General Considerations
The earlier sections dealt with the behavior of long vertical piles. The author has so far not come across any rational approach for predicting the behavior of batter piles subjected to lateral loads. He has been working on this problem for a long time (Murthy, 1965). Based on the work done by the author and others, a method for predicting the behavior of long batter piles subjected to lateral load has now been developed.

Model Tests on Piles in Sand (Murthy, 1965)
A series of seven instrumented model piles were tested in sand with batters varying from 0 to ±45°.

Aluminum alloy tubings of 0.75 in outside diameter and 30 in long were used for the tests. Electrical resistance gauges were used to measure the flexural strains at intervals along the piles at different load levels. The maximum load applied was 20 Ibs. The pile had a flexural rigidity El = 5.14 x 10^4 lb-in^2

The tests were conducted in dry sand, having a unit weight of 98 lb/ft^3 and angle of friction Ø equal to 40°. Two series of tests were conducted-one series with loads horizontal and the other with loads normal to the axis of the pile. The batters used were 0°, ± 15°, ±30° and ±45°. Pile movements at ground level were measured with sensitive dial gauges. Flexural strains were converted to moments.

Successive integration gave slopes and deflections and successive differentiations gave shears and soil reactions respectively. A very high degree of accuracy was maintained throughout the tests.

Based on the test results a relationship was established between the nh^b values of batter piles and n°h.

Figure 16.20 Effect of batter on nh^b / n°h and n (after Murthy, 1 965)

values of vertical piles. Fig. 16.20 gives this relationship between nh^b / n° and the angle of batter β . It is clear from this figure that the ratio increases from a minimum of 0.1 for a positive 30° batter pile to a maximum of 2.2 for a negative 30° batter pile. The values obtained by Kubo (1965) are also shown in this figure. There is close agreement between the two.

The other important factor in the prediction is the value of n in Eq. (16.8a). The values obtained from the experimental test results are also given in Fig. 16.20. The values of n are equal to unity for vertical and negative batter piles and increase linearly for positive batter piles up to a maximum of 2.0 at + 30° batter.

In the case of batter piles the loads and deflections are considered normal to the pile axis for the purpose of analysis. The corresponding loads and deflections in the horizontal direction may be written as

where Pt and yg , are normal to the pile axis; Pt(Hor) and yg (Hor) are the corresponding horizontal components.

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