000 lb
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 12 of 16
MD
? =if ⎛⎝ ,,≥CDRoverturnings 1.0 “OK” “NO”⎞⎠ ?
Eccentricity
Eccentricity ≔eseismic =――――
-MD MR
V ? ≔ebear =if ⎛⎝ ,,≤eseismic 0 0 ft eseismic⎞⎠ ?
=if
,,≤eseismic ― L
“OK” “NO”
Effective Width ≔B' =-⎛⎝ +L bface⎞⎠ ⋅2 ebear ?
Bearing Stability
Bearing Capacity Factors =Nc 61.4 =Nq 48.9 =Nγ 78
Factored Vertical Stress ≔σVF =― V
B'
Nominal Bearing Resistance =qn 145890 ―― lb ft2
Factored Bearing Resistance ≔qR =⋅qn Φbc 94828.5 ―― lb ft2
Bearing CDR ≔CDRbearings =―― qR σVF
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 13 of 16
Project Name: Designer:
Project No.: Checker:
Location: Date:
WALL GEOMETRY
See Figure 1 (page 2) for wall geometry and loading definitions.
Exposed Wall Height =H' 34.0 ft Slope Above Wall =βtop 14 ° Slope Rise =Hslope 1.0 ft
Embedment =Hemb 6.0 ft Distance to crest =Lcrest 4.0 ft Slope Below Wall =βbottom 45 °
Design Wall Height =H 40.0 ft
Reinforcement Length =L 28.0 ft =― L
H %70
Back Batter =α 90 °
Facing Elements
Assumed Height =Hface 8 in Unit Weight =γface 140 ―― lb ft3 Friction Angle =ϕface 45 °
Assumed Depth =bface 8 in Face Batter =ω 14 °
Traffic Loading
Traffic Live Load =qt 250 ―― lb ft2 Width of Traffic Load =bf 26.0 ft Offset to Traffic Load =d 4.0 ft
Offset to CL =dt 17.0 ft
Reinforcement Spacing
Normal Reinforcement Spacing =sv 12 in Facing Reinforcement Spacing =svf 12 in
Strength I Limit State
External Stability
=CDRsliding 2.096 =if ⎛⎝ ,,<CDRsliding 1.0 “NO” “OK”⎞⎠ “OK”
=CDRoverturn 2.66 =if ⎛⎝ ,,<CDRoverturn 1.0 “NO” “OK”⎞⎠ “OK”
=if ⎛⎝ ,,>e emax “NO” “OK”⎞⎠ “OK”
=CDRbearing 13.427 =if ⎛⎝ ,,<CDRbearing 1.0 “NO” “OK”⎞⎠ “OK”
=CDRcap 1.639 =if ⎛⎝ ,,<CDRcap 1.0 “NO” “OK”⎞⎠ “OK”
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 14 of 16
=CDRoverturnings ? =if ⎛⎝ ,,≥CDRoverturnings 1.0 “OK” “NO”⎞⎠ ?
=eseismic ? =if
,,≤eseismic ― L
“OK” “NO”
=CDRbearings ? =if ⎛⎝ ,,≥CDRbearings 1.0 “OK” “NO”⎞⎠ ?
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 15 of 16
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 16 of 16
Project Name: CO US50 Designer: DM
Project No.: CO US50 Checker: JMA
Location: Gunnison County, CO Date: 06/19/2019
WALL GEOMETRY STATION 659+00 LT
50% Reinforcement Length 8-Inch Reinf Spacing
See Figure 1 (page 2) for wall geometry and loading definitions.
Exposed Wall Height ≔H' 19 ft Slope Above Wall ≔βtop 14 deg
Embedment ≔Hemb 6 ft Distance to crest ≔Lcrest 4.0 ft
Embedment Ignored ≔Hig 6 ft
Design Wall Height ≔H =+H' Hemb 25.0 ft Slope Rise ≔Hslope =⋅Lcrest tan ⎛⎝βtop⎞⎠ 0.997 ft
Reinforcement Length ≔L 12.5 ft Slope Below Wall ≔βbottom 45 deg
Back Batter ≔α 90 deg
L
H %50
Facing Elements Traffic Loading
Assumed Height ≔Hface 8 in
Assumed Depth ≔bface 8 in Traffic Live Load ≔qt 250 ―― lb ft2
Unit Weight ≔γface 140 ―― lb ft3 Offset to Traffic Load ≔d 4 ft check offset
Width of Traffic Load ≔bf 26 ft
Friction Angle ≔ϕface 45 deg Offset to CL ≔dt =+d ⋅0.5 bf 17 ft
Face Batter ≔ω 14 deg
Reinforcement Spacing Guardrail (y/n)? ≔Rail 1
Normal Reinforcement Spacing ≔sv 8 in y=1, n=0
Facing Reinforcement Spacing ≔svf 8 in Guardrail load in reinforcement
≔Thb =| if else
＝Rail 1
5 ft sv lb ft2
0 ―― lb ft2
40 ―― lb
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 1 of 16
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 2 of 16
Dead Load Min ≔γDCmin 0.9 Earth Surcharge Min ≔γESmin 1.0
Hor. Active Earth Pres. Max ≔γEHmax 1.5 Vert. Active Earth Pres. Max ≔γEVmax 1.35
Hor. Active Earth Pres. Min ≔γEHmin 0.9 Vert. Active Earth Pres. Min ≔γEVmin 1.0
Live Load Surcharge ≔γLS 1.75
