Reese’s Stiff Clay below Water Table

Reese’s Stiff Clay below Water Table Introduction The focus of this paper is to investigate the material, which has come to be known as Reese’s Stiff Clay below Water Table. Originally, this type of soil was a major concern to the oil industry since several off shore structures encounter similar conditions on the ocean floor. Therefore, studies and tests were conducted in order to understand the properties of the material and come up with a numerical model that could be useful for analysis. The tests consisted of both static and cyclic load case. The cyclic case was intended to represent wave action encountered by offshore structures. This paper will summarize the tests conducted and their results, as well as, discuss the numerical model Reese created – how it compares to field test results and the practicality of its construction. Lastly, the computer program Florida Pier, and its incorporation of Reese’s model for stiff clay below the water table, will be examined. Test Summary The test involved two nominally 24” diameter piles and one nominal 6” diameter pile, driven into stiff clay and subjected to lateral loading under both static and cyclic loading. The surface soils consisted of stiff, preconsolidated clays of marine origins, while the water table for the tests was above the ground surface by a few inches to resemble conditions for an offshore platform. The results obtained from loading were then analyzed to obtain the corresponding p-y curves from which a procedure was used to predict p-y curves for stiff clays under the water table. Testing Procedure A pit 45ft wide by 50ft long by 3ft deep was excavated as shown in Figure 1. This pit was then flooded with water to ensure saturation of the near surface clays to emulate actual conditions of clay on the ocean floor. This flooding was done 5 months before installation of the piles and 6 months before the actual testing. After borings were conducted, an additional 2.5 foot was excavated and after installation of the piles, the top 6” of the soil was removed. This meant that the bottom of the pit was around 6ft below the original ground surface. Borings logs, triaxial tests and stress-strain curves of the soils samples (refer to Figure 2) taken were conducted and prepared to obtain the soil properties and parameters to be used in the analysis. The 24” diameter piles had a total length of 60ft and had two 5/8” semicircular thick wrappers installed around the test pile by circumferential welds at the flange and at the bottom of the wrapper section in addition to two longitudinal welds, since the existing 3/8” wall thickness of the piles was not sufficient for installation in stiff clay. It was driven using a Delmag D-12 diesel hammer. The 6” diameter pile consisted of an upper 28 foot long instrumented section and a 15 foot long un-instrumented lower section. They had wall thicknesses of 0.718” and 0.475” respectively. The instrumentation on all of the piles included stain gages. The two 24” piles were subjected to a total of six loading series each using a hydraulic ram and a load cell in series (refer to Figure 4). Three of the loading series were to relieve stress concentrations due to the addition of the 5/8” wrappers while the other three were for the purpose of recording data. A maximum load of 50,000 lb was applied which corresponded to a maximum stress of 15,000 psi. The 6” pile was subjected to a total twelve loadings (six with a free head and six with a rotational restraint at the top of represent rotational restraint for piles in jackets of offshore platforms) (refer to Figure 5). The maximum load applied was 5000 lb which corresponded to a maximum stress of 20,000 psi.

Fig. 1 Test layout

Fig. 2 Stress-Strain Curves of Soil Samples

Fig. 3 Composite Soil Profile

Fig. 4 Test Setup of 24” diameter piles

Fig. 5 Test Setup of 6” diameter piles

Analysis of Field Results The analysis of laterally loaded piles is accomplished by the following equations:

pdx

ydEI =4

4

(1)

yEp s−= (2)

To obtain the parameters that would be used for these equations and to obtain the p-y curves, and knowing the boundary conditions at the top and bottom of the pile, the experimental bending moment curves are used to obtain p and y using the following equations:

EIxMy )(

= (3)

)(2

2

xMdxdp = (4)

Equation (3) is solved numerically, while to solve Equation (4), they assumed that the soil modulus for a particular moment curves could be described using the following equation:

ns kxE = (5)

Solving these equations, p-y curves were developed as shown in Figures 6, 7, 8 and 9. It is clear that there is redundancy in the equations e.g. y could be obtained from Equation (1) and (3). This redundancy was utilized to obtain the best possible curve fitting.

