LRFD Cast-in-Place Concrete Retaining Wall August 10,...
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LRFD Cast-in-Place Concrete Retaining Wall August 10, 2011 James Luebke Wisconsin Department of Transportation
Transcript of LRFD Cast-in-Place Concrete Retaining Wall August 10,...
LRFD Cast-in-Place Concrete Retaining Wall
August 10, 2011
James LuebkeWisconsin Department of Transportation
Wall ParametersWall Parameters
Height = 20’Height (exposed) = 16’Footing Cover = 4’ Footing Width = 10’Footing Thickness = 2.0’Supports Traffic
Soil Parameters (c’ = 0)φf = 30 degreesγf = 0.120 kcfφfd = 34 degreesγfd = 0.120 kcf
Wall Design Process
Non - Propriety Wall (WisDOT/Consultants Responsibility)Soil InvestigationPreliminary Geometry and Loads (Geotechnical)External Stability, Overall Stability and Settlement (Geotechnical)Wall Design (Structural)– Final Geometry and Loads– External Stability, Structural Resistance and Serviceability
Revise Overall Stability and Settlement?
LRFD CIP Concrete Wall Example Outline
Loads and Load CombinationsExternal Stability– Bearing Resistance– Sliding– Eccentricity
Structural ResistanceOverall Stability and Settlement
Loads– Horizontal Earth Pressure (EH)– Vertical Earth Pressure (EV)– Live Load Surcharge (LS)– Dead Load (DC)
Limit States– Service – Strength I
» Max/Min load factors » Live Load
Loads and Load Combinations
Strength Ia
Strength Ib
Live Load
Active Earth Pressure Resultant
Active Earth Pressure ResultantFT = ½ γf H2 ka = ½(0.120)(20)2(0.314) = 7.55 klf
Coefficient of Active Earth Pressure (Coulomb Theory)
FT
γf H ka
HEV
VEVδ’
φf = 30.0 °β = 0.0 °θ = 87.6 °δ = 21.0 °
Γ = 2.726Γ 1sin φ f δ+( ) sin φ f β−( )sin θ δ−( ) sin θ β+( )+
⎛⎜⎝
⎞⎟⎠
2
=
kasin θ φ f+( )2
Γ sin θ( )2 sin θ δ−( )= ka = 0.314
Live Load Surcharge Resultant
Live Load Surcharge ResultantFSUR = γf heq H ka = (0.120)(2)(20)(0.314) = 1.51 klf
Equivalent height of soil for live load surcharge (heq)
FSUR
γf heq ka
WisDOT policy item:γf heq = 240 psf (w/ Traffic Loads)γf heq = 100 psf (w/o Traffic Loads)
HLSδ’
Unfactored LoadsLoad Moment
Arm Moment LRFD Load TypeItem Description Value
(kip/ft) Item Value (ft) Item
Value (kip-ft/ft)
V1 Wall stem front batter 0.51 dv1 3.8 MV1 1.9 DCV2 Wall stem 2.70 dv2 4.4 MV2 11.8 DCV3 Wall stem back batter 1.01 dv3 5.1 MV3 5.2 DCV4 Wall footing 3.00 dv4 5.0 MV4 15.0 DCV7 Soil backfill 9.45 dv7 7.8 MV7 73.8 EVV8 Soil backfill 0.81 dv8 5.4 MV8 4.4 EVV9 Soil backfill 0.00 dv9 8.3 MV9 0.0 EVV10 Live load surcharge 1.23 dv10 7.4 MV10 9.1 LSV11 Active earth pressure 2.99 dv11 10.0 MV11 29.9 EH
Unfactored Vertical Forces and Moments
Unfactored Loads
Unfactored Horizontal Forces and Moments
Load Moment Arm Moment LRFD
Load TypeItem Description Value
(kip/ft) Item Value (ft) Item Value
(kip-ft/ft)
H1 Live load surcharge 1.39 dh1 10.0 MH1 13.9 LS
H2 Active earth force 6.93 dh2 6.7 MH2 46.2 EH
FT
H2δ’
δ’= 90-87.6+21
H1 = FSURcos (δ’)H2 = FTcos (δ’)
FSUR
H1δ’
H/2H/3
Factored Loads
Factored Forces and Moments
Load Combination γDC γEV γLS_V γLS_H γEH Application
