COM624P-Based Drilled Shaft Torque and Lateral Load Analysis Method Christopher R. Byrum stiffness with low deflections. The wide grade beam gives the foundation a high ultimate torsion capacity and stiffness for cantilevertype sign torsion loading of the anchor bolt array. MDOT decided that as part of its new foundation system for large freeway signs, standard foundation designs consisting of single drilled shafts with anchor bolts at the ground surface would be developed for the sign engineer’s toolbox. The required depths of penetrations for the drilled shaft foundations depend on the size of the sign structures and the type of soil present at the site. For a single drilled shaft foundation, the size and complexity associated with the large excavation and formwork for the older style large grade beam foundation are greatly reduced, because a single upper surface casing can be used as the “form” for construction. However, the new single drilled shaft foundation designs extend much deeper and are larger in diameter than the old drilled shafts that were used. This requires larger and more-powerful drilled shaft construction equipment at the site. A single drilled shaft philosophy is structurally more flexible both laterally and in torsion, compared with the previous more massive grade beam–block type of foundation. The estimation of torque capacity for single drilled shafts was the most challenging portion of the designs for the new standard drilled shaft foundations for MDOT. This paper describes how the torque capacity was estimated for the drilled shaft foundations, while combined with large lateral shear and moment loads. What is new about this approach is that it uses the drilled shaft estimated lateral load response from the computer software LPILE/COM624P (1, 2) as the basis for the torque capacity analyses. Large cantilever-type overhead freeway signs are often supported by a single drilled shaft foundation. Under high wind loads, the cantilever arm and sign panel develop significant torque loading that is distributed to the anchor bolt array cast into the top of the drilled shaft. This torque load is applied to the drilled shaft at approximately the same time as the large lateral load and moment developed by the wind loading. An analysis procedure was used to predict the torque capacity of drilled shaft foundations during the high lateral load condition. The analysis method starts with a typical COM624P p-y–type analysis for the design lateral shear and moment at the anchor bolts. The resulting lateral soil pressures estimated along the drilled shaft sidewalls present during the lateral loading are used to estimate whether voids will be present along the drilled shaft sidewall during torque loading. The estimated drilled shaft sidewall pressures and shear strengths for areas remaining in contact are used to estimate the torque capacity of the foundation. Some applications in different soil profiles are presented. This method was used as part of the development of a standard array of drilled shaft foundations for different soil conditions for standard cantilever-type freeway sign structures used by the Michigan Department of Transportation. The Michigan Department of Transportation (MDOT) updated its standard details for large overhead-type freeways sign structures and foundations during 2004 and 2005. The previous MDOT standard cantilever overhead freeway sign foundations consisted of an upper reinforced concrete grade beam, approximately 7 to 8 ft (2.1 to 2.4 m) deep, 3 ft (0.9 m) thick, and 10 to 15 ft (3 to 4.6 m) wide, resting on a drilled shaft or two drilled shafts, which extended from below the grade beam to depths up to approximately 15 ft (4.6 m). During construction of the old type of foundation, a relatively large excavation was performed to the bottom of grade beam. The excavation was primarily needed to enable formwork construction for placing the upper grade beam reinforcement and concrete. The drilled shaft was constructed starting at the bottom of this excavation. Often, to have this large excavation adjacent to a roadway with traffic, driven sheeting or even cofferdams were needed to support adjacent traffic and utilities and manage groundwater. In more urban areas, dense utilities often make it impractical or very difficult to perform such an excavation. Special reaching-type drilled shaft construction equipment was needed to reach down into the grade beam excavation and perform the drilled shaft excavation. Once in service, the old style footing has high mass, high soil torque resistance, and high lateral LATERAL LOAD ANALYSIS METHOD The analysis of the drilled shaft foundation soil-structure interaction under lateral loading was performed with the computer program LPILE/COM624P. This software was initiated as the analysis software COM624P developed in cooperation with the FHWA. This software allows the lateral load analyses of drilled shafts simulating effects from soil yielding and peak-to-cracked flexural rigidity of shafts, and it allows simulation of loss of support along the sides of drilled shafts. Scaled centrifuge-based research