Allowable Pile Capacity
=
Where: Qall = allowable load-carrying capacity for each pile FS= Factor of Safety, ranges from 2-3. (insert table)
Load-Carrying Capacity of Pile Point Resting on Rock The ultimate unit point resistance in rock (Goodman, 1980) is approximately
Where:
= −∅ + 1
∅ ) = unconfined compression strength of rock
Nø = tan2 (45 +
qu-R ø’ = drained angle of friction
Scale Effect - As the diameter of the specimen increases, the unconfined compression strength decreases - primarily caused by randomly distributed large and small fractures and also by progressive ruptures along the slip lines. Hence it is recommended that:
− = − 5
A factor of safety of at least 3 should be used to determine the allowable loadcarrying capacity of the pile point. Thus,
= [ −∅ +1]
Elastic Settlement of Piles The elastic settlement of a pile under a vertical working load, Q w, is determined by three factors:
= + +
Where: Se = total pile settlement Se (1) = settlement of pile shaft Se (2) = settlement of pile caused by the load at the pile point Se (3) = settlement of pile caused by the load transmitted along the pile shaft
Determination of S e (1) If the pile material is assumed to be elastic, the deformation of the pile shaft can be evaluated using the fundamental principles of mechanics of materials:
= ( + )
Where: Qwp = load carried at the pile point under working load condition Qws = load carried by frictional (skin) resistance under working load condition Ap = area of the pile cross section L = length of the pile Ep = modulus of elasticity of the pile material = depends on the nature of the unit friction (skin) resistance (f (z)) distribution along the pile shaft. May vary between 0.5 – 0.67 (Vesic, 1977) 0.5 if variation of f (z) is uniform or parabolic 0.67 if variation of f (z) is linear
= =
Determination of S e(2) The settlement of a pile caused by the load carried at the pile point may be expressed as
= 1 Where: D = width or diameter of the pile qwp = point load per unit area at the pile point = Q wp/Ap Es = modulus of elasticity of soil at or below the pile point µs = Poisson’s ratio of soil Iwp = influence factor
0.85
≈
Vesic (1977) also proposed a semiempirical method to obtain the magnitude of the settlement, S e(2):
=
Where: qp = ultimate point resistance of the pile Cp = an empirical coefficient
Determination of S e(3) The settlement of a pile caused by the load carried along the pile shaft is given by:
= 1
Where: p = perimeter of the pile L = embedded length of the pile Iws = influence factor
Note that the term Q ws/pL is the average value of f along the pile shaft. The influence factor, I ws, has a simple empirical relation (Vesic, 1977)
=2+0.3 5
Vesic (1977) also proposed a simple empirical relation for obtaining S
=
Where
e(3):
Cs = an empirical constant = (0.93 + 0.16 sqrt(L/D))C p
Pile Load Test Axial Compression Test Steps: - Load is applied to the pile by a hydraulic jack. - Step loads are applied to the pile and sufficient time is allowed to elapse after each load so that a small amount of settlement occurs - Measuring the settlements using dial gauges - After desired pile load is reached, the pile is gradually unloaded. (insert fig)
The settlement of the pile head or butt (S t) has two components. One is the elastic shortening of the pile (S e), and the other is the settlement of the pile point (S At any stage of loading
net).
