α |
Angle between wall face and projection of the midline of the surcharge to the wall face [rad] |

α_{b} |
Angle between wall face and projection of the midline of the bridge surcharge to the wall face [rad] |

β |
Angle between the projections of the inner and outer edge lines of the surcharge to the wall face [rad] |

β_{b} |
Angle between the projections of the inner and outer edge lines of the bridge surcharge to the wall face [rad] |

γ |
Unit weight of soil [F/L^{3}] |

γ_{b} |
Unit weight of retained backfill [F/L^{3}] |

γ_{DC MAX} |
Maximum load factor for dead load (DL) |

γ_{DC MIN} |
Minimum load factor for DL |

γ_{EH MAX} |
Maximum load factor for horizontal earth pressure |

γ_{EH MIN} |
Minimum load factor for horizontal earth pressure |

γ_{ES MAX} |
Maximum load factor for earth surcharge |

γ_{ES MIN} |
Minimum load factor for earth surcharge |

γ_{EV MAX} |
Maximum load factor for vertical earth pressure |

γ_{EV MIN} |
Minimum load factor for vertical earth pressure |

γ_{f} |
Unit weight of foundation soil [F/L^{3}] |

γ_{LS} |
Load factor for live load (LL) surcharge |

γ_{r} |
Unit weight of reinforced backfill [F/L^{3}] |

γ_{rb} |
Unit weight of road base material [F/L^{3}] |

ε_{L} |
Lateral strain |

ε_{V} |
Vertical strain |

μ |
Friction factor between the wall base and the foundation |

σ_{h} |
Lateral pressure [F/L^{2}] |

σ_{h,f} |
Equivalent lateral stress distribution due to the retained soil behind the GRS abutment [F/L^{2}] |

σ_{h,f} |
Factored lateral pressure [F/L^{2}] |

σ_{h,bridge} |
Lateral pressure due to bridge DL surcharge within GRS [F/L^{2}] |

σ_{h,bridge,eq} |
Lateral pressure due to the equivalent bridge load [F/L^{2}] |

σ_{h,bridge,f} |
Factored lateral pressure due to the equivalent bridge load [F/L^{2}] |

σ_{h,LL} |
Lateral stress distribution due to the equivalent superstructure LL pressure [F/L^{2}] |

σ_{h,q} |
Lateral pressure due to surcharge loading [F/L^{2}] |

σ_{h,rb} |
pressure due to road base surcharge within GRS [F/L^{2}] |

σ_{h,rb,f} |
Factored lateral pressure due to road base surcharge within GRS [F/L^{2}] |

σ_{h,t} |
Lateral pressure due to traffic surcharge within GRS [F/L^{2}] |

σ_{h,t,f} |
Factored lateral pressure due to traffic surcharge within GRS [F/L^{2}] |

σ_{h,total} |
Total lateral pressure due to loads on GRS mass [F/L^{2}] |

σ_{h,W} |
Lateral stress due to weight of GRS [F/L^{2}] |

σ_{v,base,n} |
Nominal vertical pressure at the base of the GRS mass [F/L^{2}] |

σ_{v,base,R} |
Factored vertical pressure at the base of the GRS mass [F/L^{2}] |

ΣM_{D} |
Total driving moment [L-F/L] |

ΣM_{D,R} |
Total factored driving moment [L-F/L] |

ΣM_{R} |
Total resisting moment [L-F/L] |

ΣM_{R,R} |
Total factored resisting moment [L-F/L] |

ΣV |
Total vertical load [F/L] |

ΣV_{R} |
Total factored vertical load [F/L] |

φ |
Soil friction angle [deg] |

φ_{b} |
Friction angle of retained backfill [deg] |

φ_{crit} |
Critical friction angle [deg] |

φ_{design} |
Friction angle of reinforced fill used in design [deg] |

φ_{f} |
Friction angle of foundation soil [deg] |

φ_{r} |
Friction angle of reinforced backfill [deg] |

φ_{rb} |
Friction angle of road base material [deg] |

φ_{reb} |
Repose angle [deg] |

φ_{test} |
Friction angle of reinforced fill found from standard direct shear test [deg] |

Φ_{τ} |
Resistance factor for shear resistance |

Φ_{bc} |
Resistance factor for bearing capacity |

Φ_{cap} |
Resistance factor for ultimate capacity |

Φ_{reinf} |
Resistance factor of the required reinforcement strength |

ω |
Batter angle [deg] |

a |
Distance between the back of the wall face and a surcharge (setback) [L] |

a_{b} |
Setback distance between the back of the face and the beam seat [L] |

a_{rb} |
Setback distance for the road base surcharge over the GRS mass [L] |

a_{t} |
Setback distance for the traffic surcharge over the GRS mass [L] |

b |
Bearing width for bridge; beam seat [L] |

b_{block} |
Width of the facing element [L] |

b_{q} |
Width of surcharge loading [L] |

b_{q, vol} |
Width of the load along the top of the wall (including the setback) [L] |

b_{rb, t} |
Distance over which the road base DL and roadway LL surcharges act over the GRS mass [L] |

