Statnamic testing of piles in clay 2

Chapter 6 Testing data and discussions

139
CHAPTER 6

PILE TEST DATA AND DISCUSSION



6.1 Introduction

The results of the pile load tests (constant rate of penetration tests at different rates,
statnamic tests at different peak loads, and maintained load tests will be presented and
discussed in this chapter. Based on the existing models, which are used to derive the
static load-settlement curve from that of a rapid load pile test, a new model will be
proposed.

It was found that the quake values of the pile shaft resistances of the rapid load tests
were much higher than those of the static load tests. An existing theoretical model
will be modified and applied for the static load pile tests to build the relationship
between load and settlement and to quantify these quake values, and then it will be
developed for the rapid load pile tests.

The gradual decrease of the pile shaft resistance after its peak value to a residual pile
shaft resistance, which is known as the softening effect, plus the changes of pore
water pressures and the inertial behaviour of the soil around the pile will be reported
and discussed.

6.2 Typical results of the pile load tests

Several measurements for each test were obtained from the instrumented model pile

and clay bed instruments. The following definitions of the testing components will be
used:
♦ Total pile load - load applied to the pile top and measured by a load cell mounted at
the pile top.
♦ Measured pile shaft load - load measured by the shaft load cell.
♦ Pile tip load - load measured by the pile tip load cell.
Chapter 6 Testing data and discussions

140
♦ Total pile shaft load. It was not possible to measure the total pile shaft load directly.
Therefore, it was deduced by subtracting the pile tip load from the total pile load.
♦ Pile settlement - vertical displacement from its original pre-load test position
measured by an LVDT mounted at the pile top.
♦ Pile velocity - deduced from the pile settlement with time or from an accelerometer
which was incorporated in the pile.
♦ Pore water pressures at the pile tip and on the pile shaft - measured by the pile tip
and pile shaft pore water pressure transducers.
♦ Pore water pressures in the clay beds - measured by pore water pressure transducers
which were incorporated in clay beds at different locations.
♦ Soil accelerations in the clay beds at different locations - measured by
accelerometers located at different locations in the clay beds.
♦ Top and side chamber pressures. - measured by Druck PDCR 810 water pressure
transducers.

Typical results of pile load tests are shown in Figure 6.1 to 6.4. In the following
sections these results will be discussed and analysed in more detail.

6.3 Pile shaft load results and models for the pile shaft load

The total pile shaft load which was deduced from the total pile load and the pile tip
load was less reliable than the measured pile shaft load as the pile tip load cell worked
unreliably (see Section 6.4). Therefore, the measured pile shaft load acting on the
shaft load cell rather than the total pile shaft load will be presented and used in this
section.

With a CRP test, the rate of shearing was not constant but it increased gradually from
zero to the target rate (Figure 6.2). Normally, the desired rate for a CRP test was only
achieved when the pile shaft load had reached the ultimate load value. Therefore, the
rates of shearing, which were obtained from measured pile settlements, will be used in
deriving the pile shaft static load from the pile shaft rapid load. In reality a CRP test at
a high rate is similar to the first part of a statnamic test.

Chapter 6 Testing data and discussions

141
Smith (1960) worked on the dynamic resistance of a pile and proposed a linear
dependence of the damping resistance upon the shearing rate. However, the nature of
the non-linear relationship between the damping resistance and the shearing rate
cannot be ignored. For this reason, Gibson and Coyle (1968) carried out triaxial tests
at different rates of shearing for both sand and clay and proposed a non-linear
damping resistance. Following this, several researchers have worked on this problem
and proposed several soil models for the relationship between the damping resistance
and the rate of shearing.

In order to examine the capability of the non-linear damping models several typical
models will be used for analysis of the test results. Following this a new model will be
proposed to derive the load-settlement curve of a static pile load test from a statnamic
pile load test.

6.3.1 Non-linear models


The following non-linear damping resistance models will be used for examination of
the test data:
♦ Gibson and Coyle’s model (1968): This non-linear damping resistance is expressed
in the form:
R
t
= R
s
+ R
s
J
T
v
N
(6.1)
where R
t
is the total dynamic resistance
R
s
is the static resistance
J
T
is the damping factor
v is the velocity of shearing
N is the parameter drawn from the test results, which was 0.18 for clays and
0.2 for sands.

♦ Randolph and Deeks’ modified model (Hyde et al. 2000):
()
β
β
αα
τ
τ
6
101
−
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
Δ
+=
os
d
v
v
(6.2)
where τ
d
is the dynamic shear resistance
τ

s
is the static shear resistance
v
o
is the reference velocity (taken for convenience as 1 m/s)
Chapter 6 Testing data and discussions

142
Δv is the relative velocity between the pile and the adjacent soil
α, β are the damping coefficients
♦ Balderas-Meca’s model (2004):
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
⎟
⎟

⎠
⎞
⎜
⎜
⎝
⎛
+=
20.020.0
01.0
1
oos
d
vv
v
α
τ
τ
(6.3)
where τ
d
is the dynamic shear resistance
τ
s
is the static shear resistance
v
o
is the reference velocity (taken for convenience as 1 m/s)
v is the relative velocity between the pile and the adjacent soil
α is the damping coefficient. It is a function of the pile displacement and
varies linearly from zero when the pile displacement is zero to 0.9 when the

pile displacement is 1% of the pile diameter. After the pile settlement achieves
1% of the pile diameter the α parameter remains constant.
Due to the dependence of the damping parameters upon soil properties two sets of
damping parameters for each model will be used for the examination of the pile test
data. The first set of damping parameters are those proposed by the model’s authors,
and the second set is deduced from the best match between the test data and the
models. Thus, the two sets of the damping parameters for three models will be
determined as follows:
♦ Gibson and Coyle’s model: These authors only recommended N = 0.18 for clay
meaning only one set of damping parameters is applied in the model, with the J
T
value
achieved by a best match between the test data and the model.
♦ Randolph & Deeks’ modified model: α = 1 and β = 0.2 are used for the first set of
damping parameters and β = 0.2 and α achieved by the best match process are the
second set of damping parameters for the model.
♦ Balderas-Meca’s model: β = 0.2 and α increasing linearly from zero when the pile
displacement is zero to α
max
= 0.9 when the pile displacement is 1% of the pile
diameter are used for the first set of the damping parameters. β = 0.2 and α
max

obtained from the best match process are used for the second set of damping
parameters. Thus, β = 0.2 and α increasing linearly from zero when the pile
displacement is zero to α
max
when the pile displacement is 1% of the pile diameter are
Chapter 6 Testing data and discussions

143
the second set of the damping parameters. After the pile displacement reaches 1% of
the pile diameter α is constant and equals α
max
.