in the State of Florida regarding combined torque and lateral loading of drilled shafts has shown that the ultimate lateral capacities of drilled shafts with high torque are less than the ultimate lateral capacities of drilled shafts without torque for similar sizes and soil profiles (3). In other words, the presence of the torque reduces the lateral resistance available for the drilled shaft. This interaction is not currently well studied or understood. Overall lateral capacity reductions of up to approximately 50% were observed in the Florida centrifuge-based tests when torque was present. Without torque, the soil shear bands on each side of the Soil and Materials Engineers, Inc., 43980 Plymouth Oaks Boulevard, Plymouth, MI 48170–2584. Transportation Research Record: Journal of the Transportation Research Board, No. 1975, Transportation Research Board of the National Academies, Washington, D.C., 2006, pp. 28–38. 28 Byrum -1000 -500 Soil Reaction lb/in. 0 500 0 1000 1500 50 100 Shaft Depth, in. passive soil wedge in front of the laterally loaded drilled shaft were roughly equal in magnitude. When torque twists the soil socket and combines with lateral loads, the soil shear band magnitude on one side of the distorted passive wedge is increased, resulting in soil shearing at reduced lateral loads. On the basis of the previously noted lateral capacity reductions of up to approximately 50% observed in the Florida centrifuge tests for combined torque and lateral loads, the author used a minimum factor of safety for LPILE/COM624P-based drilled shaft designs for lateral loads of at least 2.0 when high torque is present. This means that the drilled shaft computer models within LPILE/COM624P, which cannot consider torque, should be large enough and deep enough to handle at least two times the maximum service lateral loads for the drilled shaft while maintaining reasonable service load deflections and stress. To have no predicted movement of the bottom of the drilled shaft or toe (i.e., fully fixed end), considerable extra shaft depth would be needed compared with LPILE/COM624P-based minimum depths determined for the sign foundations in the MDOT study. Key lateral loading design issues for that study became the amount of toe movement that is acceptable under the maximum service loading conditions and how short the drilled shaft can be. One design criterion used for the drilled shafts was based on index values for apparent permanent set for the top and toe of the drilled shafts. Permanent set, or a permanent lateral translation and rotation, of the sign foundation can occur because of plasticity of soils, transition of the steelreinforced shafts from uncracked flexural rigidity to cracked flexural rigidity on one side of the shaft versus the other, and repeated loading friction damping hysteretic effects. COM624P models typically show strain-softening behavior, and permanent set index values can be calculated from the nonlinear response curves. The largest permanent set index values were associated with the LPILE/COM624P soft clay soil p-y model. The nonlinearity of the predicted top of shaft deflection curves for these designs is often related to the drilled shaft transitioning from uncracked to reduced cracked flexural rigidity and may be mostly recoverable. The steel within the shaft is still within its elastic range. As load increases, the shaft is softening in flexure from the initial concrete cracking on the tension side of the shaft, resulting in the nonlinear deflection trend. Figure 1 shows typical LPILE/COM624P results for lateral soil reaction pressures along the full shaft length for a typical design for service load factors of 0.5, 1, 1.5, and 2. This general type of data, as shown in Figure 1, for the service loads (load factor of 1.0) is used as the basis for the drilled shaft torque capacity analysis described later in this paper. For a load factor of 0.5, some shaft cracking was predicted but with only a partial loss of shaft flexural rigidity from cracking. At a load factor of 1.0, the shaft had cracked flexural rigidity for a small portion of the length centered at approximately 130 in. (3.3 m) deep with reduced rigidity extending approximately 280 in. (7.1 m) deep. For load factors of 1.5 and 2.0, the shaft is at its fully reduced cracked section flexural rigidity to depths of approximately 250 and 290 in. (6.35 and 7.37 m), respectively. The toe pressure trend is roughly linear through the service load level, and then pressures increase significantly. This general philosophy of allowing some apparent toe deflection, but requiring toe reaction pressures to be roughly linear through the service load range, was used for the LPILE/COM624P analyses to establish the minimum shaft lengths for the lateral loading. At approximately the same time the shaft is transitioning to its reduced cracked flexural rigidity, passive soil wedge yielding is estimated to be propagating deeper and deeper along the front of the drilled shaft, further reducing stiffness of the 29 150 200 250 300 2884 350 400 1729 FIGURE 1 LPILE/COM624P predicted lateral soil reaction pressures