POINT BEARING CAPACITY Qp The ultimate bearing capacity

POINT BEARING CAPACITY, Qp The ultimate bearing capacity of shallow foundations was discussed in chapter 3. According to Terzaghi’s equations, qu= 1. 3 c. Nc + q. Nq + 0. 4ƴBN(for shallow square foundations) And qu= 1. 3 c. Nc + q. Nq + 0. 3ƴBNƴ (for shallow circular foundations) Similarly, the general bearing capacity equation for shallow foundation was given ( for vertical loading) as: qu = c. Nc. Fcs. Fcd + q. Nq. Fqs. Fqd + 1/2ƴBNƴFƴs. Fƴd

Hence, in general, the ultimate load-bearing capacity may be expressed as qu = c. N*c + q. N*q + ƴBN*ƴ (9. 9 a) where N*c , N*q , and N*ƴ are the bearing capacity factors that include te necessary shape and depth factors. Pile foundations are deep. However, the ultimate resistance per unit area developed at the pile tip, qp , may be expresses by an equation similar in form to that shown in eq (9. 9 a) , although the value of N*c , N*q , and N*ƴ will change. The notation used in this chapter for the width of a pile is D. hence substituting D for B in Eq. (9. 9 a) gives qu = qp = c. N*c + q. N*q + ƴDN*ƴ (9. 9 b)

Because the width D of a pile is relative small, the term ƴDN*ƴ may be dropped from the right of the preceding equation without introducing a serious error, or qp = c. N*c + q’N*q (9. 10) Note that the term q has been replaced by q’ in Eq. (9. 10) to signify effective vertical stress. Hence the point bearing of piles is

Qp = Apqp = Ap (c. N*c + q’N*q) Where Ap = area of pile tip c = cohesion of the soil supporting the pile tip qp = unit point resistance q’ = effective vertical stress at the level of the pile tip N*c , N*q = the bearing capacity factors

Frictional Resistance, Qs The frictional or skin resistance of a pile may be written as Qs = ∑ p ∆Lƒ Where p = perimeter of the pile section ∆L = incremental pile length over which p and ƒ are taken constant Ƒ = unit friction resistance at any depth z