It was desirable to produce highly repeatable clay beds. However, test results showed
that the five clay beds exhibited slightly different damping characteristics. To
demonstrate this two CRP tests at rates of 0.01mm/s and 100mm/s in each bed are
compared in Figure 6.5 to 6.9. The ratios of the maximum measured shaft loads of the
CRP test at a rate of 100mm/s to that of the CRP test at a rate of 0.01mm/s are 1.97,
1.54, 1.82, 1.74, and 1.95 for clay Bed 1 to Bed 5 respectively. Taking the average
value of five ratios, 1.8, as a benchmark, the deviations of the ratios from the
benchmark are: 9.30% for Bed1; 14.56% for Bed 2; 0.77% for Bed 3; 3.32% for Bed
4; and 7.81% for Bed 5. Due to this variation the matching process between the
models and the test results to deduce the damping parameters will be carried out
independently for each bed.

The pile bearing capacities in constant rate of penetration tests at the rate of 0.01mm/s
are taken as the pile static bearing capacity benchmark and are used for comparison
with the derived pile static bearing capacities. However, the pile static bearing
capacity benchmark for each clay bed was not constant since the consolidation was
maintained during the testing programmes. In addition, significant local consolidation
developed on the soil around the pile under a series of pile load tests. For this reason,
the CRP test at a rate of 0.01mm/s was repeated several times in each bed and a rapid
load pile test used the nearest CRP test at rate of 0.01mm/s as its static bearing
capacity benchmark.

A rapid load pile test and a CRP test at the rate of 0.01mm/s in each clay bed will be
used to check the suitability of the existing models. The static load-settlement curves,

which are derived from the dynamic load-settlement curves by using the chosen
models, will be compared with the measured static load-settlement curves which are
the results of CRP tests at the rate of 0.01mm/s.

Chapter 6 Testing data and discussions

144
The comparison of some load-settlement curves are shown in Figures 6.10 to 6.24.
Combining the results of all pile load tests in which some are shown in Figures 6.10
to 6.24 the following conclusions can be deduced:
♦ Rate effects are present and the damping resistance is non-linear with the rate of
shearing as suggested by Hyde et al. (2000).
♦ The quake of the pile shaft load, i.e. the penetration at which the pile shaft load
reaches the ultimate resistance, in a dynamic pile load test is larger than that of a static
pile load test. The quakes in static pile load tests for pile shaft load vary between 0.5%
to 0.9% of the pile diameter (70mm), whereas the quakes of dynamic tests vary over a
wide range and the quicker the loading rate the larger the quake value. The largest pile
shaft quake for rapid load pile tests is 5.4% of the pile diameter (B4/12/CRP-400).
♦ The pile shaft load-settlement curve of a rapid load pile test can be subdivided into
three sections as shown in Figure 6.21: i) in the first section the relationship between
the pile shaft load and the pile settlement was approximately linear; ii) in the second
section the relationship between the pile shaft load and the corresponding pile
settlement was non-linear; iii) finally, in the third the pile shaft load reached the
ultimate value and remained approximately constant with further pile settlement. On
the other hand the pile shaft load-settlement curve of a static pile load test either did
not exhibit or exhibited a much less obvious second section. Normally, in the first
section the settlement of a rapid load pile test was larger than that of a static pile load
test. Figure 6.21 shows that the first section of the rapid load pile test was complete at
a settlement of about 0.76mm whereas that of the static pile load test was complete at
a settlement of 0.6mm. Due to this it is difficult to derive the pile shaft static load-

settlement curve from that of a dynamic pile load test since the shape of the load-
settlement curve of a dynamic pile load test is not similar to that of a static pile load
test.
♦ The damping load not only depends upon the shearing rate but also upon the soil
loading stages described above. It can be seen from Figure 6.10 to 6.24 that the
damping load develops gradually from the first section to the final section.
♦ Comparing the derived load-settlement curves of the Randolph and Deeks and
Gibson and Coyle models it could be said that Randolph and Deeks’ model is only
another form of the Gibson and Coyle model.
Chapter 6 Testing data and discussions

145
♦ In general, the three models predict damping load well when the second section of
the load-settlement curve of a dynamic pile load test develops over a small settlement
(Figure 6.13 to 6.15) whereas they overpredict the damping loads of the first and the
second sections of the load-settlement curves when the second section develops over a
large settlement (Figure 6.19 to 6.24).
♦ Balderas-Meca’s model takes into consideration the development of the damping
load between the soil stages by changing the damping parameter, α, with the pile
settlement. However, quake values for the pile shaft load are over a relatively wide
range so that the quality of the derived load-settlement curve is not consistent (Figure
6.12 and 6.15).
♦ The viscous damping that occurs during a rapid load pile test can be represented by
a non-linear power law incorporating damping coefficients.
♦ Apart from the above models other models reported in the literature review have
also been examined. However, they did not provide a good prediction for statnamic
load tests. The main reason is that these models were only proposed for the ultimate
shear resistance.
♦ The soil damping characteristics depend on soil properties, i.e. liquid and plastic
limits. Summarizing data from previous studies, Hyde et al. (2000) showed that the

damping parameter, α, can vary by orders of magnitude for different clays.