B |
Base length of reinforcement not including the wall face [L] |

B' |
Effective foundation width [L] |

B_{b} |
Width of the bridge [L] |

B_{RSF} |
Width of the RSF [L] |

B_{total} |
Total base width of the GRS abutment including the block face |

c |
Cohesion [F/L^{2}] |

C_{b} |
Cohesion of retained backfill [F/L^{2}] |

C_{f} |
Cohesion of foundation soil [F/L^{2}] |

C_{r} |
Cohesion of reinforced backfill [F/L^{2}] |

C_{u} |
Undrained shear strength of foundation soil [F/L^{2}] |

d_{e} |
Clear space distance [L] |

d_{max} |
Maximum grain size [L] |

D_{50riprap} |
Mean grain size for riprap |

D_{f} |
Depth of embedment [L] |

D_{L} |
Maximum lateral displacement [L] |

D_{V} |
Vertical settlement in the GRS mass [L] |

D_{RSF} |
RSF depth [L] |

e_{B,n} |
Nominal eccentricity for bearing capacity calculations [L] |

e_{B,R} |
Factored eccentricity for bearing capacity calculations [L] |

F_{b} |
Lateral force due to the retained backfill [F/L] |

F_{n} |
Nominal driving force for direct sliding calculations [F/L] |

F_{rb} |
Lateral force due to the road base surcharge [F/L] |

F_{R} |
Factored driving force for direct sliding calculations [F/L] |

F_{t} |
Lateral force due to LL on the roadway [F/L] |

FS |
Factor of safety |

FS_{bearing} |
Factor of safety against bearing failure |

FS_{capacity} |
Factor of safety for vertical capacity using the empirical method |

FS_{reinf} |
Factor of safety for required reinforcement strength |

FS_{slide} |
Factor of safety against direct sliding |

G |
Grade [L/L] |

h_{eq} |
Equivalent height of overburden for traffic surcharge [L] |

h_{rb} |
Height of road base (equals height of bridge beam) [L] |

H |
Height of the GRS abutment including the clear space distance [L] |

H_{abut} |
Height of the GRS abutment [L] |

K_{a} |
Coefficient of active earth pressure |

K_{ab} |
Coefficient of active earth pressure for the retained backfill |

K_{ar} |
Coefficient of active earth pressure for the reinforced backfill |

K_{pr} |
Coefficient of passive earth pressure for the reinforced backfill |

L_{abut} |
Abutment length [L] |

L_{block} |
Length of a facing block [L] |

L_{span} |
Span length of the bridge [L] |

(LL + IM)_{total} |
Governing abutment reaction for the HL-93 LL model for one lane |

N_{γ} |
Dimensionless bearing capacity coefficient |

N_{block} |
Number of facing blocks in a column |

N_{c} |
Dimensionless bearing capacity coefficient |

N_{lanes} |
Number of lanes |

N_{q} |
Dimensionless bearing capacity coefficient |

q |
Surcharge load [F/L^{2}] |

q_{b} |
Equivalent superstructure DL pressure [F/L^{2}] |

q_{LL} |
Equivalent superstructure LL pressure [F/L^{2}] |

q_{n} |
Bearing capacity of the foundation soil [F/L^{2}] |

q_{n,an} |
Nominal ultimate load-carrying capacity of the foundation using the analytical method [F/L^{2}] |

q_{n,emp} |
Nominal ultimate load-carrying capacity of the foundation using the empirical method [F/L^{2}] |

q_{R} |
Factored bearing resistance [F/L^{2}] |

q_{rb} |
Surcharge due to the structural backfill (road base) DL [F/L^{2}] |

q_{t} |
Equivalent roadway LL surcharge [F/L^{2}] |

q_{ult,an} |
Ultimate load-carrying capacity of GRS using the analytical method [F/L^{2}] |

q_{ult,emp} |
Ultimate load-carrying capacity of GRS using the empirical method [F/L^{2}] |

Q_{LL} |
LL reaction load [F] |

R_{n} |
Nominal resisting force for direct sliding calculations [F/L] |

R_{R} |
Factored resisting force for direct sliding calculations [F/L] |

RF_{global} |
Global reduction factor for the geosynthetic to account for long-term strength losses due to installation damage, creep, and durability [dimensionless] |

S_{e} |
Superelevation angle [deg] |

S_{k} |
Skew angle [deg] |

S_{v} |
Reinforcement spacing [L] |

T_{@ε = 2%} |
Reinforcement strength at 2 percent reinforcement strain [F/L] |

T_{allow} |
Allowable reinforcement strength [F/L] |

T_{f} |
Ultimate reinforcement strength [F/L] |

T_{f,f} |
Factored reinforcement strength [F/L] |

T_{req} |
Required reinforcement strength [F/L] |

T_{req,f} |
Factored required reinforcement strength [F/L] |

V_{allow,an} |
Factored applied stress on top of GRS mass using the analytical method [F/L^{2}] |

V_{allow,emp} |
Factored applied stress on top of GRS mass using the empirical method [F/L^{2}] |

V_{applied} |
Applied stress on top of GRS mass [F/L^{2}] |

V_{applied,f} |
Factored applied stress on top of GRS mass [F/L^{2}] |

W |
Weight of the GRS abutment backfill [F/L] |

W_{B} |
Total width of riprap [L] |

W_{block} |
Weight of an individual facing block [F] |

W_{face} |
Weight of the facing elements [F/L] |

W_{L} |
Distance between abutment faces [L] |

W_{RSF} |
Weight of the RSF [F/L] |

W_{t} |
Total weight (weight of GRS plus weight of bridge beam plus weight of the road base over the GRS mass only) [F/L] |

W_{t,R} |
Factored total resisting weight (weight of GRS plus weight of bridge beam plus weight of the road base over the GRS mass only) [F/L] |

W_{T} |
Width of level riprap along the top [L] |

x |
Distance from the edge of the load to the point of interest for lateral pressure [L] |

Y_{sc} |
Contraction scour plus long-term degradation scour referenced to the thalweg [L] |

Y_{Tot} |
Distance from the top of riprip to the bottom of riprap [L] |

x_{RSF} |
Length of the RSF in front of the abutment wall face [L] |

Z |
Location along height of wall (measured from the top of the wall) [L] |