Geotechnical Engineering Circular No. 9 Design, Analysis, and Testing of Laterally Loaded Deep Foundations that Support Transportation Facilities
Figure A P-y curves for soft clay with free water (a) static loading and (b) cyclic loading (after
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| Figure A P-y curves for soft clay with free water (a) static loading and (b) cyclic loading (after Matlock 1970). The required parameters to construct this p-y curve include profiles of the undrained shear strength labeled in various publications presenting p-y curves as c u or S u ), unit weight (γ), and the axial strain (ε 50 ), which occurs at 50 percent of the maximum principal stress difference as measured in a triaxial testing. The following steps can be used to construct the p-y curve for soft clay with free water (above water surface. Static Loading 1. Obtain profiles with depth of undrained shear strength (C u ), effective unit weight (γ′), and strain at 50 percent of maximum deviatoric stress as measured in a triaxial test (ε 50 ). Use recommendations made in Chapter 4. 218 2. Select pile/shaft diameter D. 3. Compute the ultimate resistance (p u ) of soil per unit length of pile. Use the smaller of the following values calculated as 𝑝𝑝 𝑢𝑢 = �3 + 𝛾𝛾 ′ 𝐶𝐶 𝑢𝑢 𝑘𝑘 + 𝐺𝐺 𝐷𝐷 𝑘𝑘� 𝐶𝐶 𝑈𝑈 𝐷𝐷 Equation A) 𝑝𝑝 𝑢𝑢 = 9𝐶𝐶 𝑈𝑈 𝐷𝐷 Equation A-2) where γ′ = average effective unit weight between the ground surface to the depth z under consideration, C u = undrained shear strength at depth z, D = diameter or width of pile/shaft, and J is an experimental parameter that depends on the clay consistency. Matlock (1970) recommended to use J = 0.5 for soft clay and J = 0.25 for medium clay. 4. Compute the deflection, y 50 , that occurs at 50 percent of the ultimate soil resistance as follows 𝑦𝑦 50 = 2.5𝜀𝜀 50 𝐷𝐷 Equation A) 5. Construct the p-y curve using the following relationship 𝑝𝑝 𝑝𝑝 𝑢𝑢 = 0.5 � 𝑦𝑦 𝑦𝑦 50 � 1 Equation A-4) This curve is delimited to p = p u for y ≥ 8y 50 Cyclic Loading For cyclic loading, follow the steps indicated below to construct the p-y curve shown in Figure Ab 1. For p ≤ 0.72 p u (i.e., for y / y 50 = 3) use Equation A to construct the first part of the p-y curve for cyclic loading. 2. Find the critical depth z r . According to Matlock (1970), the critical depth z r represents what is in reality a rather indefinite point of transition from a condition of incomplete vertical restraint to one where plastic flow is confined to horizontal planes. If γ’ and C u are homogeneous in the upper zone, z r can be calculated as 𝑘𝑘 𝑐𝑐 = 6𝐶𝐶 𝑈𝑈 𝐷𝐷 (𝛾𝛾 ′ 𝐷𝐷 + Equation A) If the γ’ and C u profiles are non-homogeneous, calculate z r by solving simultaneously Equations A and A at depths where the p-y curve is applied and using the corresponding soil properties at these depths. 3. If a depth z at which the p-y curves is applied results z ≥ z r , then use p = 0.72 p u for deformations y ≥ 3y 50 . In this case, the p-y curves for cyclic and static conditions coincide. 4. If the depth z at which the p-y curves is applied results z < z r , then calculate p as a line decreasing from p = 0.72 p u at y = 3 y 50 up to a value defined by 219 𝑝𝑝 = Equation A) at y = 15 y 50. For y ≥ 15y 50 , p remains constant as given by Equation Ab A P-Y CURVE FOR STIFF CLAY WITH FREE WATER (REESE ET AL. 1975) Reese et al. (1975) developed a criterion to be used for stiff clay with water based on field tests. Stiff clays are those with undrained shear strength (S u ) ranging from 1,000 to 2,000 psf). Figures A through A show the main characteristics the original and modified p-y curves under static and cyclic loading conditions. It must be recognized that the presence of free water does not necessarily translate in conditions below the groundwater table. In fact, the presence of free water refers to the submerged conditions of the pile that was tested during the experimental studies to develop the p-y curves. The tests used to develop the criterion for stiff clay in the presence of free water were performed using cyclic loading at a site of stiff fissured clay in a submerged condition. During the application of the cyclic loading, an annular gap developed between the soil and the pile after deflections at the ground surface of about 0.4 inch. The soil response was observed to rapidly degrade with multiple cycles of load due to this localized scour adjacent to the pile, and the criterion developed for static loading also exhibits significant strain-softening behavior. This criterion will result in a substantial reduction in mobilized soil resistance compared to that of Welch and Reese (1972), which does not include such strain softening. This reduction is only appropriate for situations where stiff clay is exposed to free water at or near the ground surface, where degradation similar to that observed in the load test experiment can occur. In conditions where the groundwater surface is at depth and free water is not present at or near the ground surface, the Welch and Reese criterion is more appropriate, even below groundwater. Similarly, stiff clay strata at depth below a sand stratum would normally not be subject to degradation due to free water (unless scour removed the overlying sand. |