α |
Angle between wall face and projection of the midline of the surcharge to the wall face [rad] |
αb |
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] |
βb |
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/L3] |
γb |
Unit weight of retained backfill [F/L3] |
γDC MAX |
Maximum load factor for dead load (DL) |
γDC MIN |
Minimum load factor for DL |
γEH MAX |
Maximum load factor for horizontal earth pressure |
γEH MIN |
Minimum load factor for horizontal earth pressure |
γES MAX |
Maximum load factor for earth surcharge |
γES MIN |
Minimum load factor for earth surcharge |
γEV MAX |
Maximum load factor for vertical earth pressure |
γEV MIN |
Minimum load factor for vertical earth pressure |
γf |
Unit weight of foundation soil [F/L3] |
γLS |
Load factor for live load (LL) surcharge |
γr |
Unit weight of reinforced backfill [F/L3] |
γrb |
Unit weight of road base material [F/L3] |
εL |
Lateral strain |
εV |
Vertical strain |
μ |
Friction factor between the wall base and the foundation |
σh |
Lateral pressure [F/L2] |
σh,f |
Equivalent lateral stress distribution due to the retained soil behind the GRS abutment [F/L2] |
σh,f |
Factored lateral pressure [F/L2] |
σh,bridge |
Lateral pressure due to bridge DL surcharge within GRS [F/L2] |
σh,bridge,eq |
Lateral pressure due to the equivalent bridge load [F/L2] |
σh,bridge,f |
Factored lateral pressure due to the equivalent bridge load [F/L2] |
σh,LL |
Lateral stress distribution due to the equivalent superstructure LL pressure [F/L2] |
σh,q |
Lateral pressure due to surcharge loading [F/L2] |
σh,rb |
pressure due to road base surcharge within GRS [F/L2] |
σh,rb,f |
Factored lateral pressure due to road base surcharge within GRS [F/L2] |
σh,t |
Lateral pressure due to traffic surcharge within GRS [F/L2] |
σh,t,f |
Factored lateral pressure due to traffic surcharge within GRS [F/L2] |
σh,total |
Total lateral pressure due to loads on GRS mass [F/L2] |
σh,W |
Lateral stress due to weight of GRS [F/L2] |
σv,base,n |
Nominal vertical pressure at the base of the GRS mass [F/L2] |
σv,base,R |
Factored vertical pressure at the base of the GRS mass [F/L2] |
ΣMD |
Total driving moment [L-F/L] |
ΣMD,R |
Total factored driving moment [L-F/L] |
ΣMR |
Total resisting moment [L-F/L] |
ΣMR,R |
Total factored resisting moment [L-F/L] |
ΣV |
Total vertical load [F/L] |
ΣVR |
Total factored vertical load [F/L] |
φ |
Soil friction angle [deg] |
φb |
Friction angle of retained backfill [deg] |
φcrit |
Critical friction angle [deg] |
φdesign |
Friction angle of reinforced fill used in design [deg] |
φf |
Friction angle of foundation soil [deg] |
φr |
Friction angle of reinforced backfill [deg] |
φrb |
Friction angle of road base material [deg] |
φreb |
Repose angle [deg] |
φtest |
Friction angle of reinforced fill found from standard direct shear test [deg] |
Φτ |
Resistance factor for shear resistance |
Φbc |
Resistance factor for bearing capacity |
Φcap |
Resistance factor for ultimate capacity |
Φreinf |
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] |
ab |
Setback distance between the back of the face and the beam seat [L] |
arb |
Setback distance for the road base surcharge over the GRS mass [L] |
at |
Setback distance for the traffic surcharge over the GRS mass [L] |
b |
Bearing width for bridge; beam seat [L] |
bblock |
Width of the facing element [L] |
bq |
Width of surcharge loading [L] |
bq, vol |
Width of the load along the top of the wall (including the setback) [L] |
brb, 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] |
Bb |
Width of the bridge [L] |
BRSF |
Width of the RSF [L] |
Btotal |
Total base width of the GRS abutment including the block face |
c |
Cohesion [F/L2] |
Cb |
Cohesion of retained backfill [F/L2] |
Cf |
Cohesion of foundation soil [F/L2] |
Cr |
Cohesion of reinforced backfill [F/L2] |
Cu |
Undrained shear strength of foundation soil [F/L2] |
de |
Clear space distance [L] |
dmax |
Maximum grain size [L] |
D50riprap |
Mean grain size for riprap |
Df |
Depth of embedment [L] |
DL |
Maximum lateral displacement [L] |
DV |
Vertical settlement in the GRS mass [L] |
DRSF |
RSF depth [L] |
eB,n |
