A procedure to determine resistance factors for a newly developed rotation steel pile

A Procedure to Determine Resistance Factors

for a Newly Developed Rotation Steel Pile

Yu OTAKE a , Yusuke HONJO b and Tomohiro KUSANO c a

Niigata University, Niigata, Japan b

Gifu University, Gifu Japan c

CTI Engineering Co., Ltd., Nagoya, Japan

Abstract. The aim of this study is to establish a procedure to determine resistance factors for newly developed pile products through an example of the rotational intrusion steel pile (RI pile). RI pile is a newly developed steel pile product which has the vane type tip structure to resist reliably against vertical load and to intrude easily by rotating itself. Moreover, the RI pile is environment-friendly, i.e. reduce waste soil and less construction noise, because of the rotating intrusion method. The construction can be done with the small pile driving equipment and the pile can be reliably founded into the bearing ground by monitoring and controlling the torque value during installation. For these reasons, the RI-pile is expected to have the superior bearing capacity against vertical loads. However, the RI-pile has not been adopted in many construction projects yet because the current design method requires applying the same safety factor neglecting the level of the uncertainty of each pile type. In this study, 64 loading test data are gathered to quantify the model error of the RI-pile assisted by Public Works Research Institute (PWRI). Then, Reliability analysis is conducted based on our proposed reliability analysis scheme (GRASP) to specify the reliability level of the current design. Furthermore, the partial factor updating procedure according to the newly developed the RI pile is formulated based on the design value method. From the results, the partial factor is determined and applied to compare the RI steel pile to the traditional piles, i.e. cast in pile and driven steel pile. The difference in construction cost among the three piles has become less, and the RI pile is less expensive when the rate of the pile tip resistance is high.

Keywords. Pile foundation, LRFD, code caribration, rotational pile, statistical analysis

1. Introduction

1.1. Background and Objectives of the Study The specifications of highway bridges (SHB) is the most widely used design standard for the civil structures in Japan. The specification is under the revision from the traditional allowable stress design (ASD) with the safety factors (Fs) to LRFD (load and resistance factor design) based on the reliability analysis.

One of the issues in shifting to LRFD is how one should determine the resistance factor when a new construction method is introduced. This paper is proposing a method to determine the resistance factor based on RBD. Some of the original features of this study can me listed as follows:

(1) A new pile method is taken as an example, and its design calculation model error is quantified based on the pile loading test results.

(2) A new reliability analysis method, so called GRASP (geotechnical reliability analysis by a simplified procedure) is introduced to treat especially the spatial variation of soil SPT N-value and the statistical estimation error.

(3) Code caliburation is performed based on Monte Carlo simulation (MCS) method. The objective of this paper is to show the procedure to determine a resistance factor for a new construction method through an example, which is rotation pile method.

1.2. Rotation Pile Method

The rotation pile (RP) method is relatively new pile construction method developed by several steel companies in Japan. The pile has a wing on tip of the pile, which is used for an excavation cutter during construction, and used as a mean to increase the tip resistance of the pile by increasing the pile tip area after the construction. Furthermore, since the pile is rotated during the

© 2015 The authors and IOS Press. This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License. doi:10.3233/978-1-61499-580-7-340

installation and its torque is measured, this torque is used to ensure the tip bearing capacity for quality control of the construction.

Figure 1 illustrates the pile tip structure of the rotation pile. The ration between the pile tip wing diameter (DW) and the pile diameter (D), DW/D, typically is 1.5 or 2.0.

The safety factor assigned presently for RP in SHB is the same as that for other piles such as drilled shafts (DS) and driven steel piles (DSP), which is 2.0. How to determine a rational resistance factor for the RP is the main task of this research.

2. Reliability Analysis of Pile Foundation

2.1. Pile Foundation Design Flow in SHB

The Pile foundation design flow which is generally specified in SHB is presented in

Figure 2. The conditions for the design should

be specified first, which are the specified dead load and seismic force, dimensions and properties of a pile foundation, and soil profile and properties (i.e. SPT N-values). Based on SPT N-values, subgrade reaction coefficients for vertical and horizontal directions are estimated. These values are used in so called “displacement method”, where a pile foundation is model as a frame structure connected to ground by springs. By this displacement method, the vertical force, P, acting in each pile is calculated.

