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Reese’s Sand Model Compiled by Jinchi Lu and Liangcai He
1
Introduction
Some of the early soil models for predicting the behavior of the sand around a pile subject
lateral loading were given by Terzaghi (1955), Parker and Reese (1971), and Reese, Cox
Koop (1974). The model reported here is the one proposed by Reese, Cox and Koop (1974)
The Reese, Cox and Koop (1974) sand model is represented by a family of p-y curves of the soil at of interest (Figure 1). Each p-y curve in Figure 1 stands for the lateral response of soil at a specific
In the so-called p-y curve, p is the lateral soil resistance per unit length of pile and y is the displacem
the soil. This model is based on a series of field testing of two laterally loaded pipe piles in sand in (Cox, Reese, and Grubbs, 1974).
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Practical application
Reese, Cox and Koop (1974) noted the soil model is good for driven pile in sand above or b water table under both static and cyclic loads. However, caution shall be exercised
applying the model to other piles that greatly differ from the test piles (tests are briefly desc
in the following section), for example a pile subjected to high frequency lateral loads d earthquake.
3
Tests performed
The tests on which this model is based were carried out at a test site on Mustang Island Corpus Christi, Texas. The test site (Figure 2) was 40 ft wide by 60 ft long.
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Two soil borings were made in the test sites as shown in Figure 2. Standard penetration test
laboratory experiments were also performed. The soil in the site consisted of silty fine san
fine sand. The soil profile of the test site is shown in Figure 3. The top 40 ft of the site
medium dense sand overlain by 10 ft soft clay. Below the soft clay is 20 ft dense sand
original ground surface was 5 ½ ft above water table. Before installation of the piles, the top
ft layer was removed. The water table was thereafter maintained above the new ground su during loading.
Two piles made from 24 in diameter pipe with a wall thickness 3/8 in were tested. The
material was A-53 grade B seamless steel. Each pile consisted of 3 sections. The bottom is un-instrumented section. The middle is a 32 ft section instrumented with strain gages. The
10 ft section without strain gages. Displacement transducer and load cell were installed a pile top. The test piles were installed by driving d riving with a hammer.
Test Pile 1 ” Steel Pi e
Test Pile 1 ” Steel Pi e
10’ uninstrume
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Before pile installation, the test piles were calibrated and pile EI constants (E is You
modulus and I is inertial of moment) were obtained. During installation of the piles, the bo
section was driven into the sand first, the sections above it were then welded on it and dr continued until the pile was driven to the desired depth.
Both piles were tested under static and cyclic loadings. On pile 1, the static tests were perfo
first, and the cyclic tests were conducted one month after the static tests. But on pile 2 the c tests were performed first, the static tests were performed shortly after the cyclic tests.
During static tests, loads were first applied in increments of 2,500 lbs to 15,000 lbs and th
increments of 1,250 lbs from 15,000 lbs to a maximum of 60,000 lbs. The outputs of instrum
were recorded at each load level. Data were also taken as loads were decreased in incremen 10,000 lbs back to 0.
During cyclic tests, the same peak 1,000 lbs to 3,000 lbs was applied first in both forwar
backward directions. Subsequently the peaks applied in forward direction were between 1
and 60,000 lbs, and the peak in the backward direction was about 1/3 of the forward dire The cycle time is about 16 ~ 20 seconds. At each load level, several cycles were needed in
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4
Determination of p-y curve from test results
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which yields:
κ= (εa - ε b)/(da - d b) Equation (3) can be used to obtain the curvature of a pile at a certain cross section since (d
is the known distance from A to B. This equation has the advantage of eliminating the effec
bending in the other direction when analyzing concrete piles. Once curve is calculated, M c found by employing Equation (2).
The experimental p-y curve can then be computed by the following two equations appropriate boundary conditions
y = p =
∫ ∫ κ dx d 2 dx 2
M ( x )
Soil displacement y expressed by Equation (4) can normally be obtained by num
integration using trapezoidal rule with appropriate accuracy. However, caution should be ex
when solving Equation (5). Error from experiments will be seriously amplified if dir
differentiating experimental moment using numerical technique. To avoid this pro curve fitting the experimental moments up to the order of 6 may be required. Master polynomial your semester with Scribd Read Free Foron 30this Days Sign up to vote title & The New York Times Useful Not useful 5 Construction of p-y curve Special offer for students: Only $4.99/month.
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Step 1. Obtain soil internal friction angle φ, effective unit weight γ’, and pile diameter b Note: Pile diameter b can be in any length unit.