for full length of typical cantilever sign drilled shaft foundation for load factors of 0.5, 1, 1.5, and 2. system and forcing a greater percentage of the load to be taken by the toe zone. So just about at the design service load (load factor = 1.0), some softening of the upper portion of the drilled shaft soil system is starting to shift load downward toward the toe. ANALYSIS METHOD FOR DRILLED SHAFT TORSION RESISTANCE When a cantilever sign is subjected to a large wind gust in addition to the lateral loads as just described, significant torque is applied to the sign anchor bolt array. The torque tends to twist the shaft in place and is resisted by the interface zone between the drilled shaft and the soil surrounding the shaft. The physical properties of the zone between the drilled shaft and the surrounding soil can vary widely depending on soil types and installation methods. In general, the soils immediately surrounding the drilled shaft are disturbed initially by excavation of the drilled shaft hole. The degree and radial outward dimension of disturbance depends primarily on the soil type, the method of excavation used, and the groundwater conditions. Another major factor that affects the character of the zone between the drilled shaft and the surrounding soil is whether specialized drilling fluid is used within the shaft excavation. Some drilling fluids can leave what is referred to as “mud-cake” along the sidewalls of the drilled shaft excavation. Another major factor that will affect a drilled shaft’s torque behavior is whether a permanent steel casing is in place. The shaft interface for drilled shafts with permanent casing is smooth steel whereas the interface without a casing is a more roughened concrete surface. The torsion resistance of drilled shafts currently is not well studied, and there is in general a lack of mechanistic soil–structure interactiontype design methods for drilled shafts with combined low axial loads and high torque, moment, and lateral loads. To evaluate the torque capacity of drilled shafts with large lateral loading, a finite difference– type computer program was initiated as part of the MDOT study to perform torque capacity estimates on the basis of LPILE/COM624P 30 Transportation Research Record 1975 phenomenon had to be considered in the torque capacity estimates for cantilever-type freeway signs subject to large lateral loads and moments. The design of steel sheet pile retaining wall systems has evolved relations for allowable adhesion and friction between smooth steel sheeting and soils. Similar adhesion and friction would be expected to develop along vibrated or driven smooth steel permanent casings for drilled shafts where soils are excavated from within the steel casings. These relations use a more generic c-ϕ–type expression than the α–β method described, but they are the same. The β value is the effective K0tan(δ) for the interface. The more generic c-ϕ–type form of the α–β method is as follows: soil resistance versus depth results for the lateral load analysis (4). To estimate the torque capacity of a drilled shaft, assumptions regarding the level of friction and adhesion present surrounding the drilled shaft, or the horizontal shear strength of the interface zone, must be made. Some of methods available for estimating the sidewall interface strength are briefly described here. The α and β methods are typically used for the axial load design of drilled shafts and are described in FHWA-IF-99-025, Drilled Shafts: Construction Procedures and Design Methods (5). The general form of this relation for the maximum unit side resistance, fmax, in force per unit area along the sides of the drilled shaft is as follows: Typically for wet–clayey soils with undrained interface behavior, For clay soils, fmax = αsuc fmax = αsuc Typically for drier–sandy soils with a drained interface behavior, For sand soils, fmax = βσv fmax = K0tan(δ) σv where α β β σv z N = = = = = = where 0.55 for clay shear strength suc < 1.5 (atmospheric pressure), (N60 /15){1.5–0.254(z)0.5} for N < 15, 1.5–0.254(z)0.5 for N > 15 (1.2 > β > 0.25), soil overburden pressure, depth below ground surface in meters, and standard penetration test blow count values. α = multiplier for allowable adhesion based on estimates of suc, δ = sliding friction angle between the shaft surface and the soil, and K0 = lateral earth pressure coefficient. As the first step in this new torque capacity analysis method, the LPILE/COM624P runs are performed for the service lateral loading and moment at the top of shaft. The resulting lateral soil resistance values determined for the service loads are used as the starting point for the torque analysis. The soil overburden pressures are then superimposed onto the soil reaction pressures from LPILE/COM624P. The soil reaction pressures are considered equal magnitude and opposite sign on one side of the shaft versus the other. At any depth reporting a negative soil reaction pressure being greater in absolute magnitude than the positive overburden pressure, a gap is numerically generated on that side of the drilled shaft with no adhesion or