Strength Ia 0.90 1.00 - 1.75 1.50 Sliding, Eccentricity
Strength Ib 1.25 1.35 1.75 1.75 1.50 Bearing, Wall Strength
Service I 1.00 1.00 1.00 1.00 1.00 Overall, Settlement & Crack Control
Load Combinations
Load CombinationVert. Loads
V (kips/ft)
MomM
(kip-
ents V
kip/ft)
Horiz. L
(kips/
oads H
ft)
MomM
(kip-k
ents H ip/ft)
Strength Ia 21.2 153.6 12.8 93.5Strength Ib 29.5 208.9 12.8 93.5Service I 21.7 151.2 8.3 60.0
V_Ia n 0.90VDC 1.00VEV+ 0.00 VLS+ 1.50 VEH+( )= V_Ia= 21.2 kips
External Stability
Bearing Resistance (Nominal)qn = cNcm + γfdDfNqmCwq + 0.5γfdB’NγmCwγ
c = Cohesion (ksf)Ncm = Cohesion term **Nqm = Surcharge term**Nγm = Unit weight term **Cwq = Groundwater correction factorCwγ = Groundwater correction factorB’ = Effective footing width
= 0 ksf= Ncscic= Nqsqdqiq= Nγsγiγ= 1.0 (Dw >1.5B+Df )= 1.0 (Dw >1.5B+Df )= B-2e
** Modified bearing capacity factor (includes shape factors, load inclination factors and depth correction factor Tables 10.6.3.1.2a-2,3,4 LRFD)
External Stability
Bearing Resistance (Nominal)qn = cNcm + γfdDfNqmCwq + 0.5γfdB’NγmCwγ
c = Cohesion (ksf)Ncm = Cohesion term **Nqm = Surcharge term**Nγm = Unit weight term **Cwq = Groundwater correction factorCwγ = Groundwater correction factorB’ = Effective footing width
= 0 ksf= 15.2 = 11.3 = 8.1= 1.0= 1.0= 7.8’
qn = 0 + (0.120)(4.0’)(11.3)(1.0) + 0.5(0.120)(7.8)(8.1)(1.0) = 9.21 ksf
External Stability
Bearing Resistance (Factored)
qn = 9.21 ksf Nominal bearing resistanceφb = 0.55 Bearing resistance factor(1)
qr = φb qn Factored bearing resistance
(1) LRFD Table 11.5.6-1 (Semi-Gravity Walls)
qr = (0.55)(9.21) = 5.07 ksf
External Stability
Bearing Capacity to Demand Ratio (CDR)
Load Combination Vert. Loads V (kips/ft)
Moments (kip-kip/f
MV t)
Horiz. Loa(kips/ft
ds H )
Moments (kip-kip/f
MH t)
Strength Ia 21.2 153.6 12.8 93.5Strength Ib 29.5 208.9 12.8 93.5Service I 21.7 151.2 8.3 60.0
qr = 5.07 ksfx = (ΣMr – ΣMo)/ ΣVe = B/2 - xσv = ΣV/(B-2e) = ΣV/B’
Factored bearing resistanceDist. from toe to load resultantWall eccentricityUltimate bearing stress
= (208.9 – 93.5)/29.5 = 3.91 ft= (10/2) – 4.25 = 1.09 ft= 29.3/[10.0-(2)(0.75)] = 3.78 ksf
CDRBRG = qr/σv = 5.07/3.78 = 1.34 > 1.0 ==> OK
External Stability
Limiting Eccentricity (CDR)
Load Combination Vert. Loads V (kips/ft)
Moments (kip-kip/f
MV t)
Horiz. Loa(kips/ft
ds H )
Moments (kip-kip/f
MH t)
Strength Ia 21.2 153.6 12.8 93.5Strength Ib 29.5 208.9 12.8 93.5Service I 21.7 151.2 8.3 60.0
emax = B/4x = (ΣMr – ΣMo)/ ΣVe = B/2 - x
= 10/4 = 2.50 ft= (153.6 – 93.5)/21.2 = 2.83 ft= (10/2) – 4.25 = 2.17 ft
CDRecc= emax/e = 2.50/2.17 = 1.15 > 1.0 ==> OK
External Stability
Sliding ResistanceRR = φτRτ + φepRep
RR = Factored sliding resistanceφτ = Shear resistance factorRτ = Nominal sliding resistanceφep = Passive pressure resistance factorRep = Nominal passive resistanceV = Total vertical force (Strength Ia)
= φτRτ + φepRep= 1.0 (Table 11.5.6-1) = V tan φfd= 0.5 (Table 10.5.5.2.2-1) = TBD= 21.2 kips
Rr = (1.0)(21.2)tan(34) + 0.5 Rep
External Stability
Sliding Resistance (Passive Resistance)RR = φτRτ + φepRep
