M.R. Svinkin
VibraConsult, Cleveland, Ohio, USA
R. Skov
CP Test a/s, Vejle, Denmark
ABSTRACT: Knowledge of pile capacity over a long period of time after the end of initial driving is important for proper design, construction and estimation of the cost of pile foundations. In this paper, assessment of pile capacity as a function of time has been performed for cohesive soils. On the basis of an existing formula, a new relationship between pile capacity and time after pile installation has been derived. This relationship takes into account pile capacity at the end of driving and an actual time after pile installation. Derived results can be used as a guide for evaluation of long term capacity of piles in cohesive soils.
1 INTRODUCTION
Piles have to withstand design loads for a long period of time. Therefore the consequences of soil modification around the pile are essential with respect to changes of pile capacity. During pile installation, the soil around the pile experiences plastic deformations, remoulding, and pore pressure changes. Excess pore water pressure developed during driving reduces the effective soil shear strength and ultimate pile capacity. After the completion of pile driving, soil reconsolidation in cohesive soils, manifested by the dissipation of excess pore pressure at the soilpile interface zone, is usually accompanied by an increase in pile capacity (soil setup). The amount of increase in pile capacity and the time required for return of equilibrium conditions depend on soil properties and pile characteristics. For example, the disturbed zone around a pile is more or less proportional to the soil volume displaced during driving and dissipation of excess pore water pressure occurs faster in friction soils.
The phenomenon of timedependent strength gain in cohesive soils related to pile driving has been studied and published, for example, Fellenius et al. (1989), Randolph et al. (1979), Skov & Denver (1988), Seed & Reese (1955), Svinkin et al. (1994), Thorburn & Rigden (1980), Tomlinson (1971), Wardle et al. (1992), and others.
Assessment of pile capacity as a function of time is, of course, important in the design and construction of pile foundations. Having knowledge of general tendencies of pile capacity with time after driving would certainly be beneficial in economical standpoint. Such information may be used during construction to reduce the design penetration and pile capacity at the end of initial driving and also to choose relevant time for dynamic testing at restrikes or static loading test. In this paper, an attempt is made to present the relationships between pile capacity and elapsed time after the end of initial driving (EOID) for cohesive soils and to show some benefits for estimation of pile capacity from this approach.
2 EXISTING FORMULA
Skov and Denver (1988) found the following formula for ultimate pile capacity, R_{u}(t), as a function of relative time between different tests
(1)
Some designations in this formula are different from those given in the original expression. The pile capacity at the first restrike, R_{RSTR1}, is the lower limit for appreciable increasing in pile capacity when some time elapsed after initial driving results in developing soil setup. Quantity, t, is a time elapsed from the end of initial driving and capacity R_{RSTR1} is determined for t=t_{1}. A factor, A, is dependent on soil conditions.
Consolidation of cohesive soils around the pile after pile installation requires much more time in comparison with other soil types like sand and gravel to regain in soil strength and pilesoil adhesion after EOID. For this reason the existing formula is pertinent for clay and cohesive soils.
Case histories presented by Svinkin et al. (1994) confirmed that formula (1) is a good indicator of the pile capacity versus relative time relationship after pile installation. Besides, it was shown that the factor, A, depends not only on the soil but also on the pile type and size.
The application of formula (1) usually requires to make the first restrike in 12 days after pile driving. It might be especially convenient for dynamic testing at construction sites where many piles should be tested by restrike in a short period of time.
Nevertheless, the existing formula yields relative setup versus relative time for assessment of the pile capacity after the first restrike. This is a contradiction to the setup approach commonly used in geotechnical practice and inconvenient for certain construction sites to restrike piles on 12 days after pile installation.
3 PROPOSED FORMULA
The main goal to derive a new formula for evaluation of the setup effect of cohesive soils in pile capacity is to take into consideration the pile capacity at EOID and the actual time elapsed after pile installation.