friction. A description of the math involved in the torque capacity analysis method follows in Figures 2 through 9. The relation for β shows that for standard penetration testing (SPT) N-values less than 15 blows per foot (bpf ), allowable side friction factors linearly drop toward zero and all sands with SPT greater than 15 bpf have the same β factor at a given overburden pressure. The β method gives low allowable sidewall resistance values for the low SPT N-value sands or the loose and very loose sands. Notice how the soil overburden pressure, actually depth below ground surface, z, is typically used to estimate the allowable axial load–type side friction for drilled shafts in sand soils. For drilled shafts subject to high lateral loads, the soil pressure along the sidewall during torque loading can be much greater than the overburden on one side of the shaft, whereas a gap may be formed on the other side of the shaft. This TTop Right Side: IF M Left Side P0 (z) + PR (z) > 0 THEN Right Side Sidewall Resistance = α(z)suc + β(z)[P0 (z) + PR (z)] V z P0 (z) ELSE Assume Void Formation, loss of contact PR (z) Left Void Left Side: IF -P0 (z) P0 (z) - PR (z) > 0 THEN Sidewall Resistance = α(z)suc + β(z)[P0 (z) + PR (z)] ELSE Assume Void Formation, loss of contact Right Void FIGURE 2 P0 = overburden pressure, PR = L-pile lateral reaction α and β are adhesion and friction factors for soil/rock Simplified drilled shaft sidewall contact assumptions. Byrum 31 Relative Sidewall Contact Pressure Magnitudes Large δ Small δ VOID (b) (a) (c) FIGURE 3 Current simplification regarding shaft sidewall gap formation: (a) overburden only (full perimeter); (b) overburden small lateral loading, reaction < overburden (full perimeter); and (c) overburden large lateral loading, reaction > overburden (only half of perimeter is assumed in contact). P0 (z) + PR (z) Right Side A simplified linear average is used: P0 (z) Left Side P0 (z) Right Side Average = ½{P0 (z) + [P0 (z) + PR(z)]} = ½[2P0 (z) + PR (z)], >0 P0 (z) - PR (z) Left Side Average = ½{P0 (z) + [P0 (z) + PR (z)]} = ½[2P0 (z) - PR (z)], >0 FIGURE 4 Assumption for average pressure on each side of shaft during torque loading. Shaft Rotation, θ A sidewall rotation slip is required to mobilize the peak sidewall resistance available on the shaft ƒ(θ) perimeter. Slip beyond 0.1 in. causes sidewall resistance to reduce to a residual level by 0.2 in. It is like a lateral p-y curve but it is a torsion ƒ-θ curve. ƒ(θ) R Current simplified linear function Mobilization % (z) 100% Residual% 0 0.1 in. 0.2 in. Rθ(z) Sidewall Slip(z) = Rθ(z) FIGURE 5 Sidewall shear mobilization assumption. 32 Transportation Research Record 1975 TTop θ Moment Arm ½ Shaft Perimeter Left Side Allowable Sidewall Resistance Right Side z R Tsoil (z,θ) = ∫ RπRβ(z)[PRight (z)]Mob%(R,z,θ)dz z 0 z + ∫ RπRβ(z)[PLeft (z)]Mob%(R,z,θ)dz 0 PRight z + ∫ RπRα(z)[suc-Right (z)]Mob%(R,z,θ)dz 0 PLeft z + ∫ RπRα(z)[suc-Left (z)]Mob%(R,z,θ)dz 0 D z = ∫ tsoil (R,z,)dz 0 FIGURE 6 General theory used for soil torque resistance. To demonstrate the sidewall loss of contact concept, Figure 10 shows results for the total level of mobilized torque resistance versus depth predicted for a cantilever sign foundation loading for three different clay strengths, identified as low [suc = 400 psf (19 kPa)], medium [suc = 1,000 psf (48 kPa)], and high [suc = 2,000 psf (96 kPa)]. As expected, a shorter shaft is required for the stronger clay soil because higher levels of lateral soil resistance are available. A key observation present in Figure 11 is the effect of apparent gaps along the sides of the drilled shafts on overall torque resistance mobilized. For the low-strength clay, no gaps along the sides of the shaft are predicted during the lateral load response, and a smooth continuouslooking torque mobilization versus depth plot results. This means that sidewall friction is predicted to be available around the full perimeter of the shaft for its full depth and that overburden pressures are greater than the mobilized soil resistance pressures. For the medium-strength clay, a gap related to lateral displacement is predicted along one side of the drilled shaft extending to a depth of approximately 160 in. (4.06 m), and full contact around the perimeter is estimated below that depth. The result is that the mobilized torque resistance shown above a depth of approximately 160 in. (4.06 m) is calculated to be available only on one side of the shaft and, therefore, is shown as approximately half of the magnitude of the resistance available below 160 in. (4.06 m). For the higher strength clay model, loss of contact gaps are predicted near the top of the drilled shaft and near the bottom of the drilled shaft caused by large drilled shaft toe pressures. This is because of the higher soil reaction pressures available in the stiffer clay, which can be much larger than the overburden pressures present on the drilled shaft sidewalls, even down at the toe elevation. The integrals of the three torque responses shown in Figure 10 with respect to depth, or the areas under (to the left of) the curves, are the estimates of total torque mobilized for the drilled shafts. Each of the three cases shown had the same estimated torque capacity. The drilled shafts analyzed for Figure 10 were 72-in. (1,829-mm) diameter shafts. To convert the in.