6.3.2 A new non-linear model (the Proportional Exponent Model) for
pile shaft rate effects


In pile load tests settlement criterion, which is normally chosen as 10% of the
diameter of the pile, rather than the pile ultimate load is used for the determination of
a pile’s capacity. Therefore, it is desirable to derive the load-settlement relationship
for a static condition from that of a statnamic test. The most widely used Unloading
Point Method (UPM), which assumes that the damping load is linear with the shearing
velocity and can overestimate the ultimate static pile capacity by up to 30% for piles
in clay. The non-linear power laws reviewed in Section 6.3.1 could predict the
ultimate static pile bearing capacity well. However, in order to get a better estimate
the pile’s bearing capacity at loads below the ultimate static pile bearing capacity,
Chapter 6 Testing data and discussions

146
which is the zone of most interest in determining the pile’s serviceability, the
available non-linear power laws need to be modified.

The available non-linear power laws should be modified in such a way that they can
simulate the gradual development of the damping load from the first to the final
stages of loading. This can be achieved by gradually increasing the damping
parameters with the development of the dynamic pile load, and the damping
parameters are constant when the pile’s dynamic load reaches the ultimate value.
Thus, the new non-linear power law should be in the same form as the available
models when the pile’s dynamic bearing capacity reaches its ultimate value. It is
proposed therefore to use a model with a proportional exponent of the velocity term,
the general form of which is as follows:

⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+=
)(
1
ultimated
d
s
d
s
d
v
v
τ
τ
β

α
τ
τ
(6.4)
where τ
d
is the dynamic shear resistance
τ
s
is the assumed static shear resistance determined at a pile velocity of
0.01mm/s
τ
d(ultimate)
is the ultimate dynamic shear resistance
v
d
is the pile velocity which can vary from zero to 2500mm/s during a
statnamic test (Japanese Geotechnical Society, 2000).
v
s
is the assumed static pile velocity which is 0.01mm/s in this study.
α, β are the damping coefficients
The damping parameters depend on the soil properties. However, from previous
researches (see Section 2.9), combined with test results from this study, the damping
parameter β = 0.2 can be used for clay. Thus Equation 6.4 becomes:
⎟
⎟
⎠
⎞
⎜

⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+=
)(
2.0
1
ultimated
d
s
d
s
d
v
v
τ
τ
α
τ
τ
(6.5)
The validity of this equation will be examined by using the results of the calibration

chamber pile load tests.

When the pile shaft resistance reaches the ultimate value τ
d
/τ
d(ultimate)
= 1 and Equation
6.5 becomes:
Chapter 6 Testing data and discussions

147
2.0
)(
)(
)(
1
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+=
s
ultimated
ultimates
ultimated
v

v
α
τ
τ
(6.6)
where τ
d(ultimate)
is the ultimate dynamic shear resistance.
τ
s(ultimate)
is the ultimate static shear resistance.
v
d(ultimate)
is the shear velocity corresponding to the ultimate dynamic shear
resistance.

Due to the rate effects of the five clay beds being slightly different as mentioned in
Section 6.3.1 the damping parameter will be deduced independently for each bed.

Equation 6.6 is used to calculate the damping parameter, α, from the pile shaft load
ratio. Plots of τ
d
/τ
s
- 1 against v
d
are shown for Beds 2 to 5 in Figures 6.25 to 6.28.
The best match between the test data and Equation 6.6 was achieved using least
square regression gives the α values of 0.085, 0.135, 0.115, and 0.145 with the fitting
regression coefficient R-squared values of 0.90, 0.88, 0.87, and 0.89 for Bed 2 to Bed

5 respectively. The average damping parameter (α
average
= 0.12) is deduced for all five
clay beds as shown in Figure 6.29. It can be seen that the use of a damping parameter
varying from α = 0.068 to α = 0.16 in Equation 6.6 covers for all five beds’ pile shaft
dynamic loads (Figure 6.29). Figures 6.25 to 6.28 plus 6.29 show that damping effects
are fairly consistent for each clay bed, but vary from bed to bed. This is thought to be
attributed to the variation of the materials used as mentioned in Section 5.2.

To examine the sensitivity of the damping parameter β, several values of β (0.16;
0.18; 0.22; 0.24) are plotted in Figures 6.25 to 6.28. In general β = 0.18 and β = 0.22
are lower and upper boundaries for the test data.

In the following sections Equation 6.5 will be used to derive the full static load-
settlement curves from the rapid load pile tests for Beds 2 to 5 using the damping
values above.

♦ Clay Bed 1: As mentioned in Chapter 3 (see Sections 3.4.6 and 3.4.7) the pile was
installed into the clay bed after 14 days of triaxial consolidation under a pressure of
280kPa. After pile installation the clay bed continued to be subjected to a pressure of
Chapter 6 Testing data and discussions

148
280kPa. This installation during the triaxial consolidation caused disturbance between
the pile shaft and the bored hole which could not be eliminated during the subsequent
the second stage of consolidation. It was found that the pile bearing capacity of this
bed was much lower than that of the other beds even though the clay beds underwent
the same consolidation history. Only the results of one CRP test at a rate of 0.01mm/s
(B1/1/CRP-0.01) will be used together with two rapid load pile tests, a CRP test at a
rate of 100mm/s (B1/2/CRP-100) and a statnamic pile load test (B1/4/STN-15) since

the others tests were mainly carried out to choose the best input parameters for the
testing equipment for the pile load tests of the following beds. The CRP test at a rate
of 0.01mm/s provides the static pile bearing capacity benchmark for the two rapid
load pile load tests. The derived static load-settlement curves which are obtained from
the rapid load pile tests by the proportional exponent model are shown in Figures 6.30
and 6.31. The damping parameter α = 0.14 was obtained for clay Bed 1 from the best
fit between the pile’s measured static shaft capacity and the model. In terms of the
pile’s ultimate bearing capacity Test B1/4/STN-15 had the largest deviation (3.6%)
between the measured pile static capacity and the derived pile static bearing capacity
(Figure 6.30).

