**1.**Determine the value of nh for a particular stage of loading Pt.

**2.**Compute T from Eq. (16.14a) for the linear variation of Es with depth.

**3.**Compute y at specific depths x = x1, x = x2, etc. along the pile by making use of Eq. (16.9), where A and B parameters can be obtained from

**Table 16.2**for various depth coefficients Z.

**4.**Compute p by making use of Eq. (16.13), since T is known, for each of the depths x = x1

x = x2, etc.

**5.**Since the values of p and y are known at each of the depths x1, x2 etc., one point on the p-y curve at each of these depths is also known.

**6.**Repeat steps 1 through 5 for different stages of loading and obtain the values of p and y for each stage of loading and plot to determine p-y curves at each depth.

The individual p-y curves obtained by the above procedure at depths x1, x2, etc. can be plotted on a common pair of axes to give a family of curves for the selected depths below the surface. The p-y curve shown in

**Fig. 16.2b**is strongly non-linear and this curve can be predicted only if the values of nh are known for each stage of loading. Further, the curve can be extended until the soil reaction, pu, reaches an ultimate value, pu, at any specific depth x below the ground surface.

If nh values are not known to start with at different stages of loading, the above method cannot be followed.

Supposing p-y curves can be constructed by some other independent method, then p-y curves are the starting points to obtain the curves of deflection, slope, moment and shear. This means we are proceeding in the reverse direction in the above method. The methods of constructing p-y curves and predicting the non-linear behavior of laterally loaded piles are beyond the scope of this book. This method has been dealt with in detail by Reese (1985).

**Figure 16.2 (b)**characteristic shape of a p-y curve

**Table 16.2**The A and B coefficients as obtained by Reese and Matlock (1956) for long vertical piles on the assumption Es = nhx

Where are the equations that you refer to?

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