-lb/in. values shown to psi of shear stress present along the sidewall, first divide out the torque moment arm, which is the shaft radius; this results in units of lb/in. Then divide out the shaft perimeter, or half perimeter if gaps are estimated on one side, to get psi. So for the low strength clay model reaction shown, the mobilized sidewall resistance in psi is roughly 10,000/ [36π(72)] = 1.23 psi, or approximately 175 psf (8.4 kPa). The shear strength assumption for the low strength clay soil in the model is 400 psf (19 kPa). Therefore, the minimum α or adhesion factor needed at the service torque level for the low strength clay drilled shaft with the depth shown must exceed 175/400 = 0.44 for a factor of safety of 1.0. Because 0.55 is typically the maximum value allowed for the β factor, it could be said that the overall factor of safety for torque capacity is estimated at approximately 0.55/0.44 = 1.25 for the LPILE/COM624P-based minimum shaft length required to resist the lateral loads using that method. For the high strength clay model, the mobilized sidewall adhesion level in the middle of the shaft where both sides are in contact is roughly 23,000/[36π(72)] = 2.8 psi, or approximately 400 psf (19 kPa). The soil shear strength assumption in the higher strength clay model is 2,000 psf (48 kPa). Therefore, the α or adhesion factor needed for the high strength clay model shown would have to be at least 400/2,000 = 0.2 for a factor of safety of 1.0. The overall factor Shaft Sidewall Slip = 0.2 in. shown for Residual% = 100% Shaft Sidewall Slip = 0.1 in. ƒmax ƒmax at R/2 R R ƒresidual at R (a) (b) At Slip = 0.1 in. TBase ≈2π 2 3 R 1 2 R ƒmax At Slip ≥ 0.2 in. TBase ≈2π 3 R 4 FIGURE 7 R ƒmax + ƒresid 2 2 Base torque mobilization assumption. R + 1 R 1 3 2 2 ƒmax Byrum 33 TTop Left Side z Right Side θ= TL J= JG Soil 1 θ(z) = πR 4 G= 2 E 2(1 + μ) z 1 GJ tSoil (R, z, θ) ∫ TShaft (z)dz 0 Soil 2 For the drilled shaft torque problem; Tshaft (z)dz = TTop –Tsoil (z,θ) Soil 3 z Tshaft (z) = TTop – ∫ tSoil (R, z,θ)dz 0 Soil 4 D FIGURE 8 TSoil units are in.-lb, and tSoil units are in.-lb/in. Basic concrete shaft torsion equations. Δθi+1 Shaft Element LRi Node i RRi ΔL Node i +1 R LRi+1 Ti+1 = Ti – R(πR) RRi+1 Mobilized Sidewall Resistances LRi + LRi+1 RRi + RRi+1 + ΔL 2 2 θi+1 = θi – Δθi+1 Δθi+1 = Ti L = JG ΔLR(πR) JG LRi + LRi+1 RRi + RRi+1 + ΔL 2 2 A top-down solution approximation is used. The rotation is set at the top of shaft (nodei) and the soil torque is calculated for the first element, based on the top rotation. Then the angle change and sidewall slip for the next node are calculated based on the torque level in the first element: Slipi = Rθi Slipi+1 = R(θi – Δθi+1) Mob%i = mobilization % for Slipi FIGURE 9 LRi = β (2P0 – PR)i RRi = β (2P0 – PR)i 2 2 + α(suc)i Mob%i + α(suc)i Mob%i Turning the integrals into a finite difference problem. 34 Transportation Research Record 1975 0 5000 Torque Level, in.-lb/in. depth 10000 15000 20000 25000 0 100 Low Strength Clay Medium Clay High Clay gap Depth, in. 200 gaps 300 400 500 FIGURE 10 Soil torque resistance predictions for cantilever sign foundation loading in low-strength clay [c 400 psf (19 kPa)], medium-strength clay [c 1,000 psf (48 kPa)], and high-strength clay [c 2,000 psf (96 kPa)]. of safety would be approximately 0.55/0.2 = 2.75 for torque capacity if one uses the β method allowable side resistance factor of 0.55. A drilled shaft that just barely meets both the torque and lateral load minimum factors of safety for a given embedment can be considered optimized for both diameter and embedment depth. A design with excess torque capacity probably has a relatively large diameter and short embedment. 0.005 0.015 The author recently had an opportunity to perform site-specific designs for cantilever sign foundations at a site with bedrock close to the ground surface. One of these design case studies is provided here so others can compare this method to other methods being developed to perform this type of analysis. The soil profile consists of approx- Shear, kip Moment, in.-kip Deflection, in. -0.005 0 DESIGN EXAMPLE IN SHALLOW ROCK 0.025 -1000 0 1000 2000 3000 -150 -100 -50 0 0 0 20 20 20 40 40 40 60 60 60 100 80 100 120 120 140 140 Depth, in. 80 Depth, in. Depth, in. Very Loose Fill Silty Clay 80 100 120 140 Weak Rock 160 160 160 180 180 180 FIGURE 11 Results for initial LPILE/COM624P analysis, used as basis for torque capacity analysis of foundation, for the example problem having a short drilled shaft foundation socketed into rock. 50 Byrum 35 sidewall slip on the basis of the simplified linear mobilization function used. The maximum slip value shown of just below 0.02 in. (0.5 mm) indicates that approximately 20% of the ultimate sidewall capacity is mobilized, whereas 100% mobilization is currently assumed at 0.1 in. (2.5 mm) for all soil or rock types. In reality, different soils and rocks will mobilize