Fig. 6 p-y Curves for 24” diameter Piles (Static Case)

Fig. 7 p-y Curves for 24” Diameter Piles (Cyclic Case)

Fig. 8 p-y Curves for 6” Diameter Pile (Static Case)

Fig. 9 p-y Curves for 6” Diameter Pile (Cyclic Case)

The following comments could be made of the results obtained: • The initial slope and ultimate resistance increase with depth. • The soil resistance decreases for cyclic loading in comparison with static

loading. • At small depths, the soil resistance for the free head was larger than the

restrained head, while at larger depths, there was larger resistance from the restrained case. This result, however, could be due to the fact that each test was carried out at a different location and could be attributed to testing irregularities. The differences were considerably small from a design point of view and due to lack of sufficient data, no differences were set in the criteria for the p-y curves for both cases.

• The initial part of the p-y curve is relatively steep.

• At a particular deflection, when the ultimate soil resistance is developed, a reduction occurs with soil resistance with continued deflection.

• The ultimate soil resistance is reached with only a small deflection (less than 1% of pile diameter), which could be attributed to the brittle behavior of the stiff clay.

• The values of ultimate resistance and corresponding deflection are significantly less in the cyclic loading case compared to the static loading case.

• There was severe deterioration in the p-y curves in the cyclic case after the ultimate soil resistance was reached.

Using these observations and a procedure to be outlined shortly, a method by which p-y curves could be generated for similar sites was developed. However, only the results using the 24” diameter piles were used to reach such a procedure and there were variations between the final results obtained using the procedure and the behavior of the 6” diameter pile. However, those changes were not directly addressed. This means that this procedure might not be that suitable for other diameters and generalizing it for all other diameters does not seem to be well justified. Development of p-y Curves from Field Results The experimental p-y curves previously shown indicated that standard p-y curves could be developed with the shapes shown in Figure 10 below. The static curve that was developed consisted of an initial straight line portion, shown as the section from the origin to Point 1 in Figure 6, two parabolic sections from point 1 to 2 and 2 to 3, a straight line from point 3 to 4 and a horizontal line after point 4. The cyclic curve consisted of an initial straight line portion from the origin to Point 1 in Figure 6, a parabolic section from point 1 to 2, and two straight line portions from point 2 to 3 and a horizontal line after point 3. The slope of the straight line (from origin to point 1) was obtained from the equation:

i

isi y

pE = (6)

Fig. 10 Characteristic p-y Curves (a) Static (b) Cyclic

where Esi is the initial soil modulus and pi and yi were the coordinate of the initial section as determined from the experimental results and using the graph in Figure 11, where it was noticed that:

kxEsi = (7)

Values of k were computed based on experimental results. For other values, Reese proposed using the values suggested by Terzaghi for the static and cyclic cases, where the values for the cyclic casces were 40% of the static cases.

Fig 11 Initial Soil Modulus vs. Depth

By careful observation of the experimental p-y curves, it was clear that there is a well defined value of the ultimate soil resistance that increases with depth. The theoretical value of the ultimate soil resistance at depth H, based on the model utilizing a wedge of clay moving up and out from a pile, could be calculated as shown in Equation 8:

HcbHbcp aac 83.22 '1 ++= γ (8)

where pc1 is the ultimate soil resistance at depth H, ca is the average undrained shear strength, b is the diameter of the pile and γ’ is the submerged unit weight of the soil. The theoretical value of the ultimate soil resistance assuming the soil fails by flowing horizontally could be computed using Equation 9:

cbpc 112 = (9)

where c is the undrained shear strength of the clay at the depth for the p-y curve. The values calculated based on theory from the last two equations was higher than the experimental results. As a result, a constant A and B was computed as shown in Figure 2.12, to adjust the theoretical values to the actual values where A and B are the constants for the static and cyclic cases respectively.

c

su

ppA )(

= (10)

( )c

cu

pp

B = (11)

where (pu)s and (pu)c are the ultimate resistances from the experimental results and pc is the ultimate resistance from theory (the lowest of equations 8 and 9 above).