Figure 4 Construction of p-y curve.
Step 2. Compute following parameters α = φ /2 φ /2 β = 45 + φ /2 φ /2 K 0 = 0.4 2
K a = tan (45- φ /2) φ /2)
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K 0 tan φ sin β
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tan β
(b
tan β tan )
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(a) Wedge failure mode
(b) Block failure mode
Figure 5 Two types of soil failure mode
Step 4. Determine the point u and point m yu = 3b/80,
pu = Apu
ym = b/60,
pm = Bpu
where b is pile diameter in any length unit, A is a correction factor from empiricism that c
found from empirical curves in Figure 6(a), B is is another empirical factor factor that can be obt
from Figure 6(b). Note that for static case, use As and Bs, for cyclic case, use Ac and Bc in F
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Step 5. Find the initial slope of the p-y curve: k 0 = kz
where z is depth and k is sub-grade modulus for sand. A rough value of k can be found Table 1.
Table 1 Reese, Cox, and Koop (1974) recommended k values for sand (static and cyclic loading
Relative Density
Loose
Medium
Dense
MN/m
6.8
24.4
61.0
(lb/in.3)
(25.0)
(90.0)
(225.0)
5.4
16.3
34
(20.0)
(60.0)
(125.0)
k for Sand above water table 3
k for Submerged Sand 3
MN/m
3
(lb/in. )
Step 6. Establish the parabolic section of the p-y curve in the form:
p
= Cy 1 / n
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C =
p m 1/ n
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φ=
35o, k = 16300 kN/m3. Pile diame
0.61m. The curves in Figure 7 match those given by Reese and Impe (2001). kN/m
m
Figure 7 Reese p-y curve examples.
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Effects of subgrade modulus k
Figure 8 shows the effects of subgrade modulus k on p-y curve. It can be seen that as sub 3
modulus increases from 5,000 to 60,000 kN/m , p-y curves at 2 m depth vary only a amount. Therefore, soil subgrade modulus k has no significant effects on p-y curve.
Z = 2m
3
k = 5,000 kN/m , 16,300 kN/m3, 3 35,000 kN/m , 3 60,000 kN/m ,
Figure 8 Effects of soil subgrade modulus k on p-y curve
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Figure 9 shows the effects of soil internal friction angle
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φ = 40o φ = 35o φ = 30o φ = 25o Z = 2m
Figure 9 Effects of soil internal friction angle
7.3
φ on p-y curve
Effects of soil unit weight
Figure 10 shows the effects of soil unit weight γ on p-y curve. It can be seen that as soi 3
weight γ increases from 10 to 20 kN/m , p-y curves at 2 m depth vary a lot. Therefore, soi weight γ has significant effects on p-y curve.
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Effects of soil pile diameter
Figure 11 shows the effects of pile diameter b on p-y curve. It can be seen that as pile diam
increases from 1.0 to 2.0 m, the slope of the initial segment of the p-y curves the same d keep the same. The slope increases as depth goes deeper.
It also can be seen that the ultimate soil resistance increases as pile diameter increases. T
due to the fact that more soil was involved to resist pile deflection as pile diameter increases
The interesting thing is that the middle part of the p-y curves at 12 m depth (Figure 11
displays opposite diameter effects from those at 2 m depth (Figure 11 (b)). At 2 m depth (F
11 (a)) soil resistance in the middle part of the p-y curves increases as increasing pile diam
while at 12 m depth (Figure 11 (b)) soil resistance decreases as increasing pile diameter.
may be due to the different soil failure modes at different depth. At 2 m depth soil fails follo
the wedge failure mode (Figure 5(a)), while at 12 m depth soil fails following the block f mode (Figure 5(b)).
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kN/m
Z = 2m
m
(a)
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FB-Pier Runs
The model is a single pile subjected a lateral load at the pile head (Figure 11). The soil lay
uniform sand with water table at the pile head. The pile has a diameter of 0.5m and a heig
10m. The objective of the FB-Pier runs performed is to study the effects of the soil prop
(internal friction angle φ, subgrade modulus K and unit weight γ) on the behavior of Reese model.
(a)
(b)
Figure 12Scribd Single pile model used in FB-Pier runs Master your semester with Read Free Foron 30this Days Sign up to vote title & The New York Times Useful Not useful Cancel anytime.