♦ Clay Bed 2: The static load-settlement curves derived from rapid load pile tests by
the proportional exponent model are shown in Figure 6.32 to 6.41. The damping
parameter α = 0.085 was used for this clay bed. In terms of the pile’s ultimate bearing
capacity Test B2/19/CRP-150 had the largest deviation (9%) between the measured
pile static capacity and the derived pile static capacity (Figure 6.41).

♦ Clay Bed 3: The results of the analysis for pile load tests on Bed 3 are shown in
Figures 6.42 to 6.53. The damping parameter, α, derived for this bed was 0.135. As
mentioned earlier, the pile’s static bearing capacities obtained from CRP tests at a rate
of 0.01mm/s were not constant during testing due to local consolidation following
each test. For that reason slow rate - CRP tests were repeated after each group of
rapid load tests for a given bed. However, in some cases there was a large difference
in the pile’s static bearing capacity between two adjacent CRP tests at a rate of
0.01mm/s. In these cases both CRP tests at a rate of 0.01mm/s are used (Figures 6.42
to 6.44 and 6.46 to 6.49). One CRP test was carried out before the rapid load test,
Chapter 6 Testing data and discussions

149
giving measured static load 1, and the other, giving measured static load 2, after the

rapid load pile test. In terms of the pile’s ultimate bearing capacity Test B3/16/CRP-
300 had the largest deviation (12.9%) between the measured pile static capacity and
the derived pile static bearing capacity (Figure 6.51).

♦ Clay Bed 4: From Bed 1 to Bed 3 the clay beds underwent a similar consolidation
history, i.e. 280kPa pressure for both 1-D and isotropic triaxial consolidations. Clay
Bed 4 had a similar consolidation history to that of the first three beds only for the
first series of tests. After the first series of tests the clay bed was subjected to a triaxial
consolidation pressure of 400kPa. Although two series of tests were carried out at
different soil consolidation pressures it was found that one value of damping
parameter α = 0.115 could be used for this bed. The results of clay Bed 4 are shown
in Figures 6.54 to 6.66. In terms of the pile’s ultimate bearing capacity Test
B4/26/CRP-50 had the largest deviation (10.8%) between the measured pile static
capacity and the derived pile static bearing capacity (Figure 6.66). Although several
statnamic pile load tests were carried out in Bed 4 under a consolidation pressure of
400kPa their load-settlement curves are not used for analysis since the pile’s dynamic
bearing capacity was large in comparison with the applied load system’s capacity,
which was 41 kN, and only small settlements occurred in these statnamic pile load
tests.

♦ Clay Bed 5: This bed’s consolidation history was different from those of the first
four beds. The 1-D consolidation pressure for this bed was only 240kPa and three
series of pile load tests were carried out at three different 3-D triaxial consolidation
pressures which were 240kPa, 280kPa, and 340kPa respectively. Similar to Bed 4,
although three series of tests were at different clay soil consolidation histories only
one damping parameter α = 0.145 was used. The results of tests carried out in Bed 5
are shown in Figures 6.67 to 6.81. In terms of the pile’s ultimate bearing capacity Test
B5/32/CRP-50 had the largest deviation (8.62%) between the measured pile static
capacity and the derived pile static bearing capacity (Figure 6.81).

For a comparison between the new model and the Randolph and Deeks model,
attention is given to the pile shaft resistance below the ultimate as shown in Figures
Chapter 6 Testing data and discussions

150
6.82 and 6.83. Figure 6.83 shows that at a settlement of 0.45mm the measured static
load was 4.2kN but the derived static load from the Randolph & Deeks model was
3.3kN an underprediction of about 22% whereas the derived static load from the
proportional exponent model was 3.98kN and deviated from the measured value only
by 5%. Pile velocities are also plotted in these figures. It can be seen that during both
statnamic and CRP tests pile velocities increased gradually with the development of
the applied load.

6.3.3 Pile shaft softening effect


It has been shown by previous researchers that pile shaft load in clay is fully
mobilised at a certain pile settlement and then decreases to a residual value with
further settlement. The residual resistance was reported in some cases to be as low as
50% of the maximum resistance (Chandler & Martins, 1982). However, for pile
design purposes it is recommended that 70% of the maximum pile shaft resistance
should be used for the residual pile shaft resistance (API, 1993). This behaviour is
attributed to the parallel alignment of the clay particles to the shear direction after a
significant deformation (Lemos & Vaughan, 2004), breaking of the clay particle
interlocking and breaking the initial cementation between the pile and clay (Mitchell,
1976).

In this study it was found that softening effects were only exhibited in constant rate of
penetration tests with the rates varying from 0.01mm/s to 100mm/s. The results of
tests in which softening occurred have been placed into two groups: i) CRP tests at

the rate of 0.01mm/s; ii) CRP tests at rates larger than 0.01mm/s. The results of these
tests are shown in Figure 6.84 to 6.93.

It was found that a relatively large pile settlement was needed for the pile shaft load to
reach the residual value. However, studying softening effects was not the main object
of this study and if the residual load had been reached for every test the numbers of
tests for each bed would have reduced significantly. Therefore, in several tests the
residual load were not reached as the pile settlements were normally controlled to
about 7mm.
Chapter 6 Testing data and discussions

151
In general, the results show that the degree of softening, defined as the residual shaft
load relative to the maximum shaft load, decreased from test to test and in some cases
softening effects vanished after several tests (Figure 6.85; 6.86; 6.87; 6.90; 6.92). This
suggests that the alignment of the clay particles parallel to the shearing direction
played an important role in softening and further softening did not occur after several
tests as a result of the particle arrangement reaching a stable condition. In addition,
softening effects were not found in the pile load tests with shearing rates higher than
100mm/s. It is suggested that there is a critical shearing velocity for soil and the
modes of shearing are different depending on whether the shearing velocity is higher
or lower than the critical shearing velocity. If the shearing velocity is higher than the
critical velocity the shearing mode is turbulent as defined by Lemos & Vaughan
(2000). It suggests that the soil particles do not have enough time to rearrange, and as
a result softening effects do not occur. On the other hand if the shearing velocity is
much lower than the critical velocity the soil particles will have enough time to
rearrange and softening will occur. If the shearing velocity is just lower than the
critical shearing velocity a transitional shearing mode may be exhibited in which the
re-arrangement of the soil particles can only develop to a certain degree and in the
transitional range the higher the shearing velocity the lower the degree of softening.