Fig 12 Coefficients A and B

Regarding the rest of the p-y curve, εc which corresponds to a stress of 50% of the ultimate stress, is used. yc is then defined as follows:

by cc ε= (12)

This parameter is then used for the equation of the parabola shown in Figure 10, as follows:

5.0

5.0

=

cc y

ypp (13)

The parabolic shape of the p-y curve in Figure 10, is assumed to be from the intersection of the straight line with the parabola corresponding to Equation 13. This continues until Ayc, where A is as defined above. An offset is constructed at Ayc of the following value:

25.1

055.0

−=

c

ccoffset Ay

Ayypp (14)

Equation 14 continues until the deflection corresponding to 6Ayc, where it changes to a straight line with the following slope:

c

css y

pE 0625.0−= (15)

This straight line ends at a deflection of 18Ayc where it becomes a horizontal line. For the cyclic case, the following definition is made:

cp Ayy 1.4= (16)

The parabola for this case is defined as:

−−=

5.2

45.05.0

1p

pc y

yyBpp (17)

Again, like the static case, this parabola begins at the intersection with the straight line defined in the very beginning, but continues only until 0.6yp, where it changes to a straight line with the following slope:

c

csc y

pE 085.0−= (18)

This line continues until a deflection of 1.8yp, where it becomes horizontal. These equations were then used to develop theoretical p-y curves and comparisons were made with the deflections and bending moments obtained experimentally as shown in Figures 13-20. When compared with the 6” diameter pile, the deflections obtained experimentally were much higher. Reese considered that not to be much of a problem due to the fact the remaining results conformed well, but that does not seem to be justified, since the remaining results are expected to conform well, since the whole model was based on the experimental results for the 24” diameter pile. This appears to be a weak point in the model as a whole. In addition, the model did not take into account pile groups or restrainment of the pile head.

Fig. 13 Comparison of Computed Moment Curves with Experimental Moment Curves for

Static Case

Fig. 14 Comparison of Ultimate Soil Resistance Obtained Experimentally and the

Computed One

Fig. 15 Comparison Between Measured and Computed Maximum Bending Moment for

Static Loading (24” Diameter Pile)

Fig. 16 Comparison Between Measured and Computed Values for Deflection for Static

Loading (24” Diameter Piles)

Fig. 17 Comparison Between Measured and Computed Values of Deflection for 6”

Diameter Pile

Fig. 18 Comparison Between Measured and Computed Maximum Bending Moment for

Cyclic Loading (24” Diameter Pile)

Fig. 19 Comparison Between Measured and Computed Values of Deflection for Cyclic

Loading (24” Diameter Piles)

Fig. 20 Comparison Between Measured and Computed Bending Moment Curves for

Cyclic Loading

Examples A set of p-y curves was constructed for stiff clay for a pile with a diameter of 0.61m. The soil profile is shown in figure 21. The submerged unit weight of the soil was assumed to be 7.9 KN/m3 for the entire depth.

Fig. 21 Soil profile used for example p-y curves for stiff clay

Fig. 22 p-y curves (static) for different depth z

Fig. 23 p-y curves (static) for different diameter b

Fig. 24 p-y curves (static) for different Cu

Fig. 25 p-y curves (cyclic) for different depth z

Fig. 26 p-y curves (cyclic) for different diameter b

Fig. 27 p-y curves (cyclic) for different Cu

From the example figures above, we could see that: (1) for both static and cyclic models, soil strength increases with depth if all the other

parameters remain same. But the rate of the increasing decreases with depth. (2) for both static and cyclic models, soil strength increases with pile diameter b.

