The piles are typically rigidly connected to the integral abutments, and so are considered to be fixed-ended. However, as a first step in investigating differences in results obtained using the LPILE and Basu analyses, a simple free-ended pile is investigated. A lateral force (F) of 40 kN and a moment (M) of 40 kN.m are applied separately at the pile head and the resulting pile deflection profiles and soil-pile lateral and rotational stiffnesses from the wo analyses are compared. The Basu analyses are based on the three different sets of soil parameters shown in Tables 3-2 (a) and (b). The pile boundary conditions are assumed to be fixed at the bottom and free at the top.
Figure 3-4 shows the lateral deflections computed using the various analyses for the case of the lateral force applied at the pile head. Only deflections for the top 5 m of the pile are shown because the deflections at greater depths are negligible. For the lateral force of 40 kN, the LPILE analysis predicts the greatest pile head lateral deflection. This is approximately 52%, 36%, and 31% higher than those quantified from the Basu analyses based on the soil parameters estimated using the B- (Equation 3-2b), K-(Equation 3-4a), and L- (Equation 3-6) relationships, respectively. However, since the largest pile head deflections are less than 10 mm, the practical implications of these differences are likely slight. In addition, although the pile head lateral deflections vary between the analyses, the deflection profiles are similar. For a free-ended pile, the maximum deflection and slope
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occur at the pile head. The magnitude of the lateral deflection along the pile depth decreases until the deflection reaches zero at approximately 1.5 m below the pile head for the LPILE analysis and for the Basu analysis based on the parameters estimated using the B- relationship. The locations of the zero deflection are at approximately 1.7 m below the pile head for the Basu analyses based on parameters estimated using the K- and L- relationships. Further downwards, the pile deflects in the opposite direction with the maximum magnitude at approximately 2 m below the pile head. Further downwards, the lateral deflections decrease in magnitude and start to become negligible (|y/Δ|<0.5%, where Δ is the pile head lateral deflection) at approximately 3.5 m below the pile head for all the analyses.
Figure 3-4: Pile Lateral Deflection Profiles (F=40 kN, M=0)
The difference in pile head lateral deflection between the LPILE and Basu analyses implies that the lateral and rotational soil-pile stiffnesses at the pile head from the LPILE analysis are lower than those found using the Basu analyses.
-5 -4 -3 -2 -1 0 -0.5 0 0.5 1 1.5 2 Pi le D epth, z ( m) Lateral Deflection, y (mm) LPILE
Basu Analysis (B-relationship) Basu Analysis (K-relationship) Basu Analysis (L-relationship)
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The following are possible explanations for the difference in the stiffness responses: 1. The continuum mechanics approach (Basu’s software) captures the soil as
a continuum, so it accounts for the soil shear stiffness arising due to differential deformations of soil, whereas the p-y approach (LPILE) does not.
2. The p-y curves are determined empirically based on a limited number of field tests. These curves may not apply to the current pile and soil conditions, so the p-y approach may not accurately predict the pile responses.
3. The input soil parameters adopted for the various analyses may not be exactly equivalent, even though efforts have been made to match the soil conditions in the different idealizations.
4. The drainage states of the soil input parameters are inconsistent between the LPILE and the Basu models. The Basu analyses are based on the drained Young’s moduli and Poisson’s ratios (Basu and Salgado 2008) whereas the LPILE analyses are based on the undrained cohesion and drained effective unit weight (Isenhower and Wang 2013). Hence, the different assumed drainage states may lead to the difference in soil-pile interactions.
In addition, pile head deflections are consistent with the input soil parameters quantified using the three relationships summarized in Table 3-5. The analysis based on the B- relationship (Equation 3-2b) yields the lowest lateral deflection and the highest pile head stiffness because the B-relationship corresponds to the greatest input soil stiffness. The pile head deflection for the B-relationship is approximately 34% and 42% lower than the K- and L-relationship, respectively. However, the implications of these differences are small given the uncertainties in soil in-situ properties. Also, analyses based on the K- (Equation 3-4a) and L- (Equation 3-6) relationships yield almost identical deflected shapes and pile head stiffness because they correspond to almost identical Es’ values in Layers 1 and 3.
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for the lowest soil layer, Layer 4, but the influence of this is not significant because the lateral deflections in this layer are negligible.
Figure 3-5 shows the pile lateral deflections when the pile head is subjected to a moment of 40 kN.m. Again, only deflections for the top 5 m of the pile are shown because the deflections at greater depths are negligible. Similar to the responses for a pile subjected to a lateral force, the LPILE analysis provides the greatest pile head lateral deflection and slope. It is approximately 41%, 28% and 25% higher than those quantified from the Basu analyses based on the soil parameters estimated using the B- (Equation 3-2b), K-(Equation 3-4a), and L- (Equation 3-6) relationships, respectively. The lateral deflection profiles are similar to those for a pile subjected to a lateral force of 40 kN (Figure 3-4): the maximum deflections and rotations in all cases occur at the pile head and the deformations start to become negligible at approximately 3.5 m below the pile head. However, compared to Figure 3-4, the profiles in Figure 3-5 have greater slopes. As a result, the locations of zero deflection shift upward to approximately 0.4 to 0.6 m below the pile head.
Figure 3-5: Pile Lateral Deflection Profiles (F=0 kN, M=40 kN.m) -5 -4 -3 -2 -1 0 -0.5 0 0.5 1 1.5 2 P il e De pth(m) Lateral Deflection, y (mm) LPILE
Basu Analysis (B-relationship) Basu Analysis (K-relationship) Basu Analysis (L-relationship)
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Figure 3-5 also shows that LPILE provides the lowest soil lateral and rotational stiffness and the Basu analyses based on the B-relationship provides the highest pile head lateral and rotational stiffnesses. The Basu analyses based on the K- and L-relationships provide similar pile head lateral and rotational stiffnesses. These observations are consistent with those for the pile subjected to a lateral force, Figure 3-4.