= +
For any load Q, the net pile settlement can be calculated as When Q=Q1
When Q=Q2
Where
,_ = ⋮ , =
Snet = net settlement Se = elastic shortening of the pile itself S1 = total settlement (or settlement of the pile head) The values of Q can be plotted in a graph against the corresponding net settlement S net to get the ultimate load of the pile. The point corresponding to the point where the curve of Q versus S net becomes vertical is the ultimate load Q u. Davisson (1973) proposed another method to obtain the ultimate load Q u. The ultimate load occurs at a total settlement level (S u)
Where
=4+ + 120
Qu is in kN D is in mm L = pile length (mm) Ap = area of pile cross section (mm 2) Ep = Young’s modulus of pile material (kN/mm 2) (insert fig) Load Controlled Test - Requires the application of step loads on the piles and the measurement of settlement Constant-rate-of-penetration Test - The load on the pile is continuously increased to maintain a constant rate of penetration - Gives a load-settlement plot similar to load-controlled test Cyclic loading Test - Incremental load is repeatedly applied and removed Pile Driving analyzers - Used to determine the load carrying capacity of a driven pile - Alternative to pile load test (insert fig)
Pile Driving Formulas ENR Formula One of the earliest of these dynamic equations —commonly referred to as the engineering News Record (ENR) formula —is derived from the work-energy theory; that is, Energy imparted by the hammer per blow = (pile resistance)(penetration per hammer blow) According to the ENR formula, the pile resistance is the ultimate load, Q u, expressed as
ℎ = +
Where: WR = weight of the ram h = height of fall of the ram S = penetration of the pile per hammer blow
C = a constant -For drop hammers: C = 2.54 cm (if the units of S and h are in centimeters) -For steam hammers: C = 0.254 cm (if the units of S and h are in centimeters) Also, a factor of safety of FS = 6 was recommended to estimate the allowable pile capacity. Note that, for single- and double-acting hammers, the term W r h can be replaced by EH E (where E = hammer efficiency and H E = rated energy of the hammer). Thus,
= +
The ENR pile-driving formula has been revised several times over the years. A recent form—the modified ENR formula—is
+ ℎ = + +
where
E = hammer efficiency C = 0.254 cm if the units of S and h are in centimeters Wp = weight of the pile n = coefficient of restitution between the ram and the pile cap FS = 4-6
Danish Formula
where
= + 2
E = hammer efficiency HE = rated hammer energy Ep= modulus of elasticity of the pile material L= length of the pile Ap= area of the pile cross section
Negative Skin Friction - downward drag force exerted on the pile by the soil surrounding it. This action can occur under conditions such as the following: 1. If a fill of clay soil is placed over a granular soil layer into which a pile is driven, the fill will gradually consolidate. This consolidation process will exert a downward drag force on the pile (Figure 14.20a) during the period of consolidation. 2. If a fill of granular soil is placed over a layer of soft clay, as shown in Figure 14.20b, it will induce the process of consolidation in the clay layer and thus exert a downward drag on the pile. 3. Lowering of the water table will increase the vertical effective stress on the soil at any depth, which will induce consolidation settlement in clay. If a pile is located in the clay layer, it will be subjected to a downward drag force. (insert fig) Clay Fill over Granular Soil Similar to the β method presented in the negative (downward) skin stress on the pile is
=′ ′
Where: K’ = earth pressure coefficient = K o = 1 - sin ø’ σo = vertical effective stress at any depth z =γ’f z γ’f = effective unit weight of fill δ’ = soil –pile friction angle ≈ 0.5ø’ – 0.7ø’ Hence, the total downward drag force, Q n, on a pile is
δ′ ′ γ ∫ ′ γ′δ′ z dz= 2 where H = height of the fill. If the fill is above the water table, the effective unit weight, f
γ’f , should be replaced by the moist unit weight. Granular Soil Fill over Clay
In this case, the evidence indicates that the negative skin stress on the pile may exist from z = 0 to z = L 1, which is referred to as the neutral depth. The neutral depth may be given as (Bowles, 1982)
2γ γ = 2 + γ’ γ’
where γ’f and γ’= effective unit weights of the fill and the underlying clay layer, respectively. Once the value of L 1 is determined, the downward drag force is obtained in the following manner: The unit negative skin friction at any depth from z = 0 to z = L 1 is
=′′δ
′
where K’ = Ko σ'o = γ’f Hf + γ’ z δ’ = 0.5 ø’–0.7 ø’
1 - sin ø’
′ γ = ∫ =′γ δ′ + 2 δ′
Hence, the total drag force is
For end-bearing piles, the neutral depth may be assumed to be located at the pile tip (i.e., L 1 = L - H f ). If the soil and the fill are above the water table, the effective unit weights should be replaced by moist unit weights. In some cases, the piles can be coated with bitumen in the downdrag zone to avoid this problem. Baligh et al. (1978) summarized the results of several field tests that were conducted to evaluate the effectiveness of bitumen coating in reducing the negative skin friction.