And soil becomes more ductile as b increases. (3) for both static and cyclic models, soil strength increases with Cu. However, for

static model, the soil behave becomes more brittle as well. Florida Pier The Department of Civil & Coastal Engineering at the University of Florida developed the computer program, Florida Pier. Its primary function is to analyze the soil-structure interaction between piles, piers, and the soils in which they are placed. For this paper, single piles and group piles were modeled in order to examine how Florida Pier incorporates Reese’s model for stiff clay below the water table. In order to construct lateral p-y curves for the soil modeled, Florida Pier requires five parameters: C (undrained shear strength), γ’ (unit weight of submerged soil), Ks (sub grade soil modulus), ε50 (soil strain associated with 50% failure), Ca (average undrained shear strength). For the investigation of Florida Pier the following parameters were used:

Cu= 200 kPa; γ’ = 11 kN/m3; Ks = 135 MN/m3; ε50 = .005 m/m; Ca = 200 kPa Pile: Standard Steel (circular) Pre-Stress (square) L = 12 m L = 12m Dia. = .61 m b = .455 m Florida Pier allows one to view the p-y curve for the modeled soil. Fig. 28 and Fig. 29 compare theoretical p-y curves of Reese’s model for stiff clay below the water table with the curves generated in Florida Pier. Fig. 28 is constructed for the values above, while Fig. 29 is computed for the same values with double the diameter of the pile.

Fig. 28

Fig. 29 Fig.30, 31, 32 compare the resultant displacements, soil resistance, and moments respectively for the standard steel pile, double the diameter, and double the undrained shear strength. These pile were subjected to a lateral force of 600 kN. Also included in the figures, is the standard steel pile subjected to a lateral force of 44.5kN. From Fig 30 it is clear that despite the varying conditions, the overall behavior of the pile is the same. The majority of the displacement takes place in the upper 25% of the pile length. Doubling the Diameter and doubling the undrained shear strength of the soil result in similar deflections, which expectantly are less than the standard pile. Fig 31 shows that by doubling the diameter of the pile, the soil resistance was reduced. This is due to the increased area of soil affected. Fig 32 shows that by doubling the undrained shear strength; the moment induced in the pile is significantly reduced. It is not clear why this occurs; perhaps the stiffer soil limits the pile’s curvature and therefore reduces the induced moment.

Displacement

0

0.2

0.4

0.6

0.8

1

1.2

-1.00E-02 0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02

meters

x/l

45kN

600kN

Dbl. Dia.

Dbl. Su

Fig. 30

Soil Resistance

0

0.2

0.4

0.6

0.8

1

1.2

-200 -100 0 100 200 300 400 500 600

kN

x/l

45kN

600kN

Dbl. Dia.

Dbl. Su

Fig. 31

Moment

0

0.2

0.4

0.6

0.8

1

1.2

-5.00E+01 5.00E+01 1.50E+02 2.50E+02 3.50E+02 4.50E+02 5.50E+02 6.50E+02

kN*m

x/l

45kN

600kN

Dbl. Dia.

Dbl. Su

Fig .32

Fig. 33 compares the displacements of the standard steel pile (12 m) with the same pile of a length equal to 3 m. This causes the deflection of the pile to be distributed throughout the entire length of the pile rather than the top 25%.

Displacement

0

0.2

0.4

0.6

0.8

1

1.2

-1.00E-02 0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02

meters

x/l 3m

12m

Fig. 33

Fig. 34 compares the standard steel pile to the pre-stress pile. Both piles are loaded with the largest lateral load Florida Pier will converge for. Assuming that Florida Pier fails to

converge when the soil fails, these piles are loaded to the ultimate capacity of the soil (Steel = 600kN, Pre-Stress = 400kN). Therefore, Fig. 34 shows that the standard steel pile is more ductile than the pre-stress pile and the soil is able to accommodate larger deflections for the steel pile.

Displacement

0

0.2

0.4

0.6

0.8

1

1.2

-1.00E-02 0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02

metersx/

l Pre-Stress

Steel

Fig. 34 5.0 2x2 Pile Group A 2x2 pile group was studied using FB-Pier for both the fixed and pinned head cases. The following data was used in the analysis which was the same as the data used for the single pile case:

Pile = 0.61m steel circular tube (12m long) Pile Cap Thickness = 1.5m c = 200kPa γ = 11 kN/m3 Ks = 135 MN/m3 E(50) = 0.005 ca = 250kPa Loading applied = 1440 kN

The program utilized p-y multipliers which were 0.8 for the leading piles and 0.4 for the trailing piles. Figure 5.1 below shows a sketch of the 2x2 pile group.