GRS Capacity ≔Φcap 0.45 Soil-Sliding Resistance ≔Φτ 1.00
Reinforcement resistance ≔Φreinf 0.40 Bearing Resistance ≔Φbc 0.65
Other Constants
Unit Weight of Water ≔γwater 62.4 ―― lb ft3 Wall Friction ≔δ 0 deg
Equivalent Slope Calculations
≔βint if else
≤Lcrest L return atan
Hslope
L
‖‖ return βtop
≔βext if else
≤Lcrest +L H return atan
Hslope
+L H
‖‖ return βtop
=βint 4.562 deg =βext 1.523 deg
SOIL PARAMETERS Assumed angular rock everywhere, need testing to verify properties (MDD)
Foundation Soil Properties
Friction Angle ≔ϕf' 36 deg Cohesion ≔cf' 100 ―― lb ft2 Unit Weight ≔γf 125 ―― lb ft3
Bearing Capacity Factors by Friction Angle AASHTO 2015 Table 10.6.3.1.2a-1
≔BC 0 5.14 1.0 0.0
≔ϕf =⋅ϕf' ―― π
≔Nc =BC ,ϕf 1
50.6 ≔Nq =BC ,ϕf 2
37.8 ≔Nγ =BC ,ϕf 3
56.3
Retained Soil Properties
Friction Angle ≔ϕb' 32 deg Cohesion ≔cb' 0 ―― lb ft2 Unit Weight ≔γb 130 ―― lb ft3
Active Coefficient ≔Kab =―――――――――――――――――― sin ⎛⎝ +α ϕb'⎞⎠
⋅⋅sin ((α)) sin (( -α δ))
+1
⋅sin ⎛⎝ +ϕb' δ⎞⎠ sin ⎛⎝ -ϕb' βext⎞⎠ ⋅sin (( -α δ)) sin ⎛⎝ +α βext⎞⎠
0.312
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 3 of 16 lb ft2 Unit Weight ≔γr 125 ―― lb ft3
Assumed d=1.5 vs previous 1.0,(MDD)
Maximum diameter of fill ≔dmax 1.5 in Fill Type: Well-graded
≔Kar =―――――――――――――――――― sin ⎛⎝ +α ϕr'⎞⎠
⋅⋅sin ((α)) sin (( -α δ))
+1
⋅sin ⎛⎝ +ϕr' δ⎞⎠ sin ⎛⎝ -ϕr' βint⎞⎠ ⋅sin (( -α δ)) sin ⎛⎝ +α βint⎞⎠
0.248
Active Coefficient
Passive Coefficient ≔Kpr =―――― +1 sin ⎛⎝ϕr'⎞⎠ -1 sin ⎛⎝ϕr'⎞⎠
4.204
Geosynthetic Reinforcement Properties
Ultimate Reinforcement Strength ≔Tult 4800 ― lb ft Strength at 2% Strain ≔T2 2400 ― lb ft
Factored Reinforcement Strength ≔Tf =⋅Tult Φreinf 1920 ― lb
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 4 of 16
Reinforced Zone ≔WGRS =⋅⋅H L γr 39062.5 ― lb ft Slope ≔Wslope =⋅⋅⋅0.5 L2 tan ⎛⎝βint⎞⎠ γr 779.15 ― lb ft
Facing ≔Wface =⋅⋅H bface γface 2333.333 ― lb ft Facing assumed to have a rectangular cross section.
Calculated Lateral Forces
Retained Soil ≔PA =⋅⋅⋅0.5 Kab γb H2 12670.491 ― lb ft Angle of Action ≔ρ =+(( -90 deg α)) βext 1.523 deg
≔PAH =⋅PA cos ((ρ)) 12666.013 ― lb ft ≔PAV =⋅PA sin ((ρ)) 336.852 ― lb ft
Traffic ≔PTH =⋅⋅qt Kab H 1949.306 ― lb ft
Factored Vertical Forces
GRS ≔WGRSmax =⋅WGRS γEVmax 52734.375 ― lb ft ≔WGRSmin =⋅WGRS γEVmin 39062.5 ― lb ft
Facing ≔Wfacemax =⋅Wface γEVmax 3150 ― lb ft ≔Wfacemin =⋅Wface γEVmin 2333.333 ― lb ft
Slope ≔Wslopemax =⋅Wslope γEVmax 1051.853 ― lb ft ≔Wslopemin =⋅Wslope γEVmin 779.15 ― lb ft
Traffic ≔PTVmax =⋅⋅qt γLS ⎛⎝ -L Lcrest⎞⎠ 3718.75 ― lb ft
Earth Pressure ≔PAVmax =⋅PAV γEVmax 454.751 ― lb ft ≔PAVmin =⋅PAV γEVmin 336.852 ― lb ft
Factored Lateral Forces
Earth Pressure ≔PAHmax =⋅PAH γEHmax 18999.019 ― lb ft ≔PAHmin =⋅PAH γEHmin 11399.412 ― lb ft
Traffic ≔PTHmax =⋅PTH γLS 3411.286 ― lb ft
Sliding Stability
Total Vertical Force ≔Wmin =++WGRSmin Wfacemin PAVmin 41732.686 ― lb ft
Sliding Friction Factor ≔μf min ⎛⎝ ,tan ⎛⎝ϕf'⎞⎠ tan ⎛⎝ϕr'⎞⎠⎞⎠
Sliding Resistance ≔Rsliding =⋅⋅Wmin μf Φτ 30320.571 ― lb ft
Total Horizontal Force ≔Ptotal =+PAHmax PTHmax 22410.305 ― lb ft
Sliding CDR ≔CDRsliding =――― Rsliding
Ptotal
1.353 =if ⎛⎝ ,,<CDRsliding 1.0 “NO” “OK”⎞⎠ “OK”
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 5 of 16
Facing Moments ≔d1 =⋅H tan ((ω)) 6.233 ft ≔d3 =⋅H tan (( -90 deg α)) 0 ft ≔d2 =-bface ⎛⎝ +d1 d3⎞⎠ -5.567 ft
≔Mf1 =⋅⋅⋅⎛⎝ ⋅⋅⋅0.5 d1 H γface⎞⎠ d1 γEVmin 1 ft 45328.247 ⋅lb ft
≔Mf2 =⋅⋅⋅⎛⎝ ⋅⋅d2 H γface⎞⎠ d2 d1 γEVmin 1 ft -67214.593 ⋅lb ft
≔Mf3 =⋅⋅⋅⎛⎝ ⋅⋅⋅0.5 d3 H γface⎞⎠ d3 d1 d2 γEVmin 1 ft 0 ⋅lb ft
GRS Moment ≔MGRS =⋅⋅⋅⎛⎝ ⋅⋅L H γr⎞⎠
L bface γEVmin 1 ft 270182.292 ⋅lb ft Assumes equal front and back batter
