1. Understanding and Improving the Seismic Behavior of Pile Foundations in Soft Soils
Bradley Fleming, Sri Sritharan, & JinWei Huang
Iowa State University
Kanthasamy Muraleetharan & Gerald Miller
Oklahoma University
Hello, my name is Brad Fleming and I will be presenting the analytical portion of what was just discussed.

2. Modeling Techniques Finite Element (OpenSees)
Detailed 3D analysis
Used to understand complex interactions between
pile and improved soil
improved soil and unimproved soil
p-y Analysis Method (LPILE)
Simple 2D analysis
Attractive for engineers in industry
Account for improved soil of limited width by applying modification factors to p-y relationships
In our research we are trying to understand and improve the behavior of pile foundations in soft soil and translate our findings into a useful design methodology.
To do this, we have constructed detailed finite element models in the OpenSees and compared the results to field data to see how well we can characterize the behavior of improved piles. This has also helped us to understand the complex interactions between the pile and soil as well as the improved soil and unimproved soil.
The p-y analysis method is very attractive for engineers in industry and can easily be adopted into a design methodology. However, this method only accounts for soil layers that have constant properties to a infinite length in the horizontal direction. We have found this to be useful for practical purposes and can be applied to improved piles if the improvement is sufficiently wide. For improved soil of limited width, we have developed a simple method for modifying the p-y relationship to account for this. LPILE is a program we use to apply modification factors to known p-y curves for clay and analyze.

3. OpenSees Finite Element Model
Soil “Island” (OpenSeesPL soil mesh generation)
10.3 m long, 5.15 m wide, and 7.62 m high
3,450 nodes
2,492 soil elements
Pile (forceBeamColumn)
7.23 m total length
34 beam elements
5.3 m embedded length
Non-linear fiber section (half of pile) P
Clay
Sand
In building the finite element model we used a very useful tool called OpenSeesPL to generate the soil island, pile elements, and assign elements material properties. Only half the mesh was constructed due to symmetry.
The pile is made up of several beam elements having a cross section made up of many fibers. The uniaxial characteristics of each fiber is what makes the pile nonlinear if stressed beyond its yield point. The stiffness and yield strength of the steel in our piles was tested in the lab and applied to each fiber in the cross-section.
Contact elements between the soil and pile were added to allow for frictional slip, sticking, and separation. These elements and respective material properties were developed by Pedro from the University of Washington.
Soil elements were given uniform properties along its depth. Initially, these were calibrated to give the behavior of the unimproved pile in the field. Then improved soil was applied to the elements surrounding the pile to see if the improved pile behavior can be captured.
Contact Elements (BeamContact3D)
Soil Elements (SSPbrick)
Clay Sand
• PressureIndependMultiYield • PressureDependMultiYield
• Gmax = 3250 kN/m2 • Gmax = 1.0E+5 kN/m2
• c = 30.5 kN/m2 • φ = 37 deg.
• γsat =1.8 ton/m3 • γsat =2.0 ton/m3
Soil m1
Pile
slave m2 r

4. Pile Head Responses of Full-Scale Test and FEM
In this slide, the left image is the response of the unimproved pile and the right image is the response of improved pile for both the field test and finite element model. From this we see that the model did very well in capturing the response of the improved pile.
Unimproved Pile
Improved Pile

5. LPILE Model & Modified p-y Curves
Now I would like to discuss the p-y analysis method.
In the traditional method the pile is made up of several beam elements with nonlinear moment-curvature characteristics. The soil is represented by a series of nonlinear springs that have a resistance p to a lateral displacement y. The shape of the p-y curve is defined by known models that can be found in various publications. LPILE also has these models available in its library. For improved soil of sufficient width, the behavior of the soil can be characterized with a single spring. For improvement of limited width, the proposed method is to take the p-y models for both improved and unimproved soil and place them in series to obtain the effects of each.
But how much soil improvement is needed to be considered sufficiently long?

6. Effective Length Attenuation of stresses in soil layer
Guo and Lee (2001)
𝜙= 𝐾 0 ( 𝛽𝑟 𝑟 𝑜 ) 𝐾 0 (𝛽)
𝜙 𝐶𝐷𝑆𝑀
𝜎 𝑖𝑗 𝜎 𝑖𝑗, 𝑚𝑎𝑥 or
𝑢 𝑢 𝑚𝑎𝑥
𝜎 𝑖𝑗 𝜎 𝑖𝑗, 𝑚𝑎𝑥
𝜙 𝑠𝑜𝑓𝑡 𝑐𝑙𝑎𝑦
𝜙=0.05
𝑟 𝑟 𝑜
𝑟 𝑟 𝑜
𝑙 𝑒𝑓𝑓 𝑟 𝑜
𝑙 𝑒𝑓𝑓 𝑟 𝑜
This property we call effective length and can be found from observing the stress attenuation along the radial distance away from the pile. Guo and Lee developed a closed form solution for the attenuation. In their equation, the stresses are non-zero out to infinity. We found this to be impractical and, based on several centrifuge tests, we determined an attenuation value of 5% of the maximum stress to be sufficient for finding the effective length. Therefore, if the 5% attenuation value is located within the improved zone, the p-y relationship for the soil at that layer can be represented with a single spring. If the 5% value is outside the improved zone, the effective length is much larger because of the distribution of stresses in the soft soil and the effective stiffness of the soil is smaller.
𝑏 2 ≥ 𝑙 𝑒𝑓𝑓
𝑏<2 𝑙 𝑒𝑓𝑓
𝑘 𝐶𝐷𝑆𝑀
𝑘 𝑒𝑓𝑓