Nominal eccentricity for bearing capacity calculations [L] |
eB,R |
Factored eccentricity for bearing capacity calculations [L] |
Fb |
Lateral force due to the retained backfill [F/L] |
Fn |
Nominal driving force for direct sliding calculations [F/L] |
Frb |
Lateral force due to the road base surcharge [F/L] |
FR |
Factored driving force for direct sliding calculations [F/L] |
Ft |
Lateral force due to LL on the roadway [F/L] |
FS |
Factor of safety |
FSbearing |
Factor of safety against bearing failure |
FScapacity |
Factor of safety for vertical capacity using the empirical method |
FSreinf |
Factor of safety for required reinforcement strength |
FSslide |
Factor of safety against direct sliding |
G |
Grade [L/L] |
heq |
Equivalent height of overburden for traffic surcharge [L] |
hrb |
Height of road base (equals height of bridge beam) [L] |
H |
Height of the GRS abutment including the clear space distance [L] |
Habut |
Height of the GRS abutment [L] |
Ka |
Coefficient of active earth pressure |
Kab |
Coefficient of active earth pressure for the retained backfill |
Kar |
Coefficient of active earth pressure for the reinforced backfill |
Kpr |
Coefficient of passive earth pressure for the reinforced backfill |
Labut |
Abutment length [L] |
Lblock |
Length of a facing block [L] |
Lspan |
Span length of the bridge [L] |
(LL + IM)total |
Governing abutment reaction for the HL-93 LL model for one lane |
Nγ |
Dimensionless bearing capacity coefficient |
Nblock |
Number of facing blocks in a column |
Nc |
Dimensionless bearing capacity coefficient |
Nlanes |
Number of lanes |
Nq |
Dimensionless bearing capacity coefficient |
q |
Surcharge load [F/L2] |
qb |
Equivalent superstructure DL pressure [F/L2] |
qLL |
Equivalent superstructure LL pressure [F/L2] |
qn |
Bearing capacity of the foundation soil [F/L2] |
qn,an |
Nominal ultimate load-carrying capacity of the foundation using the analytical method [F/L2] |
qn,emp |
Nominal ultimate load-carrying capacity of the foundation using the empirical method [F/L2] |
qR |
Factored bearing resistance [F/L2] |
qrb |
Surcharge due to the structural backfill (road base) DL [F/L2] |
qt |
Equivalent roadway LL surcharge [F/L2] |
qult,an |
Ultimate load-carrying capacity of GRS using the analytical method [F/L2] |
qult,emp |
Ultimate load-carrying capacity of GRS using the empirical method [F/L2] |
QLL |
LL reaction load [F] |
Rn |
Nominal resisting force for direct sliding calculations [F/L] |
RR |
Factored resisting force for direct sliding calculations [F/L] |
RFglobal |
Global reduction factor for the geosynthetic to account for long-term strength losses due to installation damage, creep, and durability [dimensionless] |
Se |
Superelevation angle [deg] |
Sk |
Skew angle [deg] |
Sv |
Reinforcement spacing [L] |
T@ε = 2% |
Reinforcement strength at 2 percent reinforcement strain [F/L] |
Tallow |
Allowable reinforcement strength [F/L] |
Tf |
Ultimate reinforcement strength [F/L] |
Tf,f |
Factored reinforcement strength [F/L] |
Treq |
Required reinforcement strength [F/L] |
Treq,f |
Factored required reinforcement strength [F/L] |
Vallow,an |
Factored applied stress on top of GRS mass using the analytical method [F/L2] |
Vallow,emp |
Factored applied stress on top of GRS mass using the empirical method [F/L2] |
Vapplied |
Applied stress on top of GRS mass [F/L2] |
Vapplied,f |
Factored applied stress on top of GRS mass [F/L2] |
W |
Weight of the GRS abutment backfill [F/L] |
WB |
Total width of riprap [L] |
Wblock |
Weight of an individual facing block [F] |
Wface |
Weight of the facing elements [F/L] |
WL |
Distance between abutment faces [L] |
WRSF |
Weight of the RSF [F/L] |
Wt |
Total weight (weight of GRS plus weight of bridge beam plus weight of the road base over the GRS mass only) [F/L] |
Wt,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] |
WT |
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] |
Ysc |
Contraction scour plus long-term degradation scour referenced to the thalweg [L] |
YTot |
Distance from the top of riprip to the bottom of riprap [L] |
xRSF |
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] |