Reprinted from Ground Engineering Vol. 1 No. 3 May 1968

A new empirical formula for base-driven cased piles

by G. M. Cornfield M.Sc., A.C.G.I., M.I.C.E.

This article presents a new empirical dynamic pile formula for base-driven cased piles and test load data is given support of the formula. B.S.P. cased piles have been in use for about ten years in ever increasing numbers. They are formed of thin helically-welded permanent steel casings base driven with an internal drop hammer and filled with concrete. They are applicable to all types of piled foundations but they are particularly suitable for maritime structures and where site conditions are different (ref. nos. 2 and 3).

BSP Cased Piles

Cased piles are essentially concrete bearing piles, the concrete being placed in situ within a permanent thin steel lining or tube. They may be used in circumstances where bearing piles are required for the foundations of buildings, bridges, piers and other structures. The pile is formed by driving the steel casing to the required resistance making use of a special cylindrical drop hammer which operates inside the lining and strikes on a plug of earth-dry concrete deposited at the base of pile, the bottom of which is closed by a flat welded steel plate shoe. Table A shows typical sizes of cased piles for various working loads including information on casing thickness and the size of internal drop hammer required. The notes below the table indicate the range of applicability of the data given for average soil conditions and piles having a final length of up to about 50/60 ft (15.2-18.3 m). Increased working loads are applicable a given pile diameter when the piles are founded on rock, hard marl, coarse gravel or sand and similar soils, while for much longer piles some increase in the casing thickness may be necessary.

When the casings have been driven to the desired resistance they are filled concrete. No reinforcement is normally necessary when the piles are driven to full penetration for building or similar foundations. If however cased piles are used in jetty type structures, where the piles project above soil level, the upper portion of each pile is provided with reinforcement. In such structures it is also necessary to check the column strength of the exposed portion of the pile after tentative selection of a diameter for a given working load is made from Table A.

Pile-driving with an internal drop hammer

Base driving with an internal drop hammer is now the normal method of installing cased piles as much thinner casings can be used. While driving from the top was occasionally employed some years ago, experience has shown that base driving is the most suitable and economical method, and it is now invariably used. The casing is first pitched and temporarily supported in position while the concrete plug is placed. A vertical or raking casing can be supported quite simply, and four typical methods are: (1) to use a timber or similar trestle, with gates for the casing located at two levels; (2) to use gates at two levels supported by the bracing of a cofferdam; (3) to cantilever gates forward from piles already completed (applicable to a jetty type structure); (4) to use gates fixed to a pontoon or barge.

The internal drop hammer is suspended from the jib of a crane having a winch of appropriate size to operate the hammer. While it is possible to use a pile frame or hanging leaders, both for support of the casing. and operation of the hammer, these are not necessary and it is most usual to install cased piles in the manner just described. It will be observed, therefore, that the only item of pile driving equipment required is the internal drop hammer. This method of installation makes cased piles particularly appropriate for use in structures where the piles have to be driven over water, or for that matter in any situation where the access conditions are difficult, for example, within a cofferdam.

Immediately before driving is started a plug of dry concrete having a compacted height of about 2½ times the pile diameter is deposited within the casing. Experience has shown it is essential that the plug concrete, of 1: 2 : 4 mix, should be very dry with a water-cement ratio not exceeding 0.25 by weight corresponding to roughly half the amount of water used in a normal concrete mix. Driving should not continue on a plug beyond a period of 1 to 1½ hours from the time of mixing of the concrete, and after this period a further but smaller charge of similar freshly mixed concrete should be added. After driving has been completed the casings can be inspected by lowering a light to the bottom.

The above Table is normally applicable for pile lengths up to about 50/60ft in average soil conditions. Where piles are driven in two lengths, the upper length may be of lesser thickness. For longer piles an increased casing thickness is required for the lower portion of the piles.

Where piles are driven to rock, dense gravel, etc., or when the soil conditions are precisely known and results of test loadings are available, it is possible to increase the stated working load for a given diameter.

(A separate check should be made of the column strength for the portion projecting above soil level.)