Figure 5.1 Sketch of 2x2 Pile Group

Pile 1 Pile 2

Pile 4 Pile 3

1440kN

The program also gives the option of using p-y multipliers = 1. The study conducted by Reese (1975) did not cover the effect of pile groups, so it was decided for this analysis to use the p-y multipliers provided. The results from running the analysis are shown in Table 5.1:

Fixed Head

Normalized Pile Displacement(m) Soil Resistance (Horiz.

Direction)(kN) Moment

Distribution(kNm)

Length Piles 1&3 Piles 2&4 Piles 1&3 Piles 2&4 Piles 1&3 Piles 2&4

0 6.44E-03 6.44E-03 0.00 0.00 -190.00 -300.00

0.0625 4.37E-03 4.18E-03 117.71 234.07 140.00 34.00

0.125 2.31E-03 1.93E-03 140.50 234.07 150.00 190.00

0.1875 8.52E-04 4.98E-04 77.66 90.85 100.00 180.00

0.25 9.16E-05 -8.35E-05 11.13 -20.29 46.00 94.00

0.3125 -1.60E-04 -1.71E-04 -24.25 -52.04 9.70 24.00

0.375 -1.57E-04 -9.68E-05 -28.58 -35.27 -5.40 -5.80

0.4375 -8.39E-05 -2.67E-05 -17.83 -11.35 -7.10 -9.60

0.5 -2.56E-05 2.49E-06 -6.23 1.21 -4.10 -4.80

0.5625 9.06E-07 6.26E-06 0.25 3.43 -1.20 -0.90

0.625 6.49E-06 2.95E-06 1.97 1.79 0.09 0.42

0.6875 4.26E-06 4.70E-07 1.42 0.31 0.35 0.39

0.75 1.45E-06 -2.44E-07 0.53 -0.18 0.21 0.13

0.8125 4.94E-08 -1.89E-07 0.02 -0.15 0.07 0.00

0.875 -2.71E-07 -4.92E-08 -0.12 -0.04 0.00 -0.02

0.9375 -1.77E-07 9.10E-09 -0.08 0.01 0.00 -0.01

1 -1.23E-08 2.14E-08 0.00 0.01 0.00 0.00

Pinned Head

Normalized Pile Displacement(m) Soil Resistance (Horiz.

Direction)(kN) Moment

Distribution(kNm)

Length Piles 1&3 Piles 2&4 Piles 1&3 Piles 2&4 Piles 1&3 Piles 2&4

0 1.45E-02 1.45E-02 0.00 0.00 0.00 0.00

0.0625 8.95E-03 8.12E-03 109.11 226.53 210.00 330.00

0.125 4.38E-03 3.22E-03 203.62 377.15 340.00 490.00

0.1875 1.41E-03 5.42E-04 128.43 98.87 320.00 360.00

0.25 -1.28E-05 -3.61E-04 -1.55 -87.71 200.00 160.00

0.3125 -4.07E-04 -3.78E-04 -61.79 -114.96 82.00 27.00

0.375 -3.34E-04 -1.76E-04 -60.85 -64.33 11.00 -21.00

0.4375 -1.61E-04 -3.55E-05 -34.32 -15.10 -15.00 -20.00

0.5 -4.15E-05 1.24E-05 -10.08 6.02 -15.00 -8.30

0.5625 7.54E-06 1.35E-05 2.06 7.37 -7.90 -0.81

0.625 1.48E-05 5.12E-06 4.50 3.11 -2.00 1.10

0.6875 8.53E-06 3.81E-07 2.85 0.26 0.45 0.76

0.75 2.51E-06 -6.39E-07 0.92 -0.47 0.78 0.19

0.8125 -1.59E-07 -3.62E-07 -0.06 -0.29 0.42 -0.04

0.875 -6.26E-07 -6.75E-08 -0.27 -0.06 0.11 -0.05

0.9375 -3.45E-07 2.88E-08 -0.16 0.03 0.00 -0.01

1 2.56E-08 3.70E-08 0.01 0.02 0.00 0.00

Table 5.1 Results of Analysis of 2x2 Pile Group Using FB-Pier

The data above were then plotted and Figures 5.2, 5.3 and 5.4 were obtained as shown below.