at different rates, but the author is not aware of good data for lateral shear mobilization rates being available and the time and resources needed to consider this as part of this study were not available. The middle plot shows the calculated sidewall torque mobilization magnitude in units of in-kip per in. It is the integral of this function with depth, plus the base torque mobilized, that is the total soil–rock socket torque resistance mobilized. The integral value is forced to be roughly equal to the applied torque loading at the top of the shaft less the mobilized base torque, using an iterative routine. The right plot shows the distribution of torque magnitude within the drilled shaft versus depth. For this analysis, the torque at the bottom of the shaft was set to zero. If desired, a torque resistance and mobilization function for base resistance can be used, as described previously. The right plot is the service load top torque magnitude minus the integral of the middle plot with respect to depth. Figure 14 shows the drilled shaft concrete shear stress estimates for the analysis. This procedure combines estimates of both the torque shear stress and the LPILE/COM624P-based lateral shear stress versus depth for the drilled shaft concrete. In general, the drilled shaft internal shear stress analysis estimates the shear stress on the inner core of drilled shaft PCC inside the reinforcing steel cage, ignoring the cover concrete outside of the steel. Drilled shaft designs generally use a minimum steel reinforcement ratio, provided the estimated concrete shear stress just around the reinforcing steel is below the American Concrete Institute (ACI) limiting shear stress value. Reinforcing steel content is increased as shear stress estimates approach and get larger than the ACI limiting concrete shear stress levels. Figure 15 shows the mobilized torque capacity versus top of shaft sidewall slip magnitude for two rock socket models. The stiffer rock socket was modeled using an effective β factor of approximately 0.78, which would simulate a drained smooth interface with a high contact friction angle and a high lateral earth pressure coefficient. This high β value is intended to represent a clean, cored sidewall with imately 5 ft (1.52 m) of mixed sand, clay, and topsoil fill overlying silty clay with some sand extending to approximately 8 ft (2.44 m) deep. Groundwater was encountered at approximately 8 ft (2.44 m) deep. An SPT N-value in the clay was 13 bpf, with the moisture content at approximately 20%. From approximately 8 ft (2.44 m) deep to approximately 15 ft (4.57 m) deep, a weathered dolomite rock with frequent fractures was encountered, overlying fresh dolomite with occasional fractures. Two core samples from the weathered rock zone were tested for unconfined compressive strength and had strengths of 5,280 psi and 12,780 psi (36.3 MPa and 87.9 MPa). The rock quality designation values were 38% and 63%, and recoveries were 70% and 90%. The design begins with a typical LPILE/COM624P analysis to determine the minimum rock socket depth required for the lateral loading on the shaft. The estimated maximum service level loading at the top of shaft includes a 4,686-lb (2,125-kg) axial load, an applied moment of 1,943,352 in.-lb (22,397 kg-m), a horizontal shear of 6,437 lb (2,919 kg), and an applied torque of 1,158,408 in-lb (13,350 kg-m) (Michigan DOT–Type D Cantilever Sign Foundation Loads). The shaft diameter is 42 in. (1,067 mm). Concrete modulus of elasticity is assumed at 3.5 million psi (24,080 MPa). Figure 11 shows the LPILE/COM624P lateral load analysis results for the maximum service load condition. This plot shows that most of the load from the sign structure is distributed down to the rock socket portion of the shaft with large lateral soil response between approximately 96 and 140 in. (2.44 and 3.56 m) or the upper 4 ft (1.22 m) of the rock socket. On the basis of the analysis shown, a 6-ft (1.83-m) deep rock socket was recommended as the minimum shaft rock socket depth required for that site, which is just enough to provide fixed toe behavior for the design lateral loading. Figure 12 shows the lateral soil resistance from LPILE/COM624P for the rock socket drilled shaft example. In addition, the overburden pressures are shown—both positive and negative—to imply the “right side” and “left side” of the drilled shaft. The heavy solid lines represent the estimated peak pressures on the right and left sides of the drilled shaft. These left and right side pressures are used for the torque capacity analysis. Notice the areas of zero (negative) contact pressure behind areas of the drilled shaft that are heavily loaded. Figure 13 shows the results of the torque capacity analysis for the service loading condition. The left graph shows the estimated lateral -160 -120 -80 Sidewall Pressure, psi -40 0 40 0 80 120 160 20 Left Sidewall Pressure -1[P0 (z ) - PR (z ), >0] 40 Depth, in. 60 Right Sidewall Pressure P0 (z) + PR (z ), >0 80 100 120 140 PR (z ) P0 (z ) PR (z) 160 180 FIGURE 12 Plots showing overburden pressures, LPILE/COM624P reaction pressure, and assumed maximum contact pressures on each side of drilled shaft during torque loading. 