The bearing capacity of each pile is evaluated based on SPT N-values of soil layers. In the current SHB, the following formula is used to evaluate bearing resistance of a pile:

 =  +    (1)

where,

qd : tip resistance per an unit area of pile

A : pile tip area, U : circumference of pile, Li : i-th layer thickness,

fi : i-th layer side resistance per unit area

The following formulas are used to evaluate the resistance based on SPT N-values:

Drilled shaft: fi = 5N, qd = 100N

Driven steel pile: fi = 2N, qd = {100+40(LD/D)}N Rotation pile: fi = 3N, qd = 130N (2)

Finally, the obtained vertical force, P, is compared to the ultimate pile resistance, Ru, divided by the safety factor, Fs, for the verification of the design:

P < Ru / Fs (3) The default value of Fs is 2.0 in SHB for the seismic condition.

2.2. Uncertainty Sources

The uncertainty sources that need to be considered in the pile foundation reliability analysis are listed as follows:

(1) Effect of soil spatial variability on the performance of the foundation.

(2) Statistical estimation error associated with the limited number of soil investigation. (3) The design calculation model error. (4) Uncertainty in force evaluation. Figure 1. Rotation Pile tip structure

For (1) and (2), the authors have developed a method that is based on the idea of introducing local averages of soil parameters for an appropriate volume of soil. The detail of the method will not be given in this paper, and should consult with the references (Honjo, 2011; Otake and Honjo, 2013; Honjo and Otake, 2013). Only the results of evaluation will be given in the examples. However, it will be shown there that the influences of these uncertainty sources are not large in this particular problem and also common for all types of pile foundation.

The dominant uncertain source in the present problem is (3). Actually, it will be shown in the example that the contributions from the evaluation of pile tip and side resistances control the total reliability of this problem.

The uncertainty in seismic force evaluation, (4), is undoubtedly very large. However, in the present code calibration procedure of SHB does not generally take this uncertainty into account. The external forces are specified values depending on the location of the construction region and the ground type. Therefore, the reliability evaluation in this calibration procedure is a conditional one for the given external forces. In the example, the conditional reliability index and the failure probability will be evaluated.

In Figure 2, the various uncertainty sources are indicated at their origin. Among these uncertainty sources, the design calculation model error in the pile resistance forces are dominant, and the most important.

2.3. Quantification of Uncertainties

In order to quantify the design calculation errors involved in the resistance forces of the rotation pile (RP), the pile loading test results are collected. Figure 3 shows the frequency distribution of tested pile lengths and diameters. There are three different groups (actually, three different steel companies developed this pile) that carried out the loading tests, which are distinguished by the different report A, B and C,

It is understood from the figure that the lengths of the tested piles distributes from 10 to 50 m or more meters, and the diameters from very small value to more than 1 meter. There are sufficient variety among the tested rotation piles.

Figure 4 presents the pile tip resistance of

RP and the design calculation values. Figure 5 shows the same result in a different way, where the measured and the calculated tip resistances

Figure 3. Rotation pile loading tests frequencies

Figure 4. RP loading test tip resistance

Figure 5. RP loading test tip resistance (measured vs. calculated tip resistance)

are directly compared. It is clear from these figures that the design calculation predicts very conservative values of the resistance. This fact is reflected in the bias of 1.65. The COV of 0.22 is relatively small variation.

The similar data for drilled shaft that had used in the code calibration for SHB are presented in Figure 5 (Okahara et al., 1991). The bias is 1.12, which is relatively small, but the COV is 0.63, which is very large. These statistics are summarized in Table 1 for drilled shaft, driven steel pile and RP. The statistics for side and tip resistance as well as vertical and horizontal subgrade reaction coefficients are presented in this table.

It is understood from Table 1 that the tip resistance of RP has very different statistics

compared to other piles. In a word, the tip resistance of PR is very conservatively evaluated. 2.4. An Example

An example calculation is done to evaluate the reliability of different types of pile foundation. This is a bridge pier pile foundation originally designed on 4 drilled shafts. The diameter is 1 m and the length 13 m. The layer profile is

presented in Figure 7, which is in sandy layer underneath is sandy gravel.

The foundation is designed for driven steel piles and the rotation piles for the same design conditions by the standard design method, where the resulting dimensions are given in Table 2. The construction cost for the three cases are also Table 1. Summary of design calculation model uncertainty for piles

Figure 6. Drilled shaft tip resistance (after Okahara et al., 1991)

estimated and presented. RP is about two times more expensive than the other two methods..