Slope ≔Mslope =⋅⋅⎛⎝Wslopemin⎞⎠
L bface
1 ft 7012.35 ⋅lb ft
Vert. Earth Pressure ≔MAV =⋅⋅PAVmin
+bface L
1 ft 2217.612 ⋅lb ft
Resisting Moments ≔MR =+++++Mf1 Mf2 Mf3 MGRS Mslope MAV 257525.908 ⋅lb ft
Hor. Earth Pressure ≔MAH =⋅⋅PAHmax H
1 ft 158325.161 ⋅lb ft
Traffic ≔MTH =⋅⋅PTHmax H
1 ft 42641.077 ⋅lb ft
Driving Moments ≔MD =+MAH MTH 200966.238 ⋅lb ft
Overturning CDR ≔CDRoverturn =――
MR
MD
1.281 =if ⎛⎝ ,,<CDRoverturn 1.0 “NO” “OK”⎞⎠ “OK”
Total Vertical Force ≔Wmax =++++WGRSmax Wfacemax Wslopemax PAVmax PTHmax 60802.264 ― lb ft
Eccentricity ≔e =――――
-MD MR
⋅Wmax 1 ft -0.93 ft ≔emax =―――
+L bface
3.292 ft
=if ⎛⎝ ,,>e emax “NO” “OK”⎞⎠ “OK”
≔ebearing =if (( ,,≤e 0 0 ft e)) 0 ft ≔B' =-⎛⎝ +L bface⎞⎠ ⋅2 ebearing 13.167 ft
Bearing Resistance
Factored Vertical Stress ≔σVF =―― Wmax
B'
4617.894 ―― lb ft2
Nominal Bearing Resistance ≔qn =++⋅cf' Nc ⋅⋅⋅0.5 B' γf Nγ ⋅⋅γf ⎛⎝ -Hemb Hig⎞⎠ Nq 51390.208 ―― lb ft2
Factored Bearing Resistance ≔qR =⋅qn Φbc 33403.635 ―― lb ft2
Bearing CDR ≔CDRbearing =―― qR σVF
7.234 =if ⎛⎝ ,,<CDRbearing 1.0 “NO” “OK”⎞⎠ “OK”
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 6 of 16
Revised with 0.2*eqn per 2016 TF revisions,(MDD)GRS Nominal Capacity ≔qGRSn =⋅0.2
⋅0.7 sv
⋅6 dmax
Tf sv
Kpr 1763.471 ―― lb ft2
GRS Factored Capacity ≔qGRSf =⋅qGRSn Φcap 793.562 ―― lb ft2
Applied Load ≔Vappliedf =+―――― Wslopemax
L PTVmax
L
381.648 ―― lb ft2
Capacity CDR ≔CDRcap =――― qGRSf
Vappliedf
2.079 =if ⎛⎝ ,,<CDRcap 1.0 “NO” “OK”⎞⎠ “OK”
Reinforcement Strength
Matrix calculations, see summary table below. ≔z1 =-⋅2 dt bf 8 ft
Reinforcement Layers ≔z =, ‥sv +sv sv H 0.667 ft
Surcharge Load Angles of Action ≔βb =atan d z
1.406
≔αb =-atan +d bf z βb 0.143
Matrix size setup ≔i ‥0 -rows ((z)) 1
Reinforcement load due to surcharge ≔σhti qt π
+αbi
⋅sin ⎛ αbi cos ⎛
+αbi ⋅2 βbi
Kar 0.059 lb ft2
Factored reinforcement load due to earth pressure ≔σhwf =⋅⋅⋅γEHmax γr z Kar 30.96 lb ft2
Factored reinforcement load due to traffic ≔σhtf =⋅γLS σht 0.103 lb ft2
Factored reinforcement load due to vehicle impact ≔σhbi =if ⎛
,,≤z i 5 ft Thb 0⎞ lb ft2
Total factored reinforcement load ≔σhf =++σhwf σhtf σhb 71.063 lb ft2
Required factored reinforcement strength ≔Treqf =⋅―――― σhf
0.7 sv
⋅6 dmax sv 65.049 lb ft
Factored Reinforcement CDR ≔CDRreff =―― Tf
Treqf
29.516
Nominal reinforcement load due to earth pressure ≔σhw =⋅⋅γr z Kar 20.64 lb ft2
Total nominal reinforcement load ≔σh =+σhw σht 20.699 lb
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 7 of 16
0.7 sv
⋅6 dmax sv 18.947 lb ft
Nominal Reinforcement CDR ≔CDRref =―― T2
Treq
126.667
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 8 of 16
Earth Force at Face ≔Fface =+⋅⋅⋅⋅⋅0.72 γr Kar sv svf γEHmax ⋅⋅σht svf γLS 14.929 lb ft
Assumes that traffic railings are setback to AASHTO minimums and do not impart load directly on the wall face. Other scenarios may require additional loading.
Frictional Resistance ≔Rface =⋅⋅⋅⋅γface bface z ― tan ⎛⎝ϕface⎞⎠
41.481 lb ft
≔CDRface =―― Rface
Fface
2.779
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Seismic Design Parameters Site Class: Lat Long.:
Peak Ground Acceleration ≔PGA 0 Seismic parameters obtained from USGS Sesimic Design Maps online tool:
https://earthquake.usgs.gov/designmaps/us/ application.php? Spectral Acceleration at 1 sec ≔S1 0
Site Factors ≔FPGA 0
≔Fv 0.0 Seismic Load Factor ≔γEQ 1.0
Extreme Event I
Maximum Acceleration ≔kmax =⋅FPGA PGA 0
Peak Ground Velocity ≔PGV =⋅⋅38 Fv S1 0
Site Reduction Factor ≔αsite =+1 ⋅⋅0.01 ―― H
1 ft
-⋅0.5
⋅Fv S1 kmax
Average Ground Acceleration ≔kav =⋅αsite kmax ?