Special offer for students: Note thatOnly the $4.99/month. above mentioned soil properties are dependent with each other in reality. One
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Moment (KN-m) -20
140
0
20
40
60
0 120
1 2
100
) N K ( d a o L
60
Φ = 32° 40
3
) m ( h t p e D
80
Φ = 36°
4 5 6
Φ = 40°
20
Φ
7
Φ
8
Φ
9 10
0 0.00
0 .0 2
0.04
0 .06
0.08
0 .10
Pile He ad Displacement Displacement (m)
Figure 13 Load-deflection curve (left) and moment distribution (right) of the pile for different friction
8.2
Effect of the subgrade modulus
Figure 13 shows the load-deflection curve and the moment distribution of the pile for diff 3
subgrade moduli (3.75, 37.5 and 61 MN/m ), while keeping the internal friction ang 3
degrees, and the unit weight 18.7 KN/m . 3
It is noted that the curves for the subgrade modulus = 37.5 and 61 MN/m are almost the s
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-1 0
0 0
10
20
30
40
5
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Effect of unit weight
Figure 14 shows the load-deflection curve and the moment distribution of the pile for diff 3
unit weights (16, 18.7 and 21 KN/m ), while keeping the internal friction angle 36 degree an subgrade modulus K = 37.5 MN/m3.
Moment (KN-m) -10
0
10
20
30
40
50
0
140
1 120 2 100
) N K ( d a o L
3
) m ( h t p e D
80
60
40
20
0.0 2
0.03
6 7
γ = 18.7 KN/m3
8
0.04
0.0 5
γ = 16 KN/m3
γ = 18.7 KN/m
γ = 21 KN/m3 0.01
5
γ = 16 KN/m3
9
0 0 .00
4
0.06
γ = 21 KN/m3
10
Pile He ad Displacement Displacement (m)
Figure 15 Load-deflection curve (left) and moment distribution (right) of the pile for different unit we
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Special offer forFigure students: $4.99/month. 15Only shows the load-deflection curve and the moment distribution of the pile for rea
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Reese, Cox, And Koop Sand Model Uploaded by v
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Some of the early soil models for predicting the behavior of the sand around a pile subjected to lateral loading were given by Terzaghi (1955), Parker and Reese (1971), and Reese, Cox and Ko… Full description
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Reese, Lymon C._ Van Impe,
Lateral Resistance of
Numerical Modeling of
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Moment (KN-m) - 20 140
0
20
40
60
0 1
120
2 100 3
) N K ( d a o L
) m ( h t p e D
80
60
20
5 6
Loose
Medium
7
Medium
Dense
8
Dense
Loose 40
4
9 0 10 0 .0 0
0 .0 5
0 .1 0
0.15
0 .2 0
0 .2 5
0.3 0
Pile Head Displacement (m)
Figure 16 Load-deflection curve (left) and moment distribution (right) of the pile for loose, medium dense sand
9
Summary
The Reese sand model is summarized as follows:
•
The model was originally developed for the design of laterally loaded piles in sand
both static and cyclic loads in offshore structures. The tests were performed on d
in sand below water Scribd table only. Only two piles were tested. The twopiles ha Master your piles semester with Read Free Foron 30this Days Sign up to vote title frequ same diameter of 24 in. The cyclic loads applied in the tests were at very low & The New York Times Useful Not useful (about 0.05 Hz). Special offer for students: Only $4.99/month.
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Reese, Cox, And Koop Sand Model Uploaded by v
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Some of the early soil models for predicting the behavior of the sand around a pile subjected to lateral loading were given by Terzaghi (1955), Parker and Reese (1971), and Reese, Cox and Ko… Full description
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Embed
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Download
1
of 18
Reese, Lymon C._ Van Impe,
Lateral Resistance of
Numerical Modeling of
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10 References
Cox, William R., Lymon C. Reese, and Berry R. Grubbs (1974). “Field Testing of Late
Loaded Piles in Sand”, Proceedings of Offshore Technology Conference, 6200 North C Expressway Dalla, Texas, paper number OTC 2079.
Parker, Frazier and Lymon C. Reese (1971), “Lateral Pile-Soil Interaction Curves for S
Proceedings, The International Symposium on the Engineering Properties of Sea-Floor Soil
Their Geophysical Identification, University of Washington, Seattle, Washington, July 25, 1
Reese, Lymon C., William R. Cox, and Francis D. Koop (1974). “Analysis of Laterally Lo
Piles in Sand”, Proceedings of Offshore Technology Conference, 6200 North C Expressway Dalla, Texas, paper number OTC 2080.
Terzaghi, Karl (1955), “Evaluation of Coefficients of Subgrade Reaction,” Geotechnic, Vo December, 1955, pp. 297-326.
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