These results show that the degree of softening was not consistent from bed to bed.
These effects were exhibited markedly for Bed 3 (Figures 6.88 and 6.88) whereas
they were exhibited slightly for Bed 4 (Figure 6.90 and 6.91). This is thought to be
attributed to the inconsistency in the use of materials as mentioned in Section 5.2.

As mentioned above, the alignment of the clay particles parallel to the shearing
direction causes softening. It is expected to occur in the first test in any bed and as a
result softening effects are likely to decrease from test to test as further tests are
carried out in the bed. However, softening did not occur for the first test in Beds 3 and
5 (Figures 6.88 and 6.92) but occurred in later pile load tests. These results seem to
contradict the above-mentioned reason for softening. There are no clear explanations
for this.

Consistent with previous studies (Chandler & Martins, 1982), the pile shaft residual
load could be as low as 67% of the maximum pile shaft load (Pile load test B3/2/CRP-
Chapter 6 Testing data and discussions

152
10 in Figure 6.89). In practice, it is appropriate and conservative if softening is taken
into consideration to deduce the maximum pile load by 30% as recommended by API.

In this study rate effects were not separated from softening effects at ultimate
condition. However, the influence of the softening effects is not significant compared
to rate effects due to the following reasons:
♦ Softening effects did not occur during rapid load tests with the shear rates above
100mm/s.
♦ The softening effect only occurred when the pile resistance reached the ultimate
value. Therefore, below the ultimate value rate effects were not influenced by
softening effects.

♦ The residual resistances in CRP tests at the rate of 0.01mm/s, which were
considered as the static benchmark, were only different from the ultimate values by
about 5%.

6.3.4 Repeatability of the static pile shaft loads


The measured pile shaft loads for static pile load tests are shown in Table 6.1. In this
table some pile load tests have two values for the shaft load. The first value is the
maximum pile shaft load and the second value is the residual pile shaft load as a
results of softening. It can be seen from the table that the pile shaft loads of the first
test of Beds 2 to 4 were fairly consistent. They only varied from 3.50kN to 3.71kN.
With Bed 5, due to the clay bed being subjected to 1-D and isotropic triaxial
consolidation pressures of 240kPa instead of 280kPa the pile shaft load for the first
pile load test was only 2.90kN. The second CRP test at a rate of 0.01mm/s in each bed
was carried out after several rapid load tests and as a result of the local consolidation,
which developed around the pile during these tests, the pile shaft loads increased
considerably. The pile shaft loads of the second CRP tests at the rate of 0.01mm/s in
Bed 2, 3, and 4 were 4.41kN, 5.10kN, and 4.58kN. If the average value of the pile
shaft loads, 4.69kN, is used as a benchmark the maximum deviation from the
benchmark is 8.4%. The pile shaft loads of pile load tests at the rate of 0.01mm/s in
Bed 5 under a triaxial consolidation pressure of 280kPa were 4.32kN to 4.42kN and
they were quite consistent with those of later tests in Bed 2 to 4. Normally, the
Chapter 6 Testing data and discussions

153
maximum pile shaft loads of CRP tests at the rate of 0.01mm/s in each clay bed were
achieved for the final pile load tests. The maximum pile shaft loads in Beds 2 to 4
under the isotropic triaxial consolidation pressure of 280kPa were 5.41kN, 5.10kN,
4.81kN. If the average value, 5.11kN, is used as a benchmark the maximum deviation

from the average value is 6%.

Four isotropic triaxial consolidation pressures (240kPa, 280kPa, 340kPa, and 400kPa)
were used for the five clay beds. It was found that the ultimate pile shaft load was in
proportion to the radial effective stress. The ratios of the ultimate unit shaft load to the
radial effective stress of the first test in Beds 2 to 5 are 0.21, 0.21, 0.21, and 0.20
respectively (Table 6.1). In general these ratios increased for the following pile load
tests due to the development for the local consolidation of the soil around the pile
shaft and the maximum ratios of Beds 2 to 5 were 0.30, 0.30, 0.29, and 0.27
respectively.

Comparing the ratio of the maximum pile shaft loads to the radial effective stresses
and to the undrained soil shear strengths which are shown in Tables 5.4 to 5.7 it is
found that the relationship between the maximum pile shaft load and the radial
effective stress is more consistent than that between the maximum pile shaft load and
the undrained soil shear strength. It suggests that the effective stress design method
proposed by Chandler (1968) and Burland (1973) to determine the maximum pile
shaft load for clay seems to be better than the total stress design method proposed by
Skempton (1959).

6.4 Pile tip load results


Normally for clays the pile tip bearing capacity is small in comparison with the pile’s
shaft bearing capacity. Therefore, when deriving a pile’s static bearing capacity from
a rapid load pile test attention is mainly given to the pile’s shaft load. The pile tip load
was measured by a pile tip load cell (see Section 3.5.1). Pile tip load results for Bed 1
to Bed 4 are shown in Tables 6.2 to 6.5 respectively. The pile tip load cell did not
work properly for Bed 5 so its pile tip load results are not reported.

Chapter 6 Testing data and discussions

154
In several early tests in each bed the pile tip load was fully mobilised at a quake of
about 10%-12% of the pile diameter (70mm) (Figure 6.94). Due to a residual tip load
locked into the soil below the pile base this quake dropped gradually after the first
few tests and finally it was as low as 2.5%-4% of the pile diameter (Figure 6.94).