Kv is typically assumed as 0, unless PGA >0.6. More critical for bridge structure than walls. CalTrans Report CA/UCD- SESM-08-01 and Memo "Seismic Design and Selection of Standard Retaining Walls" 06/16/2013
Vertical Ground Acceleration ≔kv 0
Angle of Seismic Action ≔θ =atan kav -1 kv
Forces on GRS
Weight of GRS ≔W =⋅⋅⋅γr H ((L)) γEVmin 39062.5 ― lb ft
For wall with no bridge abutment, qb, qrb, b, ab, H2, g1 = 0
≔qb 0 ≔b 0 ≔qrb 0 ≔ab 0 ≔H2 0 ≔γ1 0
Bridge Deadload ≔Wb =⋅⋅qb b γDCmin 0
Road Base ≔Wrb =⋅⋅qrb ⎛⎝ --L b ab⎞⎠ γESmin 0 ft
Effective GRS Weight ≔Weff =⋅⋅⋅0.5 ((H)) H γr 39062.5 ― lb ft
Effective Roadbase Weight ≔Wrbeff =⋅⋅
H b ab
H2 γ1 0 ft
Average Maximum Acceleration ≔Am =⋅⎛⎝ -1.45 kav⎞⎠ kav ?
Direct Sliding
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 11 of 16
Retained Backfill ≔Fb =⋅⋅⋅0.5 γb Kab H2 12670.491 ― lb ft ≔qrb 0 ―― lb ft2
Road Base ≔Frb =⋅⋅qrb Kab H 0 ― lb ft
Traffic ≔Ft =⋅⋅qt Kab H 1949.306 ― lb ft
Inertia of GRS ≔Pir =⋅⋅γEQ Weff Am ?
Inertia of Roadbase ≔Pirb =⋅⋅γEQ Wrbeff Am ?
Inertia of Sill ≔Pis 0 For wall with no bridge, Pis = 0
Dynamic Earth Pressure Coefficient
≔KAE ⋅――――――――――
cos ⎛⎝ --ϕr' θ ω⎞⎠
⋅⋅cos ((θ)) cos ((ω)) cos (( ++δ ω θ))
+1 ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾2
⋅sin ⎛⎝ +ϕr' δ⎞⎠ sin ⎛⎝ --ϕr' θ βtop⎞⎠ ⋅cos (( ++δ ω θ)) cos ⎛⎝ -βtop ω⎞⎠
-2
=KAE ?
Dynamic Earth Force ≔PAE =⋅⋅⋅⋅0.5 γr H2 ⎛⎝ -KAE Kar⎞⎠ γEQ ?
Factored Driving Forces ≔FR =+++⋅γEHmax Fb ⋅γLS Ft Pir ⋅0.5 PAE ?
Total Vertical Forces ≔V =W 39062.5 ― lb ft
Factored Resisting Force ≔RR =⋅⋅Φτ V μf 28380.568 ― lb ft
Sliding CDR ≔CDRslidings =――
RR
FR
? =if ⎛⎝ ,,≥CDRslidings 1.0 “OK” “NO”⎞⎠ ?
Overturning Stability
Reinforced Soil Moment ≔Mb =⋅⋅γEHmax Fb ― H
158381.142 lb
Roadbase surcharge Moment ≔Mrb =0 0
Inertial Moments ≔Mi ⋅⋅γEQ Pir ― H
Dynamic Moment ≔MAE ⋅⋅⋅0.5 γEQ PAE (( ⋅0.6 H))
Total Factored Driving Moments ≔MD =++Mb Mi MAE ?
Total Factored Resisting Moments ≔MR =⋅W ― L
244140.625 lb
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 12 of 16
MD
? =if ⎛⎝ ,,≥CDRoverturnings 1.0 “OK” “NO”⎞⎠ ?
Eccentricity
Eccentricity ≔eseismic =――――
-MD MR
V ? ≔ebear =if ⎛⎝ ,,≤eseismic 0 0 ft eseismic⎞⎠ ?
=if
,,≤eseismic ― L
“OK” “NO”
Effective Width ≔B' =-⎛⎝ +L bface⎞⎠ ⋅2 ebear ?
Bearing Stability
Bearing Capacity Factors =Nc 50.6 =Nq 37.8 =Nγ 56.3
Factored Vertical Stress ≔σVF =― V
B'
Nominal Bearing Resistance =qn 51390.208 ―― lb ft2
Factored Bearing Resistance ≔qR =⋅qn Φbc 33403.635 ―― lb ft2
Bearing CDR ≔CDRbearings =―― qR σVF
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 13 of 16
Project Name: Designer:
Project No.: Checker:
Location: Date:
WALL GEOMETRY
See Figure 1 (page 2) for wall geometry and loading definitions.
