Overall Stability Moving from Service to Strength Limit State: Why? Nick Harman, MS, PE Ani Carignan, PE, LEED AP STGEC Conference October, 2018
History In 2000 FHWA mandated state DOTs begin designing bridges using LRFD instead of ASD by 2007 and other structures by 2010 The change to LRFD created a problem for Overall slope stability analysis Overall stability was performed at the Ultimate limit state in ASD Therefore since the mathematics hadn t been worked out it was decided to perform Overall stability at Service limit state (i.e., calibration hadn t been performed) 2
History (continued) Performing Overall stability at the Service limit state was only intended as a temporary measure At the Service limit the load and resistance factors equal to 1.0 This was determined to be the best way to fit Overall stability calculations into the LRFD format Loads and resistances in slope stability analysis cannot be easily separated Attempting to factor loads separately from resistances within a slope stability analysis will result in changes to the critical failure surface that are unrealistic 3
The Problem Overall stability is a collapse, not deformation, scenario and should therefore be considered at a Strength limit state Separation of driving and resisting forces difficult to do (i.e., soil is a continuum) 4
The Problem: Separation of Load and Resistance C F = driving forces (i.e., forces that must be resisted) φ s,γ s Mostly driving forces Mostly resisting forces N F R φ s,γ s Conceptually, FFFF = sssssssss sssssssssssssss aaaaaaaaaaaaaaaaaa sssssssss sssssssssssssss rrrrrrrrrrrrrrrr N = normal force R = resisting forces (i.e., shear strength available = N*Tan φ s ) 5
What is Currently Required in the LRFD Specifications (2003 2018) Current slope stability design programs are in ASD not LRFD Therefore AASHTO recommended for Overall slope stability analysis simply inversing the FS to get resistance factor φ = 1/FS φ = 1/FS = 1/1.3 0.75 (geotechnical parameters well defined, slope does not support structural element) φ = 1/FS = 1/1.5 0.65 (geotechnical parameters not well defined, or supports structural element) 6
The analysis is based on Service I limit state Focus of Overall stability is on the driving forces versus the soil shear strength available (i.e., ΣF v = ΣF h = 0, ΣM c = 0) This resistance factor φ for Overall stability is combined with an Overall stability load factor (γ p, i.e., EV) of 1.0 (AASHTO 8 th Ed. Table 3.4.1-2) All other loads, have a load factor of 1.0. They are essentially unfactored 7
Why a Change is Needed? AASHTO is adding soil nail walls to the LRFD Bridge Design Specifications Introducing structural components (i.e., soil nails) and evaluating Overall stability in the Service limit state becomes problematic Three slope stability limit equilibrium checks: Internal stability Compound stability Overall stability 8
Illustration of the Different Types of Slope Stability This also applies to MSE walls and anchored walls 9
The Solution Is Move Overall stability to the Strength limit state (adopted by AASHTO in 2018) Continue to inverse FS developed from slope stability design programs to develop a resistance factor φ = 1/FS = 1/1.3 0.75 (recommended resistance factor for Strength limit state if geotechnical conditions well known) φ = 1/FS = 1/1.5 0.65 (res. factor for Strength limit state if geotechnical conditions are variable or information is limited) Support of structural element no longer effects the selection of resistance factor Continue to use Overall stability load factor γ p-ev equal to 1.0 (i.e., vertical earth pressure) Include load factors greater than 1.0 for external found., traffic and surcharge loads 10
Parametric Study to Assess Effect of Moving Overall Stability to Strength Limit State EXAMPLE: Wall Height: 20 ft Soil nail spacing: 5 ft e.w. Incline angle: 15 degrees Tendon Bar: #9 (A =1.25 in2) Tendon tensile strength: 75 ksi Drill hole diameter: 6 in Soil-grout bond strength: 14 psi Soil : φ = 30 deg Soil Weight: ϒ = 120 pcf External Load factor LRFD (Ave. DC & LL) = 1.5 7 11
Parametric Study Design Checks Soil nails: Internal & Compound stability Soil Nail Tensile Resistance φ T R T γ p Tmax R T = A T f y tensile resistance of a tendon (kip) φ T =0.75 resistance factor for tendon in tension from AASHTO Table 11.5.7-1 γ p = the maximum load factor for vertical earth pressure EV from AASHTO Table 3.4.1-2 T max = maximum soil nail force Soil Nail Pullout φ PO R PO γ PO Tmax R PO = πq u D dh L p -nominal pullout resistance (kip); q u =bond strength per unit area (ksf); D dh =drill hole diameter (ft); L P = the length of soil nail behind the failure surface (ft) φ PO =0.65 resistance factor for soil nail pullout from AASHTO Table 11.5.7-1 γp = the maximum load factor for vertical earth pressure EV from AASHTO T.3.4.1-2 Tmax = maximum soil nail force, typically obtained by a slope stability software 12
Parametric Study (continued) Soil nails: Overall stability Soil resistance factor: φ = 1/FS = 1/1.3 0.75 whether or not external load is present* Overall stability load factor for soil loading: (γ p, i.e., EV) of 1.0 (AASHTO 8 th Ed. Table 3.4.1-2) If external load on top of slope: (γ p, i.e., DC, LL, LS): γ p, DC = 1.25 for foundation dead load, γ p, LL or γ p, LS = 1.75 for live load acting on foundation or live load sur. γ p, DC+LL = 1.5 ave. for this parametric study * geotechnical parameters well defined Goal was to compare slope stability FS obtained in Service vs Strength limit state The question we are trying to answer through this parametric study: is FS= 1.5 for unfactored Service loads is approximately the same as FS = 1.3 for factored loads at Strength limit state? 13
Design Examples Design Conditions Modeled: Non-circular, Circular and Fixed Sliding Surface 14
Design Examples Design Conditions: 2H:1V, 3H:1V, 1.5H:1V; Footing B = 5, 8, 10 ; Offset = 0, B, 2B; Earth resistance factor φ = 0.75* Load factor - Earth pressure: ϒ p-ev = 1.0; Footing: (ϒ DC+LL = 1.33 ave.); LL (ϒ LL =1.75); 15
Conclusions Moving Overall stability to the Strength limit state has little or no effect on the design outcome if: A resistance factor for Overall stability 0.75 is used with or without the presence of a foundation near the top of the slope* Overall stability load factor (i.e., EV) remains at γ p-ev = 1.0 (Table 3.4.1-2) Strength limit state foundation load factors (Tables 3.4.1-1 and 3.4.1-2) or traffic live load surcharge (LS) load factors are used (Table 3.4.1-1) If external load or structural element is not present there should be no difference between Service and Strength limit state results If a foundation load is present, the result in the Strength limit state will be within 5 to 10% of what would be obtained currently to address Overall stability in the Service limit state 16
Conclusions (continued) If a traffic surcharge (LS) is present, the result in the Strength limit state will be within 2 to 3% of what would be obtained currently to address Overall stability in the Service limit state For more information contact: Tony Allen Washington DOT Office 360-709-5450 E-mail allent@wsdot.wa.gov 17
Thank you! Questions? Nick Harman, MS, PE HarmanNE@scdot.org Ani Carignan, PE, LEED AP CarignanAP@scdot.org 18