For a soil setup straight line passing through two points corresponding pile capacity at EOID, R_{EOID}, and pile capacity at any time after pile installation, R_{u}(t), a formula with a logarithmic time scale can be written
(2)
Time is calculated in days after pile installation. The time for EOID is taken 0.1 (2.4 hours) that negligibly affects increasing in the pile capacity at EOID but gives an opportunity to use the logarithmic time scale.
After simplification formula (2) becomes
(3)
Formula (3) is similar to formula (1). However, proposed formula (3) has certain advantages. This formula (a) uses the traditional setup formulation, (b) takes into account the actual time in days passed after pile installation, (c) provides determination of the soil setup independently of the time of the first restrike.
4 CASE HISTORIES
For verification of formula (3), in the following case histories the existing and proposed expressions were used to calculate the pile capacity as a function of time after EOID.
4.1 Case 1
Three piles were considered in this study from total number of seven prestressed concrete piles tested for a bridge approach (GRL Report 1987, Svinkin et al. 1994). A pile description is presented in Table 1. The depth of penetration of each pile was approximately 24.4 m. The soil consisted of about 25.6 m of mainly gray clays followed by a bearing layer of silty sand. Water table was at the ground surface. A Delmag D 4613 hammer was employed for initial driving and restrikes. For each pile, 3 to 4 dynamic testings were performed after pile installation. For piles TP3 and TP4 static loading tests (SLT) were made as well. The elapsed time after EOID, the penetration resistance and the time dependent ultimate capacity of piles tested are shown in Table 1. Pile capacities from dynamic testings were determined by CAPWAP analysis and the Davisson criterion of failure load was used for static loading tests (GRL Manual 1993).
Pile capacity calculation according to formula (1) was made by Svinkin et al. (1994). Quantity, t_{1}, was equal to 2 days for piles TP1 and 1 day for piles TP3 and TP4. Measured data and results calculated in accordance with the existing formula have been plotted in ordinates R_{u}(t)/R_{RSTR1} and log_{10}(t/t_{1}) as broken and straight lines, respectively, in Figure 1. Note that the setup coefficients from the field tests generally match well to those obtained from the existing formula.
Table 1. Static and Dynamic Data for Prestressed Concrete and Steel Piles in Clayey Soils 

Pile 
Test 
Time after EOID (days) 
Penetration Resistance (blows/0.3 m) 
Ru (kN) 
Factor B 
Setup Measd 
Setup Calcd 

No. 
Description 

TP1 
1372 x 127 mm Cylinder Prestressed Concrete 
EOID RSTR1 RSTR2 RSTR3 
– 2 9 22 
38 >240 >240 >240 
752 2451 2927 3545 
1.60 
1 3.26 3.89 4.71 
1 3.08 4.13 4.75 
TP3 
610 x 610 mm (305 mm D. void) Prestressed Concrete 
EOID RSTR1 RSTR2 RSTR3 SLT 
– 1 10 18 31 
10 21 72 144 – 
267 912 1530 1672 1841 
2.37 
1 3.42 5.73 6.26 6.90 
1 3.37 5.74 6.35 6.91 
TP4 
762 x 762 mm (475 mm D. void) Prestressed Concrete 
EOID RSTR1 RSTR2 RSTR3 RSTR4 SLT 
– 1 4 9 18 32 
14 23 60 >240 168 – 
200 890 1299 1517 1601 2273 
3.50 
1 4.45 6.50 7.60 8.00 11.37 
1 4.45 6.61 7.84 8.90 9.77 
B2 
HP 310×94 
EOID RSTR1 RSTR2 RSTR3 SLT RSTR4 RSTR5 
– 2 6 7 15 16 132 
12 36 60 72 – 48 >120 
489 1201 – 1512 13972002 2291 
1.14 
1 2.46 – 3.09 2.86 4.09 4.69 
1 2.48 – 3.10 3.48 3.50 4.55 



For piles under consideration, the factor, B, has been found on the basis of back calculations using formula (3). This factor ranges from 1.6 to 3.5 (Table 1). Scattering of the factor, B, is the same for the existing and proposed formulae. The setup coefficients derived from both the field tests and from formula (3) are given in Table 1 and depicted in ordinates R_{u}(t)/R_{EOID} and Time after EOID in days (logarithmic scale) as broken and straight lines, respectively, in Figure 1. Good agreement is found between calculated and measured values of pile capacity as a function of time after EOID.