Exposed Wall Height =H' 19.0 ft Slope Above Wall =βtop 14 ° Slope Rise =Hslope 1.0 ft
Embedment =Hemb 6.0 ft Distance to crest =Lcrest 4.0 ft Slope Below Wall =βbottom 45 °
Design Wall Height =H 25.0 ft
Reinforcement Length =L 12.5 ft =― L
H %50
Back Batter =α 90 °
Facing Elements
Assumed Height =Hface 8 in Unit Weight =γface 140 ―― lb ft3 Friction Angle =ϕface 45 °
Assumed Depth =bface 8 in Face Batter =ω 14 °
Traffic Loading
Traffic Live Load =qt 250 ―― lb ft2 Width of Traffic Load =bf 26.0 ft Offset to Traffic Load =d 4.0 ft
Offset to CL =dt 17.0 ft
Reinforcement Spacing
Normal Reinforcement Spacing =sv 8 in Facing Reinforcement Spacing =svf 8 in
Strength I Limit State
External Stability
=CDRsliding 1.353 =if ⎛⎝ ,,<CDRsliding 1.0 “NO” “OK”⎞⎠ “OK”
=CDRoverturn 1.281 =if ⎛⎝ ,,<CDRoverturn 1.0 “NO” “OK”⎞⎠ “OK”
=if ⎛⎝ ,,>e emax “NO” “OK”⎞⎠ “OK”
=CDRbearing 7.234 =if ⎛⎝ ,,<CDRbearing 1.0 “NO” “OK”⎞⎠ “OK”
=CDRcap 2.079 =if ⎛⎝ ,,<CDRcap 1.0 “NO” “OK”⎞⎠ “OK”
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 14 of 16
=CDRoverturnings ? =if ⎛⎝ ,,≥CDRoverturnings 1.0 “OK” “NO”⎞⎠ ?
=eseismic ? =if
,,≤eseismic ― L
“OK” “NO”
=CDRbearings ? =if ⎛⎝ ,,≥CDRbearings 1.0 “OK” “NO”⎞⎠ ?
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 15 of 16
FHWA-CFL GRS Wall Calculations 04/16/2020 Page 16 of 16
Project Name: CO US50 Designer: DM
Project No.: CO US50 Checker: JMA
Location: Gunnison County, CO Date: 06/19/2019
WALL GEOMETRY STATION 659+00 LT
50% Reinforcement Length 12-Inch Reinf Spacing
See Figure 1 (page 2) for wall geometry and loading definitions.
Exposed Wall Height ≔H' 19 ft Slope Above Wall ≔βtop 14 deg
Embedment ≔Hemb 6 ft Distance to crest ≔Lcrest 4.0 ft
Embedment Ignored ≔Hig 6 ft
Design Wall Height ≔H =+H' Hemb 25.0 ft Slope Rise ≔Hslope =⋅Lcrest tan ⎛⎝βtop⎞⎠ 0.997 ft
Reinforcement Length ≔L 12.5 ft Slope Below Wall ≔βbottom 45 deg
Back Batter ≔α 90 deg
L
H %50
Facing Elements Traffic Loading
Assumed Height ≔Hface 8 in
Assumed Depth ≔bface 8 in Traffic Live Load ≔qt 250 ―― lb ft2
Unit Weight ≔γface 140 ―― lb ft3 Offset to Traffic Load ≔d 4 ft check offset
Width of Traffic Load ≔bf 26 ft
Friction Angle ≔ϕface 45 deg Offset to CL ≔dt =+d ⋅0.5 bf 17 ft
Face Batter ≔ω 14 deg
Reinforcement Spacing Guardrail (y/n)? ≔Rail 1
Normal Reinforcement Spacing ≔sv 12 in y=1, n=0
Facing Reinforcement Spacing ≔svf 12 in Guardrail load in reinforcement
≔Thb =| if else
＝Rail 1
5 ft sv lb ft2
0 ―― lb ft2
60 ―― lb
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FHWA-CFL GRS Wall Calculations 03/26/2020 Page 2 of 14
Dead Load Min ≔γDCmin 0.9 Earth Surcharge Min ≔γESmin 1.0
Hor. Active Earth Pres. Max ≔γEHmax 1.5 Vert. Active Earth Pres. Max ≔γEVmax 1.35
Hor. Active Earth Pres. Min ≔γEHmin 0.9 Vert. Active Earth Pres. Min ≔γEVmin 1.0
Live Load Surcharge ≔γLS 1.75
GRS Capacity ≔Φcap 0.45 Soil-Sliding Resistance ≔Φτ 1.00
Reinforcement resistance ≔Φreinf 0.40 Bearing Resistance ≔Φbc 0.65
Other Constants
Unit Weight of Water ≔γwater 62.4 ―― lb ft3 Wall Friction ≔δ 0 deg
Equivalent Slope Calculations
≔βint if else
≤Lcrest L return atan
Hslope
L
‖‖ return βtop
≔βext if else
≤Lcrest +L H return atan
Hslope
+L H
‖‖ return βtop
=βint 4.562 deg =βext 1.523 deg
SOIL PARAMETERS Assumed angular rock everywhere, need testing to verify properties (MDD)
Foundation Soil Properties
Friction Angle ≔ϕf' 36 deg Cohesion ≔cf' 100 ―― lb ft2 Unit Weight ≔γf 125 ―― lb ft3
Bearing Capacity Factors by Friction Angle AASHTO 2015 Table 10.6.3.1.2a-1
≔BC 0 5.14 1.0 0.0
≔ϕf =⋅ϕf' ―― π
≔Nc =BC ,ϕf 1
50.6 ≔Nq =BC ,ϕf 2
37.8 ≔Nγ =BC ,ϕf 3
56.3
Retained Soil Properties
Friction Angle ≔ϕb' 32 deg Cohesion ≔cb' 0 ―― lb ft2 Unit Weight ≔γb 130 ―― lb ft3
Active Coefficient ≔Kab =―――――――――――――――――― sin ⎛⎝ +α ϕb'⎞⎠
⋅⋅sin ((α)) sin (( -α δ))
+1
⋅sin ⎛⎝ +ϕb' δ⎞⎠ sin ⎛⎝ -ϕb' βext⎞⎠ ⋅sin (( -α δ)) sin ⎛⎝ +α βext⎞⎠
0.312
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 3 of 14 lb ft2 Unit Weight ≔γr 125 ―― lb ft3
Assumed d=1.5 vs previous 1.0,(MDD)
Maximum diameter of fill ≔dmax 1.5 in Fill Type: Well-graded
≔Kar =―――――――――――――――――― sin ⎛⎝ +α ϕr'⎞⎠
⋅⋅sin ((α)) sin (( -α δ))
+1
⋅sin ⎛⎝ +ϕr' δ⎞⎠ sin ⎛⎝ -ϕr' βint⎞⎠ ⋅sin (( -α δ)) sin ⎛⎝ +α βint⎞⎠
0.248
Active Coefficient
Passive Coefficient ≔Kpr =―――― +1 sin ⎛⎝ϕr'⎞⎠ -1 sin ⎛⎝ϕr'⎞⎠
4.204
Geosynthetic Reinforcement Properties
Ultimate Reinforcement Strength ≔Tult 4800 ― lb ft Strength at 2% Strain ≔T2 2400 ― lb ft
Factored Reinforcement Strength ≔Tf =⋅Tult Φreinf 1920 ― lb
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 4 of 14
Reinforced Zone ≔WGRS =⋅⋅H L γr 39062.5 ― lb ft Slope ≔Wslope =⋅⋅⋅0.5 L2 tan ⎛⎝βint⎞⎠ γr 779.15 ― lb ft
Facing ≔Wface =⋅⋅H bface γface 2333.333 ― lb ft Facing assumed to have a rectangular cross section.