A pile tip residual load occurred before the first to the final pile load tests. It is likely
that the residual pile tip load occurred before the first test of each bed due to the fact
that under the isotropic triaxial consolidation pressures an upward force occurred at
the pile tip. In the following tests, a residual pile tip load was generated for the
following reason additional to the above. During the test, the load cell was
compressed and the pile tip load governed the elastic deformation of the load cell
(Figure 6.95). When the test had finished, the load cell had a tendency to return to the
unload condition. This means that it needed to expand to its normal length. However,
when it expanded it was resisted at one end by soil at the pile tip and at the other end
by the upper part of the pile; in turn the upper part of the pile would have mobilised
shaft friction to resist this effect. Because of this, the load cell did not expand totally
and the pile tip residual load depended on the soil properties at the pile tip and pile
shaft friction. So when the pile tip residual loads were recorded the soil at the pile tip
was compressed with a load equal to the residual load and the pile shaft friction had a
value equal to the pile tip residual load minus pile weight. However, the shaft friction
load cell was not designed to measure this value. By and large, the pile working with
a residual tip load had a mechanism similar to that of a pile with an Osterberg cell test
at its base. For this reason, the soil beneath the tip of the pile was under two different
loads during a test. The first load was a static load equal to the residual load and the
second was the subsequent testing load.

The residual pile tip load seemed to increase over the first few tests and then it

became stable (Tables 6.2 to 6.5). This can be explained from the mechanism which
generated the residual tip load. The pile and soil compressions at the pile tip during a
pile load test are locked by the pile shaft load when the test finishes. Thus, the
magnitude of the residual pile tip load depends on both soil properties around the pile
shaft and at the pile tip. For the first few pile load tests the soil around the pile shaft
and at the pile tip developed local consolidation so that residual tip loads increased
and became stable when this local consolidation was complete.
Chapter 6 Testing data and discussions

155
The pile tip load in static pile load tests, CRP tests at a rate of 0.01mm/s and
maintained load tests, can be summarized as follows:

♦ Bed 1: It increased from about 3.69kN (B1/1/CRP-0.01) to about 5.5kN
(B1/12/CRP-0.01). Due to the soil in the vicinity of the pile base being very stiff the
hand vane test could not determine its shear strength when the clay bed was dissected.
The soil shear strength at the pile base can be determined indirectly if the following
pile base bearing capacity equation for clay is used (Meyerhof, 1952):
Q
b
= c
ub
N
b
A
b
(6.7)
where Q
b
is the pile tip bearing capacity.

c
ub
is the undrained shear strength of the soil at the vicinity of the pile tip.
N
b
is the pile tip bearing capacity factor which is 9 for a deep circular footing
clay.
A
b
is the pile tip cross sectional area.
Using Equation 6.7 the undrained shear strength of Bed 1 varied from 107kPa to
159kPa.

♦ Bed 2: The pile tip load varied from 3.79kN (B2/1/CRP-0.01) to 7.27kN
(B2/16/CRP-0.01). It was noted that after three consecutive maintained pile load tests
local consolidation of the soil at the pile tip developed significantly as the pile tip load
increased from 6.57kN (B2/12/CRP-0.01) before the maintained load tests up to
7.27kN (B2/16/CRP-0.01) after the maintained load tests. Applying Equation 6.7 the
undrained shear strength of the soil at the pile base varied from 109kPa to 210kPa.

♦ Bed 3: The pile tip load varied from 3.73kN (B3/1/CRP-0.01) to 6.82kN
(B3/22/MLT) giving a variation of the undrained shear strength of the soil at the pile
tip from 108kPa to 197kPa using Equation 6.7.

♦ Bed 4: There were two series of pile load tests for Bed 4. The first series was
carried out when the 3-D consolidation pressure of the clay bed was 280kPa. The pile
tip loads varied from 4.09kN (B4/1/CRP-0.01) to 6.59kN (B4/17/CRP-0.01) and
using Equation 6.7 the undrained shear strength of the soil at the pile tip varied from
118kPa to 190kPa. The second series was carried out when the clay bed had a 3-D
Chapter 6 Testing data and discussions

156
consolidation pressure of 400kPa. The pile tip loads varied from 8kN to 8.5kN and
using Equation 6.7 the undrained shear strength of the soil at the pile tip varied from
231kN to 245.5kN.

It can be seen that in terms of the pile tip static bearing capacity a high consistency
was achieved for the pile tip loads of the first test in each beds. The pile tip loads
were 3.69kN, 3.79kN, 3.73kN, 4.09kN for Bed 1 to Bed 4 respectively.

The undrained shear strengths of the soil at the pile base obtained using Equation 6.7
seem reasonable when compared with the soil shear strengths which were obtained in
the vicinity of the pile shaft in Bed 4 by hand vane tests (Table 5.6). The shear
strength of the soil at the pile shaft could be as large as 108kPa and the shear strength
of the soil at the pile tip was found higher than that.

The pile tip damping loads, defined as the difference between the pile tip load of a
static load test and a rapid load pile test are shown in Tables 6.2 to 6.5. The pile tip
static loads between two CRP tests at the rate of 0.01mm/s are interpolated linearly
with the number of tests from the measured pile tip loads in these two tests. Similarly,
the pile tip damping load seems to be non-linear with the pile velocity in contrast to
the linear pile base model proposed by Randolph and Deeks (1992) which can be
expressed in the form of:
aMvCwKF
bbbb
++= (6.8)
where F
b
is the total base load.
K

b
is the pile base’s spring stiffness which is given by Equation 6.9
w is the pile tip settlement.
C
b
is the dashpot constant which is given by Equation 6.10
M
b
is the lumped mass soil at the pile tip which is considered as a part of a
pile tip and is given by Equation 6.11
a is the pile tip acceleration
μ
−
=
1
2GD
K
b
(6.9)
ρ
μ
G
D
C
b
−
=
1
8.0
2

(6.10)
Chapter 6 Testing data and discussions

157
μ
μ
ρ
−
−
=
1
1.0
2
4
3
DM
b
(6.11)
where G is the soil shear modulus
D is the pile diameter
μ is the Poisson’s ratio
ρ is the soil bulk density

However, no new equation is proposed to quantify the pile tip damping load for the
following reasons:

♦ The development of the pile tip load during a rapid load pile test was not a totally
dynamic process since a relatively high residual load always existed. Therefore, it
could be considered that the soil at the pile tip underwent two steps during a rapid
load test, a static load due to the residual load and then a subsequent dynamic loading

process.