36 Transportation Research Record 1975 Sidewall Torsion Level, in.-kip/in. Sidewall Slip, in. 0.005 0.01 0.015 0.02 0 10 20 0 30 0 20 20 20 40 40 40 60 60 60 80 80 80 100 100 Depth, in. 0 Depth, in. 0 120 120 140 140 140 160 160 160 180 180 180 FIGURE 13 500 100 120 Solution for torque behavior of drilled shaft and stiff soil–rock socket at maximum service torque load. 0 50 Shaft Concrete Inner Core Shear Stress, psi 100 150 200 250 0 20 40 60 Depth, in. Depth, in. 0 Shaft Torsion Moment, in.-kip 80 100 120 140 160 Torsion Shear Horizontal Shear Total Shear 180 FIGURE 14 Estimates of lateral shear stress, torque shear stress, and combined shear stress at outer edge of inner PCC core near reinforcing steel, showing high shear stress in upper portion of rock socket. 1000 1500 Mobilized Torque, in.-kip Byrum 37 Soil Torque Capacity exceeds 6000 in.-kip Rock Socket β = 0.78 3500 3000 Combined Shaft Shear Stress at Max Service Load = 160 to 200 psi 2500 2000 1500 Max. Service Load 1000 For Rock Socket β = 0.25, Soil Torque Capacity about 2870 in.-kip 500 0 0 0.01 0.02 0.03 0.04 0.05 Sidewall Slip at Top, in. FIGURE 15 Estimated torque capacity mobilization for the two cases: a clean rock socket and a disturbed rock socket, both having drained behavior. good contact. The weaker rock socket model is based on a β factor of approximately 0.25, which would represent a sand soil–type contact friction angle of approximately 22° with an earth pressure at-rest–type lateral pressure coefficient. This low β value is intended to represent a thin layer of drained weak soil sediment or mud-cake between the concrete and the rock socket, left over from placement effects or repeated load pumping and erosion effects along the side of the shaft. The horizontal dashed line in the plot is the service load torque magnitude at the top of shaft. The drilled shaft cross section for this example is estimated to be near the ACI limiting shear stress near the reinforcing steel, in the range of 160 psi to 200 psi (1,100 kPa to 1,376 kPa) for the maximum service load level. If larger wind loads are applied to the rock socket foundation model, this model predicts shaft concrete stress failure in combined torsion and lateral shear at the top of the rock socket before soil–rock socket sidewall shear failure. The soil–rock socket torque capacity is more than adequate in this case, even for the assumption of a thin disturbance zone around the drilled shaft having an effective angle of internal friction of only 22°. This type of analysis revealed a key behavior for short rock socket drilled shafts for freeway-type cantilever sign structures. Because of the high lateral pressures on the rock socket sidewall during the torque loading, a sort of “friction lock-up” behavior for torque resistance was predicted, even for the low friction assumption along the shaft sidewall in the weak socket model. If one were to assume a low sidewall β factor and did not account for the estimated high sidewall pressure during loading, torque capacity calculations would indicate a much deeper drilled shaft would be needed, to resist the torque loading. In general, it can be said that the previous design has excess soil–rock torque capacity. However, the drilled shaft length and cross section are both optimized (about as small as allowable) for the design lateral loads. SUMMARY AND CONCLUSIONS This paper presents a simplified mechanistic soil-structure interaction analysis method for design of drilled shaft foundations subject to combined large lateral and twisting torque loads. Large cantilever arm–type overhead freeway signs are structures that develop this type of combined large torque and lateral load on their foundations. During the large lateral load condition, the drilled shaft sidewall pressures can be large on one side of the shaft, and there may be voids or loss of contact on the other side of the shaft. Drilled shaft torque capacity relies on sidewall contact pressures and shear strengths. The behavior of drilled shafts and the surrounding soils under combined large lateral loads and torque loading is complex and currently is not well understood. Recent centrifuge testing in the State of Florida, simulating this combined load condition, revealed that the interaction between torque magnitude and drilled shaft lateral response is significant. Drilled shafts subjected to large torque loading were found to have up to 50% lower ultimate lateral load capacity than shafts without torque loading. The analysis method presented herein indirectly simulates the combined torque and lateral load interaction using a simplified mechanistic finite difference–type procedure. The method developed is similar in concept to the lateral load analysis routine used within COM624P and the new torque load analysis method is linked directly to the COM624P computer output. Where the LPILE/COM624P analysis uses p-y curves (shaft sidewall pressure versus lateral deflection) to simulate the lateral load response mobilization, the torque capacity estimates described here