7. Equivalent Rigidity 𝑅 𝐼 𝑅 𝑈 𝐿 𝐼 𝐿 𝑈
Improved Soil
Unimproved Soil
𝑅 𝐼
𝑅 𝑈
𝐿 𝐼
𝐿 𝑈
R – Equivalent rigidity (analogous to AE for axially loaded member)
Leff - Length of uniform soil layer
ki – Equivalent stiffness of the p-y curve
S - Stiffness of spring
To find the effective stiffness of the combined soil, we took a simple approach to combine the equivalent stiffnesses or K of the p-y curves for both improved and unimproved soil. Since K represents the stiffness of an infinitely long soil layer, we multiply it by the effective length found from Guo and Lee’s equation to get an equivalent rigidity. This is analogous to AE for axially loaded members. Applying this rigidity to the length of improved soil or Li and unimproved soil or Lu will give the stiffness of an equivalent spring. Then, the effective stiffness of the combined springs can be calculated for two springs in series.
Li is easy to determine but Li is not because it requires the effective length for the combined soil.
𝑆 𝐼 = 𝑅 𝐼 𝐿 𝐼
𝑆 𝑈 = 𝑅 𝑈 𝐿 𝑈
𝑆 𝑒𝑓𝑓

8. Combined Properties Cont.
𝐿 𝑈 = 𝐿 𝑒𝑓𝑓,𝑈 − 𝐿 𝑒𝑓𝑓,𝑈 𝐿 𝑒𝑓𝑓,𝐼 𝐿 𝐼
𝜙 𝑆𝑜𝑓𝑡 𝐶𝑙𝑎𝑦
𝑘 𝑒𝑓𝑓 = 𝑘 𝑖, 𝐶𝐷𝑆𝑀 𝑘 𝑖,𝑠𝑜𝑓𝑡 𝑐𝑙𝑎𝑦 𝐿 𝑒𝑓𝑓,𝐼 𝑘 𝑖,𝐶𝐷𝑆𝑀 𝐿 𝑒𝑓𝑓,𝐼 − 𝐿 𝐼 + 𝑘 𝑖, 𝑠𝑜𝑓𝑡 𝑐𝑙𝑎𝑦 𝐿 𝐼
𝜎 𝑖𝑗 𝜎 𝑖𝑗, 𝑚𝑎𝑥
𝜙 𝐶𝐷𝑆𝑀
𝜙 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑
Therefore, we created a simplifying assumption to eliminate Lu. Pictured on this slide is the attenuation for fully improved, fully unimproved, and an attenuation for the combined soil. From this it is easy to see that Lu approaches zero as Li increases and Lu approaches the effective length for unimproved soil as Li decreases. This led to the development of the linear relationship shown above. After subsituting into the equation for two springs in series, we came up with an equation for the effective stiffness of the p-y curve for the combined soil.
𝜙=0.05
𝑟 𝑟 𝑜
𝐿 𝐼
𝐿 𝑈
𝐿 𝑒𝑓𝑓,𝐼
𝐿 𝑒𝑓𝑓,𝑈

9. p-y Modification Factors
We use this stiffness to interpolate the values for the full curve and calculate the modification factors to be inserted into the LPILE analysis tool. In this case omega p and omega y are used to reduce the soil resistance and increase the soil displacement of the improved p-y curve.
JinWei Huang (2011)

10. Global Response Comparisons (Centrifuge)
This slide shows the camparison of measured load-displacement response envelopes with the LPILE computed load-displacement responses using the newly developed p-y curve modification factors for test #1.
the calculated elastic lateral stiffness for piles from centrifuge test #1 were slightly higher than that obtained from the experimental data;
the calculated lateral load resistance for centrifuge test #1 increased from 100 kN to 420 kN/m, which is in close agreement with the increase from 80 kN to 420 kN/m (94.4 kips) from the experimental data;
JinWei Huang (2011)

11. Global Response Comparisons (Centrifuge)
Calculated Elastic stiffness is in excellent agreement with the average value of the push and pull experienmental data.
The calculated lateral resistance at max. target disp. increased from 55 kN to 125 kN which is really close to the increase form 55 kN to 118 kN from the experiement data.
JinWei Huang (2011)

12. Global Response Comparisons (Centrifuge)
Calculated Elastic stiffness is in excellent agreement with the average value of the push and pull experimental data, however, no significant increase in elastic stiffness can be observed for these two piles although the soil improvement dimensions increased from 13D×13D×9D to 17D×17D×12D.
JinWei Huang (2011)

13. Field & LPILE Global Responses
The calculated elastic lateral stiffness increased by 480% from 759 kN/m to 4396 kN/m, which agrees well to the 420% increase obtained from the experimental data.
Then calculated lateral resistance in the inelastic region for unimproved pile agrees well with the test data while the lateral resistance in the inelastic region for the improved pile is about 20% lower than the measured values.
It should also be noted that the pile in the improved ground failed at the first cycle of loading at lateral displacement of 8 in., primarily due to local buckling at the side wall just above the ground surface, & fractured the pile as a result of low cycle fatigue.
JinWei Huang (2011)

14. Field & LPILE Test Local Responses
Calculated max. moment location is about 1.5 m below the ground for pile with no ground improved, & at the ground surface for pile with ground improvement. Which agrees very well with the experimental data.
The moment decreased to zero at a depth of 1.4 m below the ground surface in both calculated & measured moment profiles for the improved pile, which indicates that the effective depth of the ground improvement is a lot less the actual improvement depth used in the test.
JinWei Huang (2011)

15. Conclusions
Both LPILE and OpenSees closely resembles centrifuge and field behavior
OpenSees is an effective analysis tool but requires specialized knowledge and involves high computation costs
LPILE is an attractive tool for engineers and has flexibility to modify p-y curves
The proposed method for modifying p-y curves does well in characterizing the behavior of piles in improved soil of limited width