Figure 1. Pile capacitytime relationship for prestressed concrete and steel piles in clayey soils
4.2 Case 2
Initial data for this case were taken after Fellenius et al. (1989). An Hpile 310×94 (mm, kg/m) with length of 47.2 m was driven and restruck by a Vulcan 010 hammer with a nominal energy of 44 kJ. Restrike No. 4 of this pile was performed by drop hammer with nominal energy of 65 kJ. The soil at the site consisted of about 6.1 m of miscellaneous earth fill followed by about 19.8 m of soft to medium stiff compressible postglacial silty clay and clayey silt underlain by about 27.4 m of glacial material deposited on dolomite bedrock. The water table was about 2.5 m below grade. The Hpile was founded in the glacial material.
Five restrikes were made for pile tested. Pile capacities from dynamic testings were determined by CAPWAP analysis (GRL Manual 1993). The static loading test for this pile did not show a plunging behavior. Failure load from the static loading test was 1397 kN (Davisson 1972), 1957 kN (Butler & Hoy 1977), and 2535 kN (Fuller & Hoy 1970). The capacity from the static loading test was evaluated from the Davisson criterion. The results of dynamic and static tests are shown in Table 1.
Pile capacity calculation according to formula (1) was made by Svinkin et al. (1994) and shown in Figure 1. It can be seen the calculated setup line averages measured values of pile capacity.
Measured soil setup and calculated setup in accordance with formula (3) are presented in Table 1 and displayed in Figure 1 as well. For the Hpile, the proposed formula provides better fit to results tested than the existing formula.
5 SUMMARY
The application of the proposed formula shows that the magnitude of gain in pile capacity in cohesive soils depends on soil conditions, pile material and dimensions. However, the same equation with a different factor, B, can be applied for assessment of soil setup in cohesive soils during relatively long elapsed time after pile installation.
The existing and proposed formulae demonstrate similar tendency of the setup effect of cohesive soil in pile capacity. However, there are substantial differences between two approaches.
The existing formula yields relative setup versus relative time for assessment of the pile capacity after the first restrike. This is a contradiction to the setup approach commonly used in geotechnical practice. Also, it is inconvenient for certain construction sites to restrike piles on 12 days after pile installation. Moreover there is no standard time for the first restrike. If this time is different for various piles, the existing formula yields different assessment of soil setup at the same site and obtained results of increasing in pile capacity cannot be compared.
The proposed formula uses the traditional setup formulation, calculates the pile capacity at the actual time after EOID, and provides determination of the soil setup independently of the time of the first restrike.
The proposed formula provides determination of pile capacity as a function of time after pile installation using pile capacity values obtained through dynamic testing at EOID and one restrike or one static loading test. This approach is identical for any construction site. Obtained information would be beneficial to choose sensible pile penetration depth at EOID and search the proper times in days after EOID to verify setup in cohesive soils with an additional dynamic testing or the static loading test.
6 CONCLUSIONS
Determination of long term pile capacity is important for proper design and construction of pile foundations in cohesive soils.
A new relationship like a linear equation in a logarithmic time scale has been derived to predict an increase in pile capacity with time after pile installation. Soil setup for several piles in cohesive soils was verified on the basis of the existing and proposed formulae. The latter has certain advantages. Obtained results showed that changes of pile capacity with time in cohesive soil may be predicted well.
Results presented in this paper certainly do not mean that pile capacity will change with time exactly like shown above. However, the demonstrated pile capacity versus time relationships can be used as guide for assessment of pile capacity with respect to time. Presented results give a chance to safe significant amount of time, energy and materials taking into account the gain of pile capacity from soil setup. Derived relationship can also be useful in choosing representative times for both static loading test and dynamic restrike testing.
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