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2.1The Robertson et al, Pushed in PMT Method (1986)
Robertson et al. (1986) suggested a method that uses the results of pushed-in PMT to evaluate p-y curves of a driven pile. According to the authors, the results provide an excellent comparison with lateral loaded pile test measurements. The pressure component of the PMT curve is multiplied by an α-factor to obtain the corrected p-y curve. Using finite element analysis Byrne and Atukorala (1983) confirmed this factor, which was initially suggested by Hughes et al. (1979), Robertson et al. (1986) corrected the factor α near the surface assuming that the PMT response is affected by the lower vertical stress. The factor increases linearly up to a critical depth, which is assumed to be four pile diameter (Dc = 4) as shown in Figure 2.16.
Figure 2.16 Correction Factor “α” versus Relative Depth (From Robertson et al,. 1986)
To obtain the p-y curve, the PMT curve is re-zeroed to the lift-off pressure that is assumed to be equivalent to the initial lateral stress around the pile. The stress is multiplied by the pile width and the strain component is multiplied by the pile half width. For a small strain condition is assumed equal to where R and V are radius and volume of the PMT respectively.
Since the installation of the pushed in PMT produces an initial pressure on the probe, an unload/reload sequence is often used. The portion of the corrected PMT curve from the beginning of reload through the maximum volume is recommended for determining p-y curves of driven piles, while the initial slope from the PMT tests is recommended for constructing p-y curves for augured piles. The following equations outline the process for driven piles:
a) Determine the initial radius of the probe:
(2.15)
b) Calculate the initial volume of the probe (Vo):
(2.16)
c) Determine P in units of force / length:
First a correction factor, , is applied to P according to Figure 2.16, where the relative depth is the depth from the ground surface to the center of the membrane. Note that for for sands andfor clays and if then can be found as follows:
(2.17)
(2.18)
Then
(2.19)
where: Bpile = pile diameter or width.
d) Determine y in units of length according to the following equation:
(2.20)
2.2The Briaud et al, Method (1992)
Briaud et al (1992) recommended that the p-y curves be constructed from the addition of the front and side resistance components along the pile. The total soil resistance P as a function of lateral movement y of the pile, is given by the equation:
P = F + Q(2.21)
where
F= friction resistance
Q= front resistance
Briaud suggested for the full displacement driven piles, that the reload portion of the PMT curves be used. Graphically, the p-y curve is shown as the addition of the F-y curve and the Q-y curve in Figure 2.17.
Figure 2.17 Front and side resistance components for P-y curve construction
Smith (1983) showed excellent correlations between the pressures obtained from the PMT response and those acting on the pile. The front pressure contribution, Q, is found from the net limit pressure pL* determined as:
(2.22)
where; pL is the limit pressure and p0 is the horizontal stress at rest pressure obtained from the PMT curve. The frontal resistance, Q is obtained by choosing pressure points from the reduced PMT plot and using the equation:
(2.23)
The side friction, F(side), of the pile is taken as a constant with depth and is given by the equation:
(2.24)
To obtain the associated lateral pile deflections, choose PMT deflections and apply the following equation. The deflections must be less than those obtained from the PMT test and would equate to the change in radii obtained during expansion.
(2.25)
Where: Q(front)= soil resistance due to front reaction with unit of force /unit length of pile
F(side)= soil resistance due to friction resistance with unit of force /unit length of pile
p(pmt)= pL* = net pressuremeter pressure
B(pile)= pile width or diameter
τ(soil)= maximum soil shear stress-strain at the soil-pile interface
S(Q)= shape factor ( = 0.8 or π/4 for circular piles, 1.0 for square piles)
S(F)= shape factor ( = 1.0 for circular piles, 2.0 for square piles)
y(pile) = lateral deflection of the pile
y(pmt) = increase in radius of the soil cavity in the PMT test or radial displacement.
R(pile) = pile half-width or radius
R0(pmt) = R0= initial radius of the soil cavity in PMT test
This method does rely on an accurate estimate of the shear strength, which could be found from other field-testing performed during the site investigation.
The displacement of soil around the laterally loaded pile is also influenced by the ground surface. A reduction in the corrected PMT pressures is recommended for values near the ground surface. A critical depth (Dc), to which pressures and displacements are influenced, depends on the pile load, diameter and stiffness. Briaud suggested using a relative rigidity factor, RR, given by:
(2.26)
EI = pile flexural stiffness (E= pile modulus, I = pile moment of inertia)
= pile diameter or width
pL* = net PMT limit pressure
Briaud et al. (1992)relationship results in relative rigidities slightly greater than 10 for most laterally loaded piles in soft clays and the resulting critical depth will be near 4, therefore Robertson’s value of 4 is recommended. The critical depths for the PMT as recommended by (Baguelin et al., 1978) are 15 PMT diameters for cohesive soils, and 30 PMT diameters for cohesionless soils.
