B – diameter of a circular pile e – eccentricity of the pile Ep – stiffness of the pile material Es – stiffness of the soil. Φ – angle of shear resistance of the soil Su – undrained shear strength of soil z – depth of soil medium.
Lateral Loads and Piles
Load Transfer Mechanisms(statics) of Piles
As a pile attempts to move downward, the soil mass beneath the base of the pile provides compressive resistance to the movement. The pile presses on the soil in front of it (ie, the mass of soil lying in the direction of the applied load), generating compressive and shear stresses and strains in the soil that provides resistance to the movement of the pile.
Kinematics and Failure Modes of Laterally Loaded Piles
Problem Definition
Limitations of Existing Methods
Subgrade Reaction Method
IS Code Method
Objectives
Layout of Report
Introduction
A Summary of Previous Research on Laterally Loaded Piles
- Winkler Approach
- p-y Method of Analysis
- Elasticity Theory
- Finite Element Method
The soil model used in the technique is discontinuous, i.e. linear elastic Winkler springs behave independently and thus displacements at a point are not affected by displacements or stresses at other points along the pile (Jamiolkowski and Garassino 1977). The finite difference form of the beam bending equation is used to determine the displacements of the piles.
IS Code Method
Background
A more widely accepted relationship between the modulus of subgrade reaction and the material properties of elastic soils, suggested by Vesic (1961) is: 4.2) The dimensions of the soil model are shown in Fig. 4.1. A pile with a length of 5m in a circular section with a diameter of 0.5m is used. The graphic presentation of Table 4.1 is presented in Fig. 4.2. The deformations obtained from the IS code are overestimated for higher values of Ƞh when compared to numerical modeling, while for lower values of Ƞh the difference is smaller.
Deformations and Moments
Subgrade Reaction Method
Equation (2.20) is applied to all nodes of pile elements as shown in Fig. 2.6. Thus the equations are framed for each pile node and then when these are solved using Matlab, the deflections at the corresponding pile nodes are obtained.
General
Material Models
Linear Elastic Model
Mohr Coulomb Model
Limitations
Linear Elastic Model
Mohr Coulomb Model
The normalized diagrams for various e/B ratios and Ep/Es ratios for L/B = 15 are shown in Fig. 4.10. The normalized diagrams for various e/B ratios and Ep/Es ratios for L/B = 20 are shown in Fig. 4.11. Due to the large range, the charts are proposed separately for different consistencies. The soil stiffness for clay varies between 2-200*103 kPa and for pile material the stiffness varies between kPa.
The normalized maps for various e/B ratios and Ep/Es ratios for L/B = 10 are shown in Fig 5.10. The normalized maps for various e/B ratios and Ep/Es ratios for L/B = 15 are shown in Fig 5.11. The normalized maps for various e/B ratios and Ep/Es ratios for L/B = 5 are shown in Fig 5.13.
For the same maximum load of 1000 kN, the stiff clay did not enter the plastic phase because it has linear deformations as above due to high undrained shear strength, while for soft clay we observed that the graphs are nonlinear. The deformations increase with the increase in eccentricity. The normalized plots for different e/B ratios and Ep/Es ratios for L/B = 10 are shown in Figure 5.14. The normalized plots for different e/B ratios and Ep/Es ratios for L/B = 15 are shown in Figure 5.15.
Modelling and Soil Behaviour
Basic Model Parameters in Relation to Real Soil Behaviour
To understand the five basic model parameters, consider typical stress-strain curves as obtained from standard drained triaxial tests (Figure 3.1). In this second phase of loading, geomaterials tend to produce curves as shown in Figure 3.1a.
Model
The increase in volume (or volumetric strain) is typical for sand and is also frequently observed for rock. The figure gives an indication of the importance and influence of the five basic model parameters.
Elements
Mesh Properties
Staged Construction
Mesh Convergence and Boundary Conditions Study
The deformation profile along the depth for loads 425kN and 765kN is obtained from PLAXIS for different mesh sizes and compared with field values. From the above deformation contours, it can be observed that the maximum deformation contour in red color is around the pile, while the deformation contour near the boundaries has zero deformation. From fig. 3.4 it can be seen that the stress contour near the boundaries has a value of 0 kPa.
From Figure 3.5 above, it can be seen that the lateral deformation at depths greater than 20 m is almost zero. The PLAXIS results overestimate the maximum lateral deformation that occurs at the top for the free head of the pile.
Comparison of Pile Responses of IS Code Method, Subgrade Reaction Method and
Maximum Lateral Deformation
In general, the deviation of deformations from the IS code when compared to numerical modeling is about 35% for lower values of Ƞh and about 50% for higher values of Ƞh. For the lowest values of Ƞh the deviation is 50% while for the highest values of Ƞh it is 15%.
Bending Moment
The normalized diagrams for various e/B ratios and Ep/Es ratios for L/B = 5 are shown in Fig. 4.4. The normalized diagrams for various e/B ratios and Ep/Es ratios for L/B = 5 are shown in Fig. 4.8. The normalized diagrams for various e/B ratios and Ep/Es ratios for L/B = 5 are shown in Fig. 5.5.
The normalized maps for various e/B ratios and Ep/Es ratios for L/B = 20 are shown in Fig 5.12. The normalized maps for various e/B ratios and Ep/Es ratios for L/B = 20 are shown in Fig 5.16.