♦ The pile tip load cell was subjected to the residual load for a long period of time in
each clay bed. Normally it was about 2 months from the pile installation until the clay
bed was stripped down. Due to this, creep occurred to the pile tip load cell and it
altered the zero load reading of the pile tip load cell. This was recognized when there
was a difference of the zero load reading of the load cell before the pile installation
and after the bed had been stripped down. This problem became more severe after the
maintained load tests. The alteration of the zero load reading made the pile tip loads
unreliable for the quantification of tip damping load.

6.5 Application of the proportional exponent model to the pile total
load


As mentioned in Section 6.4 the measured pile tip loads were not reliable. Therefore,
no attempt has been made to build a model for the pile tip load. However, in practice
the model for the pile tip bearing capacity should not be too important for a pile
installed in clay as the pile tip bearing load is normally much smaller than the pile
Chapter 6 Testing data and discussions

158
shaft bearing capacity. As a simplification the model for the pile shaft load can be
applied to the total pile load.

This section will use the new model which was proposed in Section 6.3.2 and
expressed by Equation 6.5 to derive the pile static bearing capacity from the pile
dynamic bearing capacity. The inertial forces of the pile were taken into
consideration. Although in practice it was found that they were negligible as the
model pile weight was only 19kg. The damping parameters, α, for Beds 1 to 5 are

those which were used for the pile shaft loads and the results are shown in Figure 6.96
to 6.100. It can be seen from these figures that the model can be applied fairly well to
find the total static pile load-settlement curve.

Brown (2004) laboratory test data was also used to check the model. Due to the same
test method having been applied for the two studies an average damping parameter, α
= 0.12, was used to derive the equivalent static load-settlement curve (Figure 6.101).
It can be seen from the figure that the model works well for Brown (2004) data and
this gives a confidence in the consistency of the test method.

6.6 A simple theoretical approach for the load transfer mechanism


In this section a simple theoretical method will be developed which can be employed
to establish the relationship between the pile settlement and its shaft load. The method
was suggested by Seed and Reese (1957) and then developed by Randolph and Wroth
(1978); Kraft et al. (1981
a
) and Armaleh and Desai (1987).

6.6.1 Available models for load transfer


The method was developed from the following assumptions:
♦ The pile shaft will transfer shear stresses to the soil and to a certain distance from
the pile called the influence zone beyond which these shear stresses are negligible.
♦ The load-settlement behavior of the pile shaft may be considered separately from
that of the pile base. The interaction between the soil above and below the pile base
level is taken into account by reducing the influence zone, r
m

, to a limited radius
(Figure 6.102).
Chapter 6 Testing data and discussions

159
♦ The displacement pattern of the soil around the pile shaft can be considered as
concentric cylinders in shear (Figure 6.102). Radial soil displacements due to pile
loads are assumed negligible when compared to vertical soil deformations. Thus, a
simple shear condition prevails in the soil.
♦ The influence zone, r
m
, is given by the following empirical formula (Randolph and
Wroth, 1978):
)1(5.2
μρ
−= Lr
m
(6.12)
where L is the length of pile shaft embedded in the soil.
ρ is the heterogeneous factor defined as the ratio of the shear modulus of the
soil at the depth of L/2 to that at the depth of L.
μ is the Poisson’s ratio.

Consider a soil element which is a radial distance r away from the pile centre (Figure
6.102). The vertical deformation of the element, dw, is given by:
dr
G
dw
Gdr
dw

rr
ττ
γ
=⇒==
(6.13)
where γ is the shear strain.
G is the soil’s shear modulus.
τ
r
is the shear stress on the soil element which is a radial distance of r away
from the pile centre.
The vertical settlement at the pile shaft, w
ro,
can be obtained by integration of the
element deformation given by Equation 6.14 from the pile shaft with a radius of r
o
to
the influence zone, r
m
.
∫
=
m
o
o
r
r
r
r
dr

G
w
τ
(6.14)
The shear stress, τ
r
, on the soil element which is away from the pile shaft a distance of
r can be obtained from the equilibrium condition (Figure 6.102) and it is given by:

r
r
or
r
o
τ
τ
= (6.15)
where τ
r
o

is the shear stress at the pile shaft and r
o
is the pile radius.
Substituting τ
r
from Equation 6.15 to Equation 6.14 the vertical deformation at the
pile shaft is given by:
Chapter 6 Testing data and discussions

160
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
o
m
o
r
r
r
G
r
w
o
r
o
ln
τ
(6.16)
If the soil shear modulus, G, is considered constant then Equation 6.16 gives a linear
relationship between the pile deformation and the pile shaft load. In reality the
relationship is non-linear. To take this non-linearity into consideration Kraft et al.
(1981
a

) developed the model by proposing a hyperbolic expression for the soil’s shear
modulus:
)](1[
max
τ
τ
fo
i
R
GG −= (6.17)
where G is the shear modulus at an applied shear stress τ
o
; G
i
is the initial shear
modulus at small strains (G
i
= E
i
/[2(1+μ)]).
R
f
is the stress-strain curve-fitting constant which should be taken from 0.9 to 1
(API, 1993).
τ
max
is the shear stress at failure.
μ is the Poisson’s ratio.
Using the new model proposed by Kraft et al. (1981
a

) the vertical deflection at the
pile shaft is given by:
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎝
⎛
−
−
=
max
max
ln
τ
τ
τ
τ
τ
fro
o
fro

m
i
oo
r
Rr
r
Rr
r
G
r
w
o
o
o
(6.18)
Equations 6.16 and 6.18 give a relationship between the pile shaft load and the pile
settlement for a static pile load test. In the following section some modifications will
be suggested to the model for static tests and then the model will be developed for
rapid load pile tests.