The casings are manufactured from mild steel by a process in which steel strip is formed into a continuous helix and the adjoining edges are butt-welded together using internal and external weld passes. As the process is continuous, the lengths of casings available are limited only by transport considerations. One of the advantages, however, of the cased pile system is the ease with which casings may be shortened or lengthened on site during installation. Cutting to final length after driving is done by flame-cutting, while casings are lengthened by welding an extension length in position over the part already driven. It is therefore unnecessary when installing very long piles to use casings of the final length, and it is thus not necessary to employ very high equipment or a crane with a very long jib to accommodate the total length of long piles. An extension length of casing is connected to one already driven by means of a butt-weld having a throat thickness not less than the casing thickness.

Stages in formation of base-driven cased piles

Empirical Formula for Base-Driven Cased Piles

When base-driven B.S.P. cased piles are driven to predetermined set, the final length of each pile will be determined during installation. The following simple dynamic formula has been devised for use with these base driven piles.

The formula is essentially empirical in nature and is based on the results of experience to date.

Ru = 3.6W(3.0+h)/(S+0.5)

Where Ru= Estimated ultimate driving resistance - TONS

W = Weight of internal drop hammer - TONS

h = Actual hammer drop at final set - FEET

S = Final set - INCH PER BLOW

This formula is intended to be applicable only when the hammer drop at final set is between 4 and 6 ft (1.3 and 1.8m) (for vertical piles) and when final set is less than 0.2 in (5 mm) per blow, that is, equivalent to more five blows per inch. In addition the inclination of the pile must be strictly in accordance with the standard driving procedure applicable to these piles. As with any dynamic pile formula, it should only be used for piles driven to soils as sand, gravel, rock, hard marl, very stiff clay. A re-drive test should tried out to confirm that the set on re-driving is not greater than the set on the first drive. As given the formula applies to vertical piles and an appropriate adjustment must be made for raking piles.

The following typical example of the use of the formula illustrates its simplicity in application. A base driven cased pile having an internal diameter of 16 in (40.6 cm) and a casing thickness of 9 s.w.g. (0.144 in) is fitted with a standard flat plate shoe. The pile is driven to a final set of 0.15 in (3.8 mm) per blow in a gravel stratum using a 2½ ton internal drop hammer operating on the recommended earth-dry concrete plug, the hammer drop at final set being 4ft-6 in (1.4 m). The ultimate resistance of the pile is then determined thus:

Ru = 3.6 x 2.5 (3.0+4.5)/(0.15+0.5) = 104 tons

This pile would be satisfactory for a working load of 52 tons using a factor of safety of 2.0 on the ultimate load, subject to certain other factors referred to later.

Table B gives worked out values of Ru based on the formula, for different diameters, final sets and hammer drops.

Note:— Applicable to vertical piles 1 ton=2240 lb.

A  typical working load in average soil conditions

B  typical working load when final set obtained in dense gravel, dense sand, rock, hard marl, etc. for factor of safety of 2.0 on ultimate load.

Comparison of Formula with Test Load Results

Table C gives essential data relating to 37 B.S.P. cased piles which have been test loaded on a large number of different sites over the past ten years. These represent all the data available to the author at time of writing this article and no attempt has been made to exclude any case because of apparently unfavourable results except where some of the data was incomplete or doubtful.

As with all loading tests of bearing piles, there is the problem of estimating the ultimate or failure load from the test data. There are many different criteria for obtaining the failure load even when the piles have been clearly loaded to the apparent failure condition. The author has, however, selected as the criterion that load at which the residual settlement of the head of the pile, after removal of the load, is 1/3 in (8 mm). Unfortunately bearing piles are not always tested to full ultimate load, and in fact due to the cost of load testing the maximum test load may be well below the ultimate load. In an attempt to obtain as much data as possible for comparison with the empirical formula it was decided to use all available results even where loading has not clearly been carried out to failure and an estimate has therefore been made of the minimum ultimate failure for these cases. Based on experience and an examination of the results of many bearing piles of all types loaded to failure, it was considered conservative to estimate in the following manner. Where the maximum load applied resulted in a residual pile head deflection of less than 0.20 in (5 mm) but more than 0.10 in (2.5 mm) the minimum estimated ultimate load has been taken as 10 per cent greater than the maximum load applied during the test. When the residual deflection was 0.10 in (2.5 mm) or less the minimum ultimate load was estimated at 25 per cent over the maximum applied load. It is felt that these estimates are on the safe side and the actual ultimate loads may in some cases be significantly greater than the minimum figures estimated in this manner.

