LIST OF SYMBOLS. - diameter of drilled shaft or width of spread foundation; dilatometer B reading

Transcription

1 LIST OF SYMBOLS ENGLISH LETTERS - UPPER CASE A A tip A v B CIUC CU CPT COV COV F COV G COV K COV Ko COV Q COV R COV e COV su COV V COV w COV ε COV ξa - dilatometer A reading - tip or base area - area exposed to wind - diameter of drilled shaft or width of spread foundation; dilatometer B reading - consolidated isotropic undrained triaxial compression test - consolidated undrained triaxial compression test - cone penetration test - coefficient of variation - coefficient of variation of load - coefficient of variation of shear modulus - coefficient of variation of the operative horizontal soil stress coefficient - coefficient of variation of the in-situ horizontal soil stress coefficient - coefficient of variation of capacity - coefficient of variation of capacity ratio - coefficient of variation of measurement error - coefficient of variation of undrained shear strength - coefficient of variation of the annual maximum wind speed - coefficient of variation of inherent variability - coefficient of variation of model uncertainty - coefficient of variation of spatial average xxxii

2 COV ξd COV φ C f D DMT D K D r DS E ECPT E D E PMT F F 50 F Dn F Ln F N FORM F Q ( ) F V ( ) F S FS F n G G r - coefficient of variation of design property - coefficient of variation of the effective friction angle - force coefficient - depth of drilled shaft or spread foundation - dilatometer test - model slope for s u and q T correlation - relative density - direct shear test - Young s modulus - electrical cone penetration test - dilatometer modulus - pressuremeter modulus - generic load - 50-year return period load - nominal dead load - nominal live load - load (normal random variable) - First-Order Reliability Method - probability distribution function of capacity - probability distribution function of the annual maximum wind speed - load (standard normal random variable) - factor of safety - nominal load - shear modulus - gust response factor xxxiii

3 H(,, ) H h H ha H han H hn H sh H shn H th H thn I D I r I rc I rr K K D K a K i K o K onc K p LRFD L LI LV L 2 L a - objective function - ultimate lateral capacity - allowable lateral capacity based on displacement limit - nominal allowable lateral capacity - nominal ultimate lateral capacity - side resistance under lateral-moment loading - nominal side resistance under lateral-moment loading - tip resistance under lateral-moment loading - nominal tip resistance under lateral-moment loading - dilatometer material index - rigidity index - critical rigidity index - reduced rigidity index - operative horizontal stress coefficient - dilatometer horizontal stress index - coefficient of active soil stress - initial stiffness of load-displacement response - in-situ coefficient of horizontal soil stress - K o for normally consolidated soils - coefficient of passive soil stress - Load and Resistance Factor Design - spread foundation length - liquidity index - laboratory vane shear test - failure load defined at the initiation of the final linear region - averaging length xxxiv

4 M MCPT M h N - safety margin - mechanical cone penetration test - ultimate moment capacity - standard penetration test value N c, N γ, N q - bearing capacity factors N p OCR P( ) PMT PI P S (, ) Prob( ) Q Q 5 Q 50 Q N Q S Q c Q ca Q can Q cn - lateral bearing factor - overconsolidation ratio - performance function - pressuremeter test - plasticity index - transformed performance function in standard normal space - probability of an event occurring - generic capacity - 5% exclusion limit of Q - 50% exclusion limit of Q - capacity (normal random variable) - capacity (standard normal random variable) - compression capacity - allowable compression capacity based on displacement limit - nominal allowable compression capacity - nominal compression capacity R Q cn - reference nominal compression capacity Q m Q n Q sc Q scn - measured capacity - nominal capacity - compression side resistance - nominal compression side resistance xxxv

5 Q su Q sun Q tc Q tcm Q tcn Q tcp Q tu Q tun Q u Q ua Q uan Q ud Q un - uplift side resistance - nominal uplift side resistance - compression tip resistance - measured compression tip resistance - nominal compression tip resistance - predicted compression tip resistance - uplift tip resistance - nominal uplift tip resistance - uplift capacity - allowable uplift capacity based on displacement limit - nominal allowable uplift capacity - design capacity in uplift - nominal uplift capacity R Q un - reference nominal uplift capacity Q ω RBD RP R SBPMT S.D. SPT T( ) TC UC UU V - ω% exclusion limit of Q - Reliability-Based Design - return period in years - capacity ratio - self-boring pressuremeter test - standard deviation - standard penetration test - transformation model - triaxial compression test - unconfined compression test - unconsolidated-undrained triaxial compression test - annual maximum wind speed xxxvi

6 VST W W n Z v - vane shear test - weight of foundation and enclosed soil - nominal weight - terrain factor ENGLISH LETTERS - LOWER CASE a, b - curve-fitted parameters for the normalized load-displacement relationship c i c n d df dz dq e exp( ) f f F ( ) f Q ( ) f Q,F (, ) S f d f d g 1, g 2 h i - structural influence coefficient - nominal cohesion - average distance between intersections of the fluctuating property and its trend function - infinitesimal increment in f - infinitesimal increment in z - infinitesimal increment in q - measurement error - exponential function - one possible value of the load - probability density function of load - probability density function of capacity - joint probability density function of load and capacity - load design point in standard normal space - load design point - parameters for the Gumbel distribution - eccentricity of the applied lateral load - dummy index xxxvii

7 k ln( ) log 10 ( ) m DK m F m FN m G m K m Ko m M m Q m QN m R m V m VW m a, m b m su m µ m ξ m ξd m σp m φ n p L p T p a - deterministic wind load constant - natural logarithm - base 10 logarithm - mean of D K - mean of load - mean of load (normal random variable) - mean of shear modulus - mean operative horizontal soil stress coefficient - mean in-situ horizontal soil stress coefficient - mean of safety margin - mean of capacity - mean of capacity (normal random variable) - mean capacity ratio - mean of the annual maximum wind speed - mean of the weekly maximum wind speed - mean of the curve-fitted parameters, a and b, respectively - mean undrained shear strength - mean correction factor for vane shear test - mean soil property - mean design soil property - mean preconsolidation stress - mean effective friction angle - number of data points - pressuremeter limit stress - target probability of failure - atmospheric pressure xxxviii

8 p f p o p u q q T q a q c S q d q d s F s FN s M s Q s QN s R s V s e s u s w s ε s ξa s ξd t( ) u i v v 50 - probability of failure; pressuremeter yield stress - pressuremeter total horizontal stress - ultimate lateral soil pressure - one possible value of the capacity - corrected q c - average vertical effective stress from depths D to D+B - cone tip resistance - capacity design point in standard normal space - capacity design point - standard deviation of load - standard deviation of load (normal random variable) - standard deviation of safety margin - standard deviation of capacity - standard deviation of capacity (normal random variable) - standard deviation of capacity ratio - standard deviation of the maximum wind speed - standard deviation of measurement error - undrained shear strength - standard deviation of inherent variability - standard deviation of model uncertainty - standard deviation of spatial average - standard deviation of design soil property - trend function - initial pore water stress at the tip - one possible value of the annual maximum wind speed - 50-year return period wind speed xxxix

9 v i w( ) w L w P w n x y y 50 y a y f z z b z i z r z t - maximum wind speed for the ith year - fluctuating component - liquid limit - plastic limit - water content - dummy variable - foundation displacement - foundation displacement at 50% of the failure load - allowable displacement limit - foundation displacement at failure - depth - bottom coordinate of a depth interval - ith depth coordinate - depth of rotation - top coordinate of a depth interval GREEK LETTERS - UPPER CASE Γ 2 ( ) u β Φ( ) Φ -1 ( ) Ψ - variance reduction function - volumetric strain - change in pore water stress caused by undrained loading - average deviation from the target reliability index in the calibration domain - standard normal probability distribution function - inverse standard normal probability distribution function - resistance factor xl

10 Ψ c Ψ sc Ψ tc Ψ h Ψ u Ψ w Ψ sh Ψ su Ψ th Ψ tu - compression resistance or deformation factor - compression side resistance factor - compression tip resistance factor - lateral-moment resistance or deformation factor - uplift resistance or deformation factor - weight resistance factor - lateral-moment side resistance factor - uplift side resistance factor - lateral-moment tip resistance factor - uplift tip resistance factor Ω φ /2 GREEK LETTERS - LOWER CASE α α n β β i β T β FORM γ γ γ c γ d γ φ γ D - adhesion factor - nominal adhesion factor - reliability index - reliability index for the ith point in the calibration domain - target reliability index - reliability index obtained using FORM - total soil unit weight - effective soil unit weight - partial factor of safety for cohesion - dry unit weight - partial factor of safety for friction angle - partial factor of safety for dead load xli

11 γ L δ δ v δ h ε ζ cs ζ cd ζ cr ζ crn ζ qs ζ qd ζ qr ζ γs ζ γd ζ γr η η D η L ν ξ ξ a ξ d ξ m ρ f σ vm σ vo - partial factor of safety for live load - effective interface friction angle - vertical scale of fluctuation - horizontal scale of fluctuation - uncertainty about regression equation or transformation model - foundation shape modifier for N c - foundation depth modifier for N c - soil rigidity modifier for N c - nominal soil rigidity modifier for N c - foundation shape modifier for N q - foundation depth modifier for N q - soil rigidity modifier for N q - foundation shape modifier for N γ - foundation depth modifier for N γ - soil rigidity modifier for N γ - load factor - dead load factor - live load factor - Poisson s ratio. - in-situ soil property - spatial average - design soil property - measured soil property - air density factor - average total vertical stress - total overburden stress xlii

12 σ p σ v - preconsolidation stress - vertical effective stress σ vm - average vertical effective stress over the foundation depth σ vo - effective overburden stress φ φ φ cv φ n ϕ( ) - friction angle - effective stress friction angle - constant volume effective stress friction angle - nominal friction angle - standard normal probability density function ψ - φ /2 ω - exclusion limit in percent xliii