Calculated Lateral Forces
Retained Soil ≔PA =⋅⋅⋅0.5 Kab γb H2 12670.491 ― lb ft Angle of Action ≔ρ =+(( -90 deg α)) βext 1.523 deg
≔PAH =⋅PA cos ((ρ)) 12666.013 ― lb ft ≔PAV =⋅PA sin ((ρ)) 336.852 ― lb ft
Traffic ≔PTH =⋅⋅qt Kab H 1949.306 ― lb ft
Factored Vertical Forces
GRS ≔WGRSmax =⋅WGRS γEVmax 52734.375 ― lb ft ≔WGRSmin =⋅WGRS γEVmin 39062.5 ― lb ft
Facing ≔Wfacemax =⋅Wface γEVmax 3150 ― lb ft ≔Wfacemin =⋅Wface γEVmin 2333.333 ― lb ft
Slope ≔Wslopemax =⋅Wslope γEVmax 1051.853 ― lb ft ≔Wslopemin =⋅Wslope γEVmin 779.15 ― lb ft
Traffic ≔PTVmax =⋅⋅qt γLS ⎛⎝ -L Lcrest⎞⎠ 3718.75 ― lb ft
Earth Pressure ≔PAVmax =⋅PAV γEVmax 454.751 ― lb ft ≔PAVmin =⋅PAV γEVmin 336.852 ― lb ft
Factored Lateral Forces
Earth Pressure ≔PAHmax =⋅PAH γEHmax 18999.019 ― lb ft ≔PAHmin =⋅PAH γEHmin 11399.412 ― lb ft
Traffic ≔PTHmax =⋅PTH γLS 3411.286 ― lb ft
Sliding Stability
Total Vertical Force ≔Wmin =++WGRSmin Wfacemin PAVmin 41732.686 ― lb ft
Sliding Friction Factor ≔μf min ⎛⎝ ,tan ⎛⎝ϕf'⎞⎠ tan ⎛⎝ϕr'⎞⎠⎞⎠
Sliding Resistance ≔Rsliding =⋅⋅Wmin μf Φτ 30320.571 ― lb ft
Total Horizontal Force ≔Ptotal =+PAHmax PTHmax 22410.305 ― lb ft
Sliding CDR ≔CDRsliding =――― Rsliding
Ptotal
1.353 =if ⎛⎝ ,,<CDRsliding 1.0 “NO” “OK”⎞⎠ “OK”
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 5 of 14
Facing Moments ≔d1 =⋅H tan ((ω)) 6.233 ft ≔d3 =⋅H tan (( -90 deg α)) 0 ft ≔d2 =-bface ⎛⎝ +d1 d3⎞⎠ -5.567 ft
≔Mf1 =⋅⋅⋅⎛⎝ ⋅⋅⋅0.5 d1 H γface⎞⎠ d1 γEVmin 1 ft 45328.247 ⋅lb ft
≔Mf2 =⋅⋅⋅⎛⎝ ⋅⋅d2 H γface⎞⎠ d2 d1 γEVmin 1 ft -67214.593 ⋅lb ft
≔Mf3 =⋅⋅⋅⎛⎝ ⋅⋅⋅0.5 d3 H γface⎞⎠ d3 d1 d2 γEVmin 1 ft 0 ⋅lb ft
GRS Moment ≔MGRS =⋅⋅⋅⎛⎝ ⋅⋅L H γr⎞⎠
L bface γEVmin 1 ft 270182.292 ⋅lb ft Assumes equal front and back batter
Slope ≔Mslope =⋅⋅⎛⎝Wslopemin⎞⎠
L bface
1 ft 7012.35 ⋅lb ft
Vert. Earth Pressure ≔MAV =⋅⋅PAVmin
+bface L
1 ft 2217.612 ⋅lb ft
Resisting Moments ≔MR =+++++Mf1 Mf2 Mf3 MGRS Mslope MAV 257525.908 ⋅lb ft
Hor. Earth Pressure ≔MAH =⋅⋅PAHmax H
1 ft 158325.161 ⋅lb ft
Traffic ≔MTH =⋅⋅PTHmax H
1 ft 42641.077 ⋅lb ft
Driving Moments ≔MD =+MAH MTH 200966.238 ⋅lb ft
Overturning CDR ≔CDRoverturn =――
MR
MD
1.281 =if ⎛⎝ ,,<CDRoverturn 1.0 “NO” “OK”⎞⎠ “OK”
Total Vertical Force ≔Wmax =++++WGRSmax Wfacemax Wslopemax PAVmax PTHmax 60802.264 ― lb ft
Eccentricity ≔e =――――
-MD MR
⋅Wmax 1 ft -0.93 ft ≔emax =―――
+L bface
3.292 ft
=if ⎛⎝ ,,>e emax “NO” “OK”⎞⎠ “OK”
≔ebearing =if (( ,,≤e 0 0 ft e)) 0 ft ≔B' =-⎛⎝ +L bface⎞⎠ ⋅2 ebearing 13.167 ft
Bearing Resistance
Factored Vertical Stress ≔σVF =―― Wmax
B'
4617.894 ―― lb ft2
Nominal Bearing Resistance ≔qn =++⋅cf' Nc ⋅⋅⋅0.5 B' γf Nγ ⋅⋅γf ⎛⎝ -Hemb Hig⎞⎠ Nq 51390.208 ―― lb ft2
Factored Bearing Resistance ≔qR =⋅qn Φbc 33403.635 ―― lb ft2
Bearing CDR ≔CDRbearing =―― qR σVF
7.234 =if ⎛⎝ ,,<CDRbearing 1.0 “NO” “OK”⎞⎠ “OK”
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 6 of 14
Revised with 0.2*eqn per 2016 TF revisions,(MDD)GRS Nominal Capacity ≔qGRSn =⋅0.2
⋅0.7 sv
⋅6 dmax
Tf sv
Kpr 1003.302 ―― lb ft2
GRS Factored Capacity ≔qGRSf =⋅qGRSn Φcap 451.486 ―― lb ft2