Using the results of Table C, Graph D shows minimum estimated ultimate resistance obtained by test loading plotted against the result obtained by application of the formula. The points on the graph suggest reasonable correlation with the formula. The scatter of the points is in fact no better or worse than that applicable to more known formulae, such as the Hiley formula, which are often used for top-driven piles of all types. Graph D scatter indicates that the base driven formula will give results, when correctly applied, which are generally not unsafe.

It is interesting to observe that the accuracy of measurement of the observed driving data is in itself a source of scatter of results. The hammer drops can be measured in practice to an accuracy of about 10 per cent, and there may be some lack of accuracy measuring sets and so on - the result is that there could be an inaccuracy of possibly 5 to 10 per cent due such causes. This of course applies to any pile driving formula.

Table C also records pile lengths and estimates of ultimate load obtained from tests and the formula respectively. Plotting these against each other showed no correlation of any sort even for a particular group of soils.

There tends to be a bigger scatter of results (Graph D) for cohesive soils than for sand, rock, etc. This is not unexpected and will be chiefly due to the sensitivity of cohesive soils and the effect of the time interval between driving and test loading.

General Comments

The base-driving formula is as already stated an empirical one. When the earliest cased piles were driven both top and base-driving were sometimes employed and it was therefore possible by comparison using the Hiley formula for top driving to produce a first trial formula for base driving. Subsequent results from test loading of various piles enabled adjustment to be made to the constants. From other work on top driving formula (Ref. Nos. 4 and 5) it seemed to the author that pile length and weight were relatively insensitive variables, and these were therefore omitted from the formula. The shape of curves of ultimate resistance plotted against blows per inch at final set would appear generally to have a certain form for most dynamic formulae and this is confirmed also by work done by various investigators applying computer analysis to the wave equation of stress propagation in piles. One further factor observed by the author in earlier test load/formula investigations was that the ratio of ultimate resistance to hammer size and energy was the most significant factor and this depended chiefly on the final set. The various points mentioned above led to the gradual evolution of the present base-driving formula.

It should not be assumed that a pile-driving formula can give results that are anything but a rough estimation. In view of this it is inadvisable to rely solely on a formula. Estimates should also be made from the soil data, though this is likely to be reasonably accurate only for cohesive soils. In addition test loading of one or more piles is usually essential. Experience suggests that a combination of all these methods, i.e. (1) formula, (2) test loading and (3) estimation from soil data, should be employed at the present state of our knowledge of driven piles of any type. (Ref. No. 1).

Certain limits of applicability of the base-driving formula have already been mentioned such as the range of sets, range of hammer drop, the use of a re-drive check, the type of soils in which the pile is founded and so on. Other points to be considered are pile group effects, particularly in clays, negative friction, the choice of factor of safety, the presence of a soft stratum below the pile tip and so on. (Ref. No. 1). In the case of piles used in a jetty structure the column strength of the portion upstanding above soil level needs to be separately checked. Uplifting of piles adjacent to the one being driven will of course invalidate the use of any formula. One further comment applies to chalk: load testing is particularly desirable as the application of a formula will usually result in unnecessarily long piles.

Conclusion

The comparison of test load results to the empirical base-driving formula given in this article indicates reasonable correlation and it is suggested that the formula may be employed with confidence subject to the various precautions mentioned. It is hoped to improve the formula when significant additional test data is available. Even with the data now available it may be possible to upgrade the formula slightly for piles driven into cohesionless soils or to rock. Heavier hammers are now being introduced for base driven B.S.P. cased piles in order to improve on the driving rate and to enable higher loads to be applied to a given diameter of pile - it is considered that the formula is equally applicable to such heavier hammers and it is hoped to collect sufficient further test load data in due course.

References:

Ref. 1 Civil Engineering Code of Practice No. 4 - Foundations. Institution of Civil Engineers.

Ref. 2 ‘Cased Piles and their Application to some Maritime Structures’, G. M. Cornfield. ‘Dock & Harbour Authority’ February ISM.'

Ref. 3 "Further Examples of Cased Piles in Maritime Structures" G.M.C., ‘Dock & Harbour Authority’, August 1964.

Ref. 4 ‘Simplified Hiley Formula for RC Piles’ G. M. Cornfield ‘Engineering’ 14th July 1961.

Ref. 5 ‘Hiley Formula Simplified Without Graphs’ G.M.C., ‘Engineering’ 20th December, 1963.

Paper reproduced by kind permission of BSP International Foundations Ltd www.bsp-if.com