use a concept called f-θ curves (shaft sidewall friction/adhesion versus sidewall slip) to simulate sidewall torque resistance mobilization. The torque capacity model could be intimately linked to LPILE/COM624P analysis in many ways because it shares a similar analysis format. Because of budget and time restraints for this project, many simplifying assumptions were made to finish the project on time and within budget. Theoretical refinements and empirical calibrationtype refinements based on instrumented test shafts are needed. The key areas that need verification and further evaluation to improve the model are highlighted as follows: 1. Gap formation and loss-of-contact areas. The current model uses only the overburden pressures and the lateral reaction pressures to estimate whether a gap is formed. More complex relations for different soil and rock types and consistencies could be developed. The rock example provided here indicates that in addition to sidewall pressure, drilled shaft lateral deflection magnitude obviously should be included in the gap prediction logic. Gaps were predicted for the rock socket example, even at very small lateral deflections caused by high sidewall pressures, much greater than overburden pressures, during lateral loading. The sidewall roughness profile also would affect this behavior. 2. Layered elastic half-space torque distortion. This method does not include an estimate for the elastic distortion of the earth surrounding the drilled shaft embedment. This mostly recoverable elastic distortion would occur simultaneously with sidewall slip and would be superimposed onto the sidewall slip values calculated with the sidewall shear mobilization f–θ function. In soil profiles with both soft and hard layers, the elastic effect may be significant with respect to sidewall torque shear mobilization. The elastic distortion of the socket may be orders of magnitude larger than the sidewall slip related rotation values in some cases. Therefore, total shaft rotations could be much higher than indicated when looking only at sidewall slip. Only the sidewall slip is addressed in this analysis procedure. 3. Sidewall resistance mobilization f–θ curves. The current mobilization function is a simplified piecewise linear function simulating a peak value at 0.1 in. (2.5 mm) of sidewall slip, and transition to a residual value at 0.2 in. (5 mm) of slip. More realistic sidewall torque mobilization curves could be developed for various soil and rock types and consistencies. For example, adhesion-type resistance may mobilize much faster than friction-type resistance. 4. α and β factors for torsion resistance. The current guides for α and β are based primarily on the vertical mobilization of sidewall resistance under axial loading. Future guides regarding horizontal mobilization may or may not be similar. 38 5. “Cracked shaft” torsion constants. This method did not attempt to reduce the shear area available on the drilled shaft cross section for areas of the drilled shaft predicted to have cracked section bending behavior with reduced flexural rigidity during torque loading. This concept needs to be further considered and combined with a design envelope for combined horizontal shear and torque shear for these types of drilled shafts with very small compressive stresses but large shear and bending stresses. The current software uses a 34-node, 33-element shaft model programmed in spreadsheet software. The initial LPILE/COM624P analysis is always set up to generate 34-node summary tables for each lateral load case, and the results table for the service load condition is cut-and-pasted into the spreadsheet and a generic solver is used to perform iterations and force convergence of the torque capacity solution. The spreadsheet program can be customized on a case-by-case basis to handle any type of base and sidewall torque mobilization functions, different sidewall contact assumptions, and site-specific factors such as variable shaft diameter and soil layers. Transportation Research Record 1975 REFERENCES 1. Reese, L. C., S. T. Wang, W. M. Isenhower, J. A. Arrellaga, and J. Hendrix. Computer Program LPILE Plus Version 4.0 User’s Guide. Ensoft Corporation, Austin, Texas, 2000. 2. Wang, S. T., and L. C. Reese. COM624P-Laterally Loaded Pile Analysis Program for the Microcomputer, Version 2. FHWA-SA-91-048. FHWA, U.S. Department of Transportation, 1991. 3. McVay, M. C., R. Herrera, and Z. Hu. Determination of Optimum Depths of Drilled Shafts Subject to Combined Torsion and Lateral Loads Using Centrifuge Testing. Florida DOT Report BC354-09. University of Florida, Gainesville, 2003. 4. Byrum, C. R., and T. H. Bedeni. Geotechnical Design for MDOT Standard Plan Drilled Shaft Foundations for Overhead Freeway Signs: MDOT JN 78573. Project No. PP46913. Soil and Materials Engineers, Inc., Plymouth, Mich., 2004. 5. O’Neill, M. W., and L. C. Reese. Drilled Shafts: Construction Procedures and Design Methods. FHWA-IF-99–025. FHWA, U.S. Department of Transportation, 1999. The Foundations of Bridges and Other Structures Committee sponsored publication of this paper.

1/--страниц