Figure 5.2 Pile Displacement vs. Normalized Pile

Pile Displacement vs. Normalized Length Along Pile for 2x2 Pile Group

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-2.00E-03 0.00E+00 2.00E-03 4.00E-03 6.00E-03 8.00E-03 1.00E-02 1.20E-02 1.40E-02 1.60E-02 Pile Displacement (m)

Normalized Length Along Pile

Fixed Piles 1&3 Fixed Piles 2&4 Pinned Piles 1&3 Pinned Piles 2&4

Soil Resistance vs. Normalized Length Along Pile for 2x2 Pile Group

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-200.00 -100.00 0.00 100.00 200.00 300.00 400.00 500.00

Soil Resistance (kN)N

orm

aliz

ed L

engt

h A

long

Pile

Fixed Piles 1&3Fixed Piles 2&4Pinned Piles 1&3Pinned Piles 2&4

Figure 5.3 Soil Resistance vs. Normalized Length Along Pile

Moment Along Pile vs. Normalized Length Along Pile for 2x2 Pile Group

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-400.00 -300.00 -200.00 -100.00 0.00 100.00 200.00 300.00 400.00 500.00 600.00

Moment (kNm)N

orm

aliz

ed L

engt

h A

long

Pile

Fixed Piles 1&3

Fixed Piles 2&4

Pinned Piles 1&3

Pinned Piles 2&4

Figure 5.4 Moment Distribution vs. Normalized Length Along Pile

The following could be noted from the graphs above: 1. The leading and trailing piles were effectively displaced the same distance. 2. The piles in the pinned case had a much higher displacement in the top 25% of the pile length, but at 25% and below, the displacements are effectively the same in the pinned case and fixed case. 3. More soil resistance occurs behind the trailing piles as compared to the leading piles. The soil forces, however, are almost negligible after 50% of the pile length. 4. The soil forces are higher in the pinned case as compared to the fixed case. 5. The maximum moment in the pinned pile group is more than double the maximum moment in the fixed pile group. 6. For the fixed case, the maximum moment occurs at the pile cap, while for the pinned case, the maximum moment occurs at a distance of approximately 15% of the pile length from the pile head. 7. For both the fixed head and pinned head cases, the moment dies out at around 40% of the pile length from the pile head.

Comments/Conclusions The following are key points to remember when working with Reese’s model for stiff clay below the water table: Stiff clay below the water table fails at relatively small deflections. The material behavior is brittle, especially under cyclic testing. This was shown by the field test conducted by Reese and is incorporated in his model. The applicability of Reese’s model to varying diameters is questionable. The model shows favorable results for piles of 24” diameter. However, the model was formulated from the results of testing 24” diameter piles. It was discussed earlier that the model did not compare well with the field tests of 6” diameter piles. Yet, there have been no efforts to improve upon the model. Reese’s Model fails to take effects of the following into consideration: Fixed Head Case, Pile Groups, P-Delta effect. All three of these are present in most practical applications and their influence should be taken into consideration. While the methodology of constructing p-y curves would not be considered tedious, it is fairly complex. For most practicing engineers the curve construction process is a “black box.” It is difficult to ascertain the physical meaning and relevance of the p-y curve. Finally, instances and conditions of Florida Pier’s analysis not converging appear to be arbitrary. During the investigation there were times where the program would not converge for the same values it converged for earlier. It is recommended that results of a pile loaded in the elastic range of the pile and soil be cross-referenced with other programs or hand calculations before continuing on with an inelastic analysis.