Applied Load ≔Vappliedf =+―――― Wslopemax
L PTVmax
L
381.648 ―― lb ft2
Capacity CDR ≔CDRcap =――― qGRSf
Vappliedf
1.183 =if ⎛⎝ ,,<CDRcap 1.0 “NO” “OK”⎞⎠ “OK”
Reinforcement Strength
Matrix calculations, see summary table below. ≔z1 =-⋅2 dt bf 8 ft
Reinforcement Layers ≔z =, ‥sv +sv sv H 1 ft
Surcharge Load Angles of Action ≔βb =atan d z
1.326
≔αb =-atan +d bf z βb 0.212
Matrix size setup ≔i ‥0 -rows ((z)) 1
Reinforcement load due to surcharge ≔σhti qt π
+αbi
⋅sin ⎛ αbi cos ⎛
+αbi ⋅2 βbi
Kar 0.19 lb ft2
Factored reinforcement load due to earth pressure ≔σhwf =⋅⋅⋅γEHmax γr z Kar 46.44 lb ft2
Factored reinforcement load due to traffic ≔σhtf =⋅γLS σht 0.333 lb ft2
Factored reinforcement load due to vehicle impact ≔σhbi =if ⎛
,,≤z i 5 ft Thb 0⎞ lb ft2
Total factored reinforcement load ≔σhf =++σhwf σhtf σhb 106.774 lb ft2
Required factored reinforcement strength ≔Treqf =⋅―――― σhf
0.7 sv
⋅6 dmax sv 171.791 lb ft
Factored Reinforcement CDR ≔CDRreff =―― Tf
Treqf
11.176
Nominal reinforcement load due to earth pressure ≔σhw =⋅⋅γr z Kar 30.96 lb ft2
Total nominal reinforcement load ≔σh =+σhw σht 31.151 lb
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 7 of 14
0.7 sv
⋅6 dmax sv 50.119 lb ft
Nominal Reinforcement CDR ≔CDRref =―― T2
Treq
47.886
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 8 of 14
Earth Force at Face ≔Fface =+⋅⋅⋅⋅⋅0.72 γr Kar sv svf γEHmax ⋅⋅σht svf γLS 33.77 lb ft
Assumes that traffic railings are setback to AASHTO minimums and do not impart load directly on the wall face. Other scenarios may require additional loading.
Frictional Resistance ≔Rface =⋅⋅⋅⋅γface bface z ― tan ⎛⎝ϕface⎞⎠
62.222 lb ft
≔CDRface =―― Rface
Fface
1.843
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 9 of 14
Seismic Design Parameters Site Class: Lat Long.:
Peak Ground Acceleration ≔PGA 0 Seismic parameters obtained from USGS Sesimic Design Maps online tool:
https://earthquake.usgs.gov/designmaps/us/ application.php? Spectral Acceleration at 1 sec ≔S1 0
Site Factors ≔FPGA 0
≔Fv 0.0 Seismic Load Factor ≔γEQ 1.0
Extreme Event I
Maximum Acceleration ≔kmax =⋅FPGA PGA 0
Peak Ground Velocity ≔PGV =⋅⋅38 Fv S1 0
Site Reduction Factor ≔αsite =+1 ⋅⋅0.01 ―― H
1 ft
-⋅0.5
⋅Fv S1 kmax
Average Ground Acceleration ≔kav =⋅αsite kmax ?
Kv is typically assumed as 0, unless PGA >0.6. More critical for bridge structure than walls. CalTrans Report CA/UCD- SESM-08-01 and Memo "Seismic Design and Selection of Standard Retaining Walls" 06/16/2013
Vertical Ground Acceleration ≔kv 0
Angle of Seismic Action ≔θ =atan kav -1 kv
Forces on GRS
Weight of GRS ≔W =⋅⋅⋅γr H ((L)) γEVmin 39062.5 ― lb ft
For wall with no bridge abutment, qb, qrb, b, ab, H2, g1 = 0
≔qb 0 ≔b 0 ≔qrb 0 ≔ab 0 ≔H2 0 ≔γ1 0
Bridge Deadload ≔Wb =⋅⋅qb b γDCmin 0
Road Base ≔Wrb =⋅⋅qrb ⎛⎝ --L b ab⎞⎠ γESmin 0 ft
Effective GRS Weight ≔Weff =⋅⋅⋅0.5 ((H)) H γr 39062.5 ― lb ft
Effective Roadbase Weight ≔Wrbeff =⋅⋅
H b ab
H2 γ1 0 ft
Average Maximum Acceleration ≔Am =⋅⎛⎝ -1.45 kav⎞⎠ kav ?