kp = tan(45 + φfd/2)2
= tan(45 + 34/2)2 = 3.54 σH = kp γfd (y2+y1)/2
= (3.54)(0.120)(5+4)/2 = 1.91 ksfRep = σH (y2 – y1)
= (1.91)(5-4) = 1.91 kips
Rr = (14.3) + 0.5 (1.91) =15.3 kips
Rep
y
External Stability
Sliding Resistance (CDR)
Load Combination Vert. Loads V (kips/ft)
Moments (kip-kip/f
MV t)
Horiz. Loa(kips/ft
ds H )
Moments (kip-kip/f
MH t)
Strength Ia 21.2 153.6 12.8 93.5Strength Ib 29.5 208.9 12.8 93.5Service I 21.7 151.2 8.3 60.0
Rr = 15.3 kipsRu = 12.8 kips
Factored sliding resistanceFactored sliding force
CDRSliding = Rr/Ru = 15.3/12.8 = 1.19 > 1.0 ==> OK
Structural Resistance
Loads (Strength Ib & Service)Element Capacities & Checks
Structural Resistance
Loads (Strength Ib)– Heel– Toe– Stem
Critical Sections (Vu & Mu)
Structural Resistance
Element Capacities & Checks– Shear LRFD [5.8.3.3]
Vr > Vu
– Flexure LRFD [5.7.3.2]
Mr > Mu
– Min. Flexural Reinforcement LRFD [5.7.3.3.2] Mr > lesser of (1.2Mcr and 1.33Mu )
– Crack Control (Service Loads) LRFD [5.7.3.4]
smax > s– Temp. & Shrinkage Steel LRFD [5.10.8]
Structural Resistance
Element Capacities & Checks– Shear LRFD [5.8.3.3]
Vr = φvVn = φv min[ 0.0316β(f’c)1/2bdv , 0.25f’cbdv ]– Flexure LRFD [5.7.3.2]
Mr = φfMn = φfAsfy(ds-a/2)– Min. Flexural Reinforcement LRFD [5.7.3.3.2]
Mcr = Scfr = (Ig/yt)0.37f’c1/2
– Crack Control (Service Loads) LRFD [5.7.3.4]
smax = (700γe/βsfss)-2dc
– Temp. & Shrinkage Steel LRFD [5.10.8]
Overall Stability11.6.2.3 LRFD • Limiting equilibrium methods of analysis (FS = 1.857)• Service I Load Combination• φ=0.75• CDR = FS*φ > 1.0
CDROverall = FS*φ = (1.857)(0.75)= 1.39 > 1.0 ==> OK
SettlementHough’s Method10.6.2.4.2 LRFD– Settlement of Footings on Cohesionless Soils
1. Subdivide subsurface ( 2 x base width & 10’ layers)2. Determine corrected SPT values (N1)603. Use Figure 10.6.2.4.2-1 to determine Bearing Capacity
Index C’4. Calculate effective vertical stresses (σ’o) and increase in
stresses at mid-height of layers (Δσv)5. Determine layer settlement
6. Determine total settlement
SettlementBearing Capacity Index C’
Figure 10.6.2.4.2-1 LRFD
Sand & Gravel
N1 = Corrected SPT Value (N1)60= 30
C’ = Bearing Capacity Index= 100
Source: Figure 10.6.2.4.2-1 LRFD(AASHTO, 2010; modified after Hough, 1959)
Settlement
10’
10’
Layer 1
Layer 2
σv= Equivalent Vertical Stress (Service)= 2584 psf
σ’o = Dlayer 1 γfd= (4+10/2)(120) = 1080 psf
Δσv = σv [B’/(B’+a)]= 2584 [8.4/(8.4+5)]= 1620 psf
9’4’2:1 Method
Calculate Stresses
σv = ΣV/B’
Settlement
ΔH1 = Elastic settlement of Layer 1Hc = 120” C’ = 100σ’o = 1080 psfΔσv = 1620 psf
Determine Layer Settlement
ΔH1 = (120”)(1/100) log [(1080+1620)/1080]= 0.48”
Settlement
ΔH1 = 0.48”Hc = 120” C’ = 100σ’o = 2280 psfΔσv = 928 psf
Check Total Settlement
ΔH2 = (120”)(1/100) log [(2280+928)/2280]= 0.18”
Se = 0.48”+0.18”
Se = 0.66”
(Eqn. 10.6.2.4.2-3)
(Eqn. 10.6.2.4.2-2)
< 1.0” ==> OK
LRFD CIP Concrete Wall Example Summary
Loads and Load CombinationsExternal Stability– Bearing Resistance– Sliding– Eccentricity
Structural ResistanceOverall Stability and Settlement
Questions?
GOT CONCRETE?