Group Piles – Efficiency - piles are used in groups to transmit the structural load to the soil - A pile cap is constructed over group piles. - When the piles are placed close to each other, a reasonable assumption is that the stresses transmitted by the piles to the soil will overlap thus reducing the load-bearing capacity of the piles. Ideally, the piles in a group should be spaced so that the load-bearing capacity of the group is no less than the sum of the bearing capacity of the individual piles. In practice, the minimum center-tocenter pile spacing, d, is 2.5D and in ordinary situations is actually about 3D to 3.5D. (insert fig)
= ∑
The efficiency of the load-bearing capacity of a group pile may be defined as
Where: η = group efficiency Qg(u) = ultimate load-bearing capacity of the group pile Qu = ultimate load-bearing capacity of each pile without the group effect Piles in Sand Based on the experimental observations of the behavior of group piles in sand to date, two general conclusions may be drawn: 1. For driven group piles in sand with d ≥ 3D, Qg(u) may be taken to be ΣQ u, which includes the frictional and the point bearing capacities of individual piles. 2. For bored group piles in sand at conventional spacings (d ≈ 3D), Qg(u) may be taken to be 2/3 to 3/4 times ΣQu (frictional and point bearing capacities of individual piles). Piles in Clay The ultimate load-bearing capacity of group piles in clay may be estimated with the following procedure:
= [9] =
1. Determine ΣQu = n 1n2(Qp + Qs).
where cu(p) = undrained cohesion of the clay at the pile tip. 2. Determine the ultimate capacity by assuming that the piles in the group act as a block with dimensions of L g X Bg X L. The skin resistance of the block is
=2 + =∗ = ∗ = ∗ + 2( +)
Calculate the point bearing capacity from
The Variation of N* c with L/B g and L g/Bg is illustrated. Thus the ultimate load is
3. Compare the values obtained. The lower of the two values is Q (insert fig)
Piles in Rock
g(u)
For point bearing piles resting on rock, most building codes specify that Q g(u) = ΣQu, provided that the minimum center-to-center spacing of piles is D +300 mm. For H-piles and piles with square cross sections, the magnitude of D is equal to the diagonal dimension of the pile cross section. General Comments A pile cap resting on soil will contribute to the load-bearing capacity of a pile group. However, this contribution may be neglected for design purposes because the support may be lost as a result of soil erosion or excavation during the life of the project.
Elastic Settlement of Group Piles The simplest relation for the settlement of group piles was given by Vesic (1969) as
Where
= Sg(e) = elastic settlement of group piles Bg = width of pile group section D = width or diameter of each pile in the group Se = elastic settlement of each pile at comparable working load
For pile groups in sand and gravel, Meyerhof (1976) suggested the following empirical relation for elastic settlement:
Where
= 0.926√
q (kN/m 2) = Qg/(Lg Bg) Lg and Bg = length and width of the pile group section, respectively (m) N60 = average standard penetration number within seat of settlement (≈ B g deep below the tip of the piles) I = influence factor = 1 - L/8B g ≥ 0.5 L = length of embedment of piles (m) Similarly, the pile group settlement is related to the cone penetration resistance as:
= 2
where qc = average cone penetration resistance within the seat of settlement.
Consolidation Settlement of Group Piles The consolidation settlement of a pile group can be estimated by assuming an approximate distribution method that is commonly referred to as the 2:1 method. The calculation procedure involves the following steps: 1. Let the depth of embedment of the piles be L. The group is subjected to a total load of Qg. If the pile cap is below the original ground surface, Q g equals the total load of the superstructure on the piles minus the effective weight of soil above the pile group removed by excavation. 2. Assume that the load Q g is transmitted to the soil beginning at a depth of 2L/3 from the top of the pile, as shown (z = 0). The load Q g spreads out along 2 vertical:1 horizontal lines from this depth. Lines aa ’ and bb’ are the two 2:1 lines. 3. Calculate the effective stress increase caused at the middle of each soil layer by the load Q g:
′ = + +
where
Δσ’i = effective stress increase at the middle of layer i Lg, Bg = length and width of the plan of pile group, respectively zi = distance from z = 0 to the middle of the clay layer, i (insert fig)
=1+
4. Calculate the settlement of each layer caused by the increased stress:
Where: ΔSc(i) = consolidation settlement of layer i Δe(i) = change of void ratio caused by the stress increase in layer i eo(i) = initial void ratio of layer i (before construction) Hi = thickness of layer i 5. Calculate the total consolidation settlement of the pile group by
= Note that the consolidation settlement of piles may be initiated by fills placed nearby, adjacent floor loads, and lowering of water tables.