6.6.2 Modifications to the existing models for load transfer for static
pile load tests and a new model for rapid load pile tests


To apply this method to the pile load tests of this study a modification is proposed to
the influence zone, r
m
, which was originally suggested by Randolph and Wroth
(1978), and then the method is developed for rapid load pile tests. It should be made
clear that the method establishes the relationship between the pile shaft load and the

Chapter 6 Testing data and discussions

161
pile shaft deflection before failure and no attempt will be made to take the post failure
softening effect into consideration.

Randolph and Wroth (1978) proposed the influence zone had a radius which was
given by Equation 6.12 and that it remained constant during the development of the
pile shaft resistance. Other researchers still use this assumption. However, in reality it
is believed that the radius of the influence zone, r
m
, depends on the pile shaft
resistance and increases with the development of the pile shaft resistance. The
influence zone reaches a maximum value when the pile shaft resistance reaches the
ultimate pile shaft resistance. For simplicity of the subsequent integrations a simple
influence zone equation is proposed.

om
r
m
rrr
o
+=
max
max
τ
τ
(6.19)
where r
m

is the influence zone when the pile shaft resistance is τ
r
o
.
τ
max
is the ultimate pile shaft resistance.
r
m
max
+ r
o
is the maximum influence zone when the pile shaft resistance
reaches τ
max
.
If it is assumed that the soil’s shear modulus is constant during loading the vertical
settlement at the pile shaft of a static pile load test is given by:
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎝
⎛

+
=
o
o
r
m
or
r
r
rr
G
r
w
o
o
o
max
max
ln
τ
τ
τ
(6.20)
If it is assumed that the soil’s shear modulus follows the hyperbolic model proposed
by Kraft et al. (1981
a
) then the pile shaft settlement of a static load pile test is given
by:
⎟
⎟

⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛
−
−
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⎟
⎟
⎠
⎞
⎜

⎜
⎝
⎛
=
max
maxmax
max
ln
τ
τ
τ
τ
τ
τ
τ
fro
o
fro
o
r
m
i
or
Rr
r
Rr
rr
G
r
w

o
oo
o
(6.21)
Similarly, the pile shaft settlement of a rapid load pile test is still given by:
∫
=
m
o
o
r
r
r
r
dr
G
w
τ
(6.22)
Chapter 6 Testing data and discussions

162
However, the distribution of the shear stress away from the pile shaft is different from
that of a static pile load test, which is given by Equation 6.15, if the inertial force is
taken into consideration. The equilibrium condition for a soil element (Figure 6.102)
is then given as follows:
'''''''''' DCBA
z
zrDCBABCDAsoilDDAArABCDz
Sdz

z
maVSS
⎟
⎠
⎞
⎜
⎝
⎛
+=−++
δ
δσ
σγτσ


CCBB
r
r
Sdr
r
''
⎟
⎠
⎞
⎜
⎝
⎛
++
δ
δτ
τ

(6.23)
where S is the symbol denoted for areas (Figure 6.102)
σ
z
is the vertical stress.
γ
soil
is the soil bulk density
a
r
is the acceleration of the soil element which is a radial distance of r away
from the pile centre.
V is the volume of the soil element.
m is the mass of the soil element.
The areas, volume, and mass in the Equation 6.23 are given by the following
equations:

⎟
⎠
⎞
⎜
⎝
⎛
+==
2
''''
dr
rdrdSS
DCBAABCD
θ

(6.24)
dzrdS
DDAA
θ
=
''
(6.25)
dzddrrS
CCBB
θ
)(
''
+= (6.26)
dz
dr
rdrddzSV
ABCDDCBABCDA
⎟
⎠
⎞
⎜
⎝
⎛
+==
2
''''
θ
(6.27)
'''' DCBABCDA
soil

V
g
m
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
γ
(6.28)
Substituting the areas, volume, and the soil mass of the element given by the above
equations into Equation 6.23 the equilibrium condition for the element becomes:
r
soil
rrz
a
grdr
d
dz
d
⎟
⎟
⎠
⎞
⎜
⎜

⎝
⎛
−=++
γ
γ
ττσ
(6.29)
Ignoring the vertical stress which is induced by the pile shear stress, the following
expression can be obtained:
soil
z
dz
d
γ
σ
=
(6.30)
Chapter 6 Testing data and discussions

163
Substituting Equation 6.30 into Equation 6.29 the equilibrium condition becomes:
r
soil
rr
a
grdr
d
⎟
⎟
⎠

⎞
⎜
⎜
⎝
⎛
−=+
γ
ττ
(6.31)
The acceleration of the soil element can be obtained from the pile acceleration, a
r
o
, by
using Equation 6.32 with the assumption that the soil deformation at a location in the
influence zone is reciprocally proportional to its distance from the pile shaft.
om
m
rr
rr
rr
aa
o
−
−
=
(6.32)
Substituting Equation 6.32 into Equation 6.31 the equilibrium condition then
becomes:
om
m

r
soil
rr
rr
rr
a
grdr
d
o
−
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−=+
γ
ττ
(6.33)

By integration the solution for Equation 6.33 is given by:
CrBr
r
A
r
++=

2
τ
(6.34)
where A, B, and C are parameters which can be obtained by substituting Equation
6.34 into Equation 6.33 and these parameters are given as follows:
ooo
r
soil
om
om
r
soil
om
o
or
a
grr
rr
a
grr
r
rA
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛

−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−=
γγ
τ
)(2)(3
23
(6.35)
o
r
soil
om
a
grr
B
⎟
⎟
⎠
⎞
⎜
⎜

⎝
⎛
−
=
γ
)(3
1
(6.36)
o
r
soil
om
m
a
grr
r
C
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−=
γ
)(2
(6.37)

Substituting A, B, and C given by Equations 6.35 