Direct Sliding
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 10 of 14
Retained Backfill ≔Fb =⋅⋅⋅0.5 γb Kab H2 12670.491 ― ft ≔qrb 0 ―― lb ft2
Road Base ≔Frb =⋅⋅qrb Kab H 0 ― lb ft
Traffic ≔Ft =⋅⋅qt Kab H 1949.306 ― lb ft
Inertia of GRS ≔Pir =⋅⋅γEQ Weff Am ?
Inertia of Roadbase ≔Pirb =⋅⋅γEQ Wrbeff Am ?
Inertia of Sill ≔Pis 0 For wall with no bridge, Pis = 0
Dynamic Earth Pressure Coefficient
≔KAE ⋅――――――――――
cos ⎛⎝ --ϕr' θ ω⎞⎠
⋅⋅cos ((θ)) cos ((ω)) cos (( ++δ ω θ))
+1 ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾2
⋅sin ⎛⎝ +ϕr' δ⎞⎠ sin ⎛⎝ --ϕr' θ βtop⎞⎠ ⋅cos (( ++δ ω θ)) cos ⎛⎝ -βtop ω⎞⎠
-2
=KAE ?
Dynamic Earth Force ≔PAE =⋅⋅⋅⋅0.5 γr H2 ⎛⎝ -KAE Kar⎞⎠ γEQ ?
Factored Driving Forces ≔FR =+++⋅γEHmax Fb ⋅γLS Ft Pir ⋅0.5 PAE ?
Total Vertical Forces ≔V =W 39062.5 ― lb ft
Factored Resisting Force ≔RR =⋅⋅Φτ V μf 28380.568 ― lb ft
Sliding CDR ≔CDRslidings =――
RR
FR
? =if ⎛⎝ ,,≥CDRslidings 1.0 “OK” “NO”⎞⎠ ?
Overturning Stability
Reinforced Soil Moment ≔Mb =⋅⋅γEHmax Fb ― H
158381.142 lb
Roadbase surcharge Moment ≔Mrb =0 0
Inertial Moments ≔Mi ⋅⋅γEQ Pir ― H
Dynamic Moment ≔MAE ⋅⋅⋅0.5 γEQ PAE (( ⋅0.6 H))
Total Factored Driving Moments ≔MD =++Mb Mi MAE ?
Total Factored Resisting Moments ≔MR =⋅W ― L
244140.625 lb
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 11 of 14
MD
? =if ⎛⎝ ,,≥CDRoverturnings 1.0 “OK” “NO”⎞⎠ ?
Eccentricity
Eccentricity ≔eseismic =――――
-MD MR
V ? ≔ebear =if ⎛⎝ ,,≤eseismic 0 0 ft eseismic⎞⎠ ?
=if
,,≤eseismic ― L
“OK” “NO”
Effective Width ≔B' =-⎛⎝ +L bface⎞⎠ ⋅2 ebear ?
Bearing Stability
Bearing Capacity Factors =Nc 50.6 =Nq 37.8 =Nγ 56.3
Factored Vertical Stress ≔σVF =― V
B'
Nominal Bearing Resistance =qn 51390.208 ―― lb ft2
Factored Bearing Resistance ≔qR =⋅qn Φbc 33403.635 ―― lb ft2
Bearing CDR ≔CDRbearings =―― qR σVF
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 12 of 14
Project Name: Designer:
Project No.: Checker:
Location: Date:
WALL GEOMETRY
See Figure 1 (page 2) for wall geometry and loading definitions.
Exposed Wall Height =H' 19.0 ft Slope Above Wall =βtop 14 ° Slope Rise =Hslope 1.0 ft
Embedment =Hemb 6.0 ft Distance to crest =Lcrest 4.0 ft Slope Below Wall =βbottom 45 °
Design Wall Height =H 25.0 ft
Reinforcement Length =L 12.5 ft =― L
H %50
Back Batter =α 90 °
Facing Elements
Assumed Height =Hface 8 in Unit Weight =γface 140 ―― lb ft3 Friction Angle =ϕface 45 °
Assumed Depth =bface 8 in Face Batter =ω 14 °
Traffic Loading
Traffic Live Load =qt 250 ―― lb ft2 Width of Traffic Load =bf 26.0 ft Offset to Traffic Load =d 4.0 ft
Offset to CL =dt 17.0 ft
Reinforcement Spacing
Normal Reinforcement Spacing =sv 12 in Facing Reinforcement Spacing =svf 12 in
Strength I Limit State
External Stability
=CDRsliding 1.353 =if ⎛⎝ ,,<CDRsliding 1.0 “NO” “OK”⎞⎠ “OK”
=CDRoverturn 1.281 =if ⎛⎝ ,,<CDRoverturn 1.0 “NO” “OK”⎞⎠ “OK”
=if ⎛⎝ ,,>e emax “NO” “OK”⎞⎠ “OK”
=CDRbearing 7.234 =if ⎛⎝ ,,<CDRbearing 1.0 “NO” “OK”⎞⎠ “OK”
=CDRcap 1.183 =if ⎛⎝ ,,<CDRcap 1.0 “NO” “OK”⎞⎠ “OK”
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 13 of 14
=CDRoverturnings ? =if ⎛⎝ ,,≥CDRoverturnings 1.0 “OK” “NO”⎞⎠ ?
=eseismic ? =if
,,≤eseismic ― L
“OK” “NO”
=CDRbearings ? =if ⎛⎝ ,,≥CDRbearings 1.0 “OK” “NO”⎞⎠ ?
FHWA-CFL GRS Wall Calculations 03/26/2020 Page 14 of 14
APPENDIX B
GRS Wall Analysis Preliminarily
Global Stability
1.471.471.471.47
Material Name Color Unit Weight (lbs/ 3) Strength Type Cohesion
(psf) Phi (deg)
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