The Briaud et al. (1992) suggested reduction factor is shown in Figure 2.18 as a function of relative depth (z/zc). The PMT curve is then corrected by using:
(2.27)
Figure 2.18 Briaud’s recommended PMT pressure reduction factor for values near the ground surface
2.3Dilatometer P-y curves
Unlike the PMT, which produces a comparatively large radial deformation (approximately 3.5 mm over 24 cm in length), the DMT only produces 1.1 mm of lateral deformation at the center of a 60 mm ring. The deformation is produced by a single volume injection; therefore, there are no increments of pressure with which to develop a load-deformation curve.
The basic soil properties determined from the DMT indices are used in conjunction with a parabolic function to develop p-y curves. For this research, curves determined from DMT tests were developed based on the method presented by Robertson et al. (1989).
2.3.1Cohesive Soils
For cohesive soils the following cubic parabolic curve is suggested:
(2.28)
Where: (2.29)
With ycin cm, Bpile = pile diameter, cm, and an empirical stiffness factor, Fc 10. The evaluation of the ultimate lateral resistance Pu is again given in a bearing capacity format as:
(2.30)
At considerable depths Np 9, but near the surface it reduces to 2 to 4; the non-dimensional factor is calculated as:
< 9.0(2.31)
where z = depth,
vo = effective stress at depth z, and
J = empirical stiffness factor set to 0.5 for soft clay and 0.25 for stiff clay.
The value of Su can either be obtained from DMT values, or PMT estimates as
(2.32)
With Su and pL in kPa.
Cohesionless Soils
For cohesionless soils, use the above cubic parabola (equation 2.28), where Pu is based on the findings of Reese et al. (1974) and Murchison and O’Neill (1984) and is the lesser of:
(2.33)
or and is 45o + ’/2(2.34)
and ycis:
(2.35)
where F is an empirical factor equal to 1 for cohesionless soil.
2.4References
- Cosentino, Paul J., Edward Kalajian, , Ryan Stansifer, ,J Brian Anderson, Kishore Kattamuri, Graduate Research Assistant, Sunil Sundaram, Graduate Research Assistant, Farid Messaoud, Thaddeous J. Misilo, Marcus A Cottingham (2006) Draft Final Report, Standardizing the Pressuremeter Test for Determining p-y Curves for Laterally Loaded Piles, Florida Institute of Technology, Civil Engineering Department, Florida Department of Transportation, Contract Number BC-819.
- Briaud, J.L., 1997. “Simple Approach for Lateral Loads on Piles”. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 123, No. 10 pp. 958-964.
- Robertson, P. K., Campanella, R. G., Brown, P. T., Grof, I., and Hughes, J. M., (1985). “Design of Axially and Laterally Loaded Piles Using In Situ Tests : A Case History”, Canadian Geotechnical Journal, Vol. 22, No. 4, pp.518-527.
- Robertson, P.K., Davis, M.P., Campanella, R.G.. (1989). “Design of Laterally Loaded Driven Piles Using the Flat Dilatometer”, ASTM Geotechnical Testing Journal, Vol.12, No. 1, pp30-38.
- Robertson, P.K., Hughes, J.M.O., Campanella, R.G., and Sy, A., 1983. “Design of Laterally Loaded Displacement Piles Using a Driven Pressuremeter”. ASTM STP 835, Design and Performance of Laterally Loaded Piles and Piles Groups, Kansas City, Mo.
- Robertson, P.K., Hughes, J.M.O., Campanella, R.G., Brown, P., and McKeown, S., 1986. “Design of Laterally Loaded Displacement Piles Using the Pressuremeter”. ASTM STP 950, pp. 443-457.
- Robertson, P.K., and Hughes, J.M.O., 1985. “Determination of Properties of Sand from Self-Boring Pressuremeter Tests”. The Pressuremeter and Its Marine Applications, Second International Symposium.
- Robertson, P.K., Davies, M.P., and Campanella, R.G., 1989. “Design of Laterally Loaded Driven Piles Using the Flat Dilatometer”. Geotechnical Testing Journal, GTJODJ, Vol. 12, No. 1, pp. 30-38.
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