The reliability analyses are performed for the three cases for changing the diameters of

piles, where the results are shown in Figure 8. The statistics presented in Table 1 is used in the reliability analysis

As indicated in Figure 8, if the same level of reliability, i.e. the PF of 0.028, the diameter of RP can be reduced from 0.8 m to 0.6 m, which results considerable cost reduction. On the other hand, the driven steel pile need to increase its diameter from 1.0 m to 1.2 m.

The change of cost for each pile type when designed by the current design method and by the reliability analysis are compared in Figure 9. The drilled shaft remains to be unchanged because this is the base. The cost of the driven pile increased a little because the diameter need to be increased to 1.2 m. There is considerable reduction in cost of RP since this pile has very reliable tip resistance as discussed before.

The sensitivity of uncertainty sources are analyzed and shown in Figure 10. It is apparent form this result that the pile tip and side resistances are dominant uncertainty sources in the drilled shaft and the driven piles. The sensitivity of these uncertainties in the RP is considerably small.

Based on this example results, it is rational to reconsider the pile tip resistance formula and its resistance factor of RP, which is the topic of the next chapter.

3. Determination of the Resistance Factor

3.1. A Procedure for the Determination.

The method employed in this study to determine the resistance factor is rather simple. The design verification equation is given as,

R

R

S

J

t

J

Figure 8. Reliability Analysis results

Figure 9. Cist reduction of RP

where,

Rk: characteristic value of the resistance,

Sk: characteristic value of the external force. JR: resistance factor. JS: load factor (=1.0)

The resistance characteristic value is obtained by the design calculation equation where the characteristic values of geotechnical parameters are inputted. The input values are close to the mean values, thus Rk is close to the mean value with no safety margin. Thus, it should be discounted by the resistance factor to reserve the safety margin for the uncertainties. On the other hand, the characteristic value of the external force is already set for very large value, for example seismic force of 100 years return period. Therefore, the load factor is set to 1.0, implying that only the resistance factor be determined in the calibration.

The procedure is rather simple. MCS is repeatedly run by changing the soil conditions and pile dimensions. The cases that give target reliability level are collected, and the resistance factors for these cases are obtained by simply taking the ratio of the characteristic force and the characteristic resistance at these cases.

The ground condition set for the calibration is presented in Figure 11. The thickness of the second sand layer changes according to the pile length.

3.2. Results of the Analysis

The result of the calibration is presented in

Figure 12. For a purpose of comparison, both

drilled shaft and RP are calculated. The obtained resistance factors are plotted against pile length. Also inverse value of the safety factor, i.e. 0.5, is plotted by the dash line.

It is interesting to see that the current safety factor for drilled shaft does not give a constant

safety margin for the various pile length. On the other hand, RP provide the consistent safety margin for all pile length. However, the resistance factor of 0.5 is too small if the safety margin be set to the same level to other piles. The resistance factor of 0.60 may be recommended for the RP to provide the same reliability level.

Further cost study has been performed to show the competitiveness of RC to the conventional piles. It is obtained that RP is superior to other pile types when the bearing layer is relatively shallow, i.e. less than 20 m.

Acknowledgement

This study is partially supported by a research grant from the MLIT entitled “A study on design verification method based on the performance based design concept focusing on the revision of SHB”. The authors are grateful for this support.

References

Honjo, Y.(2011): Challenges in Geotechnical Reliability Based Design -2nd Wilson Tang Lecture-, Geotechnical Safety and Risk, (Proc. 3rd ISGSR, N.Vogt et al. ed.), pp.11-28 .

Otake, Y., Honjo, Y (2013).: A simplified reliability of spatial variability employing local average of geotechnical parameters, ICOSSAR2013

Honjo, Y., Otake, Y. (2013): Statistical estimation error evaluation theory of local averages of a geotechnical parameters, ICOSSAR2013

Okahara, M., Nakatani, S., Taguchi, K., Matsui, K. (1991). A study on the vertical penetration resistance of piles, J. of Geotechnical Eng., JSCE, No.418,/III-13. (in Japanese) Honjo, Y., Kieu Le, T.C., Hara, T., Shirato, M., Suzuki, M.,

Kikuchi, Y. (2009). Code calibration in reliability based Figure 11. Ground condition for the calibration

design level I verification format for geotechnical structures, Geotechnical Safety and Risk (Proc. of IS-Gifu) (eds. Y. Honjo, M. Suzuki, T. Hara and F. Zhang), CRC press, pp.435-452.