Normalised Load Deflection Charts
Using LE Model
The normalized diagrams for various e/B ratios and Ep/Es ratios for L/B = 10 are shown in Fig. 4.5. The normalized diagrams for various e/B ratios and Ep/Es ratios for L/B = 15 are shown in Fig. 4.6. The normalized diagrams for various e/B ratios and Ep/Es ratios for L/B = 20 are shown in Fig. 4.7.
The graphs with the lowest Ep/Es ratio have the highest Es value, the highest ρEs/pB value and the lowest distortion. Similarly, the graphs are applicable for different values of Ep and Es for the same Ep/Es ratio.
Using MC Model
For example, if we observe chart 1-a, the graphs Ep/Es = 10000 and Ep/Es = 20000 coincide, while if we observe 4-a, they do not coincide and are different. Similarly, those with the highest Ep/Es ratio have a lower Es value, a lower ρEs /p B value, and the highest deformation. Normalized plots for different e/B ratios and Ep/Es ratios for L/B = 10 are shown in Figure 4.9.
When the same lengths and diameters are implemented as above for given L/B and e/B ratios with other changes in Ep and Es values than those used in modeling for a given Ep/Es ratio, the error about 5%. Similarly, when the same values of Ep and Es are implemented as above for a given Ep/Es ratio, and L, B and e values are changed for the same ratios, the error is about 10%.
Comparison of Normalised Charts of LE and MC model
For the same length of the pole as the eccentricity increases, pole deformations increase. Thus, the above design charts can undoubtedly be implemented for various pile geometries and various soil and pile properties with an error of less than 10%.
Study of Plastic Zone Formation
Figure 4.13 shows that the plastic zones first started on the left side of the pile, which is on the tensile side of the soil. At a load of 50 kN for e/B=0, a clear plastic zone is visible on the left side of the pile, while plastic zones have started to form on the right side of the pile. At e/B = 6, the plastic zones are clearly formed on both the left and right sides of the pile.
It is observed that for a load of 500 kN wedge-shaped plastic zones form on both sides of the pile for both e/B = 0 and e/B = 6. It can be observed that the plastic zones extend to the boundary away from the pile with increasing load .
Comparison of Pile Responses of IS Code Method and Numerical Modelling for
For e/B = 6 as shown in fig. 5.1 (b) is the IS code under estimation of the deformations for all the loads. The deformations of the IS code are overestimated in both cases Fig. 5.4 (a) and (b) and the deviation is more for e/B = 0. The normalized diagrams for different e/B ratios and Ep/Es ratios for L/ B = 10 are shown in Fig. 5.6.
The normalized plots for different e/B ratios and Ep/Es ratios for L/B = 5 are shown in Figure 5.9. It can be observed that the deformations are larger for a pile with eccentricity of 4 m than for a pile without eccentricity.
Normalised Load Deflection Charts
Soft Clay
From fig. 5.6, it can be observed that the deformations of L/B = 10 for all subcases are smaller than the deformations of L/B = 5. The normalized diagrams for different e/B ratios and Ep/Es ratios for L/ B = 15 are shown in fig. 5.7. The normalized diagrams for various e/B ratios and Ep/Es ratios for L/B = 20 are shown in Fig. 5.8.
Finally, it can be concluded that the Ep/Es ratio with the lowest Es values gives the highest deformations. If two soils have different Ep and Es values, the soil with the lowest Es value experiences the greatest deformation even though it has the highest Ep value than the other.
Medium Stiff Clay
If two soils have the same Es value, the pile with the highest Ep value transfers less load to the soil and thus results in less deformations. The normalized design charts for medium stiff clay for a pile L/B ratio 5 are given in Fig 5.9. The graphs are linear and they move away from each other with increasing e/B ratio.
Of the Ep/Es ratios, the extremes, such as 200 and 50,000, undergo large deformations compared to others. Of the Ep/Es ratios 200 and 50,000, the Es value of 50,000 is lower than the others, so that it undergoes large deformations.
Stiff Clay
The graphs in Figure 5.14 are all linear, although the MC model is used, because the deformations did not enter the plastic stage. The graphs are all very close together for e/B = 0 and they move away from each other with increasing eccentricity. It can be concluded that in all graphs the graphs remain linear for a maximum applied load of 1000 kN due to the high undrained shear strength.
Comparison of Normalised Charts of Soft Clay, Medium Stiff Clay and Stiff Clay
It is observed that the graph for Su=15kPa and Su=20kPa is non-linear in both cases (a) and (b), which means that the soil enters the plastic phase. While for Su=100 and 200 kPa the strength is so high that it still remains in an elastic state under the same load. The graphs of Su=100 and 200kPa coincide because the load on them is so small and at lower loads the deformations coincide.
The graphs of Su=100 and 200 kPa are linear, the soil is in an elastic state and overlap each other.
Study of Plastic Zone Formation
It can be observed that for e/B = 0 plastic zones started to form on both sides of the pile. It can be observed that the plastic zones are growing deeper for the case of e/B =0 and for e/B = 6 plastic zones in addition to the deeper growth from the top, they also started to form from the bottom of the pile. For a load of 5000 kN, the plastic zones grew much deeper and started to form even from the bottom of the pile.
For e/B = 6 case, the plastic zones grew towards each other from top and bottom and finally the plastic zone formed around the depth of the pile. The formation of plastic zones for clay was evolved to increase with increasing load along the depth of the pile.
