Rock-Socketed Shafts for Highway Structure Foundations (2006)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

102 ENGLISH LETTERS—UPPERCASE Ab = cross-sectional area of the foundation base. Ac = cross-sectional area of concrete inside of spiral steel. Ag = gross cross-sectional area of concrete shaft. As = surface area of the side of the foundation. Ast = total cross-sectional area of longitudinal rein- forcement. Av = area of concrete in the cross section that is effec- tive in resisting shear. Avs = cross-sectional area of shear reinforcement. B = foundation diameter. Bls = diameter of a circle passing through the center of the longitudinal reinforcement. C = correlation factor relating point load strength to uniaxial compressive strength of rock; correlation coefficient relating uniaxial compres- sive strength to ultimate unit side resistance. D = foundation depth; distance between point loads in point load test; rock-socket diameter. D s = depth of embedment in rock; thickness of soil layer overlying rock. E = elastic modulus; modulus of deformation. Eb = elastic modulus of rock mass below the shaft base. Ec = elastic modulus of the concrete shaft. Ed = small-strain dynamic modulus. Ee = effective elastic modulus of concrete shaft. Eir = initial elastic modulus of rock mass. EM = rock mass modulus of deformation. Ep = elastic modulus of the pile (shaft) material. Er = elastic modulus of intact rock; modulus of rock mass above the base. ER = elastic modulus of intact rock. Es = elastic modulus of the shaft. G* = equivalent shear modulus of rock mass. Gr = shear modulus of the elastic rock mass. GSI = Geological Strength Index H = horizontal load acting on a drilled shaft. ID = slake durability index. IGM = intermediate geomaterial. Is = uncorrected point load strength index; moment of inertia of reinforced-concrete shaft. Is(50) = point load strength corrected to a diameter of 50 mm. Iρ = dimensionless influence factor for elastic deformation. J = coefficient used to evaluate ultimate lateral resis- tance in soil; bearing capacity correction factor that depends on the ratio of horizontal dis- continuity spacing to socket diameter. Ja = joint alteration number. Jn = joint set number. Jr = joint roughness number. Jw = joint water reduction factor. K = normal stiffness of rock-concrete interface. Kb = socket depth factor. Kir = initial slope of p-y curve. Ko = in situ coefficient of lateral earth pressure. Kp = coefficient of passive earth pressure. L = socket length. LδM = length of equivalent fixed-end column consider- ing lateral deflection owing to moment. LδV = length of equivalent fixed-end column consider- ing lateral deflection owing to shear. LθM = length of equivalent fixed-end column consider- ing rotation owing to moment. LθV = length of equivalent fixed-end column consider- ing rotation owing to shear. Ls = nominal socket length. Lt = total travel distance along socket wall profile for roughness determination. M = bending moment. N = standard penetration test value. N60 = corrected N for field procedures corresponding to 60% hammer efficiency. Nc = bearing capacity factor. Ncr = bearing capacity factor. Nq = bearing capacity factor. Nγ = bearing capacity factor. Nφ = bearing capacity factor. OCR = overconsolidation ratio. P = axial load acting on a drilled shaft; load at rupture in a point load test. Pr = factored axial resistance. Pu = factored axial load. Pz = axial load on a deep foundation. Q = Tunneling Quality Index. Q' = modified Tunneling Quality Index. Qb = load transmitted to the base of a rock socket; ul- timate resistance at the socket base. Qc = compressive force applied to the top of a drilled shaft. Qi = intercept on the vertical axis (wc = 0) of axial load-displacement curve. QOC = Osterberg cell test load. Qs = total side resistance (force). Qt = total compressive load applied to the top of the shaft. REC = average percent recovery of rock core. RF = roughness factor. RMR = rock mass rating. RQD = rock quality designation. SRF = stress reduction factor. S = joint spacing. EQUATION SYMBOLS

103 S1 = slope of the initial portion of axial load-displace- ment curve. S2 = slope of the full-slip portion of axial load-dis- placement curve. Vc = nominal shear resistance provided by concrete. Vn = nominal shear resistance of reinforced concrete. Vp = compressional wave velocity. Vr = factored shear resistance of reinforced concrete. Vs = shear wave velocity; nominal shear resistance provided by transverse steel. ENGLISH LETTERS—LOWERCASE a = empirical constant in Hoek–Brown strength cri- terion for rock mass. b = empirical factor to account for effect of rough- ness on side resistance. c = rock mass cohesion; soil cohesion. cpeak = peak interface adhesion. cresidual = residual interface adhesion. cu = undrained shear strength. d = effective shear depth of reinforced concrete. ds = socket diameter. f = shear wave frequency (hertz). fc' = compressive strength of concrete at 28 days. fdes = design unit side resistance. fsu = ultimate unit side resistance. fy = yield strength of reinforcing steel. kir = dimensionless constant used in p-y curve criterion. krm = constant used to establish the overall stiffness of a p-y curve. mb = empirical constant in Hoek–Brown strength cri- terion for rock mass. n = ratio of rock mass modulus to uniaxial compres- sive strength of intact rock. p = lateral soil or rock reaction per unit length of foundation. p1 = limit pressure determined from a pressuremeter test. pa = atmospheric pressure. pA = horizontal active earth pressure. pL = limit normal stress. po = at-rest total horizontal stress. pur = rock mass ultimate lateral resistance. pult = ultimate lateral resistance of soil or rock mass. qu = uniaxial compressive strength of intact rock. qult = ultimate bearing capacity. qt = split tensile strength. r = radius of drilled shaft. rs = nominal socket radius. s = empirical constant in Hoek–Brown strength cri- terion for rock mass; vertical spacing of the ties or pitch of the spiral for shear reinforcement. sc, sγ, sq = shape factors used in bearing capacity analysis. sv = vertical spacing between discontinuities. td = aperture (thickness) of discontinuities. u = lateral displacement at the groundline of socketed shaft. w = distributed load along the length of the shaft. wc = axial displacement at the top of a socketed shaft. xr = depth below rock surface. y = lateral deflection of a deep foundation. z = depth below rock mass surface. zy = depth of yielding in soil and/or rock mass. GREEK SYMBOLS—UPPERCASE Δr = dilation or increase in shaft radius. Δr = mean roughness height. Δrh = average height of asperities. GREEK SYMBOLS—LOWERCASE α = ratio of design to ultimate unit side resistance; ratio of rock mass modulus to modulus of intact rock; empirical adhesion factor relating unit side resis- tance to uniaxial strength of intact rock. γ = total unit weight of rock or soil. γ ' = effective unit weight of rock or soil. δr = relative shear displacement between concrete and rock. δM = lateral deflection owing to moment. δV = lateral deflection owing to shear. ε = strain. υ = Poisson’s ratio. υc = Poisson’s ratio of concrete. υb = Poisson’s ratio of rock mass beneath the base of a rock socket. υr = Poisson’s ratio of rock mass. ηc = construction method reduction factor. ρ = mass density. ρs = ratio of spiral steel reinforcement volume to vol- ume of concrete core. σ'1, σ'3 = major and minor principal effective stresses. σ'h = horizontal effective stress. σn = interface normal stress; fluid pressure exerted by concrete at the time of placement. σp' = preconsolidation stress. σv = vertical total stress. σv' = vertical effective stress, τ = shear strength. τmax = shearing resistance at shaft-rock interface. θ = shaft rotation. θM = rotation owing to moment. θV = rotation owing to shear. φ = friction angle; resistance factor. φ' = effective stress friction angle. φpeak = peak interface friction angle. φrc = residual angle of interface friction between rock and concrete. φresidual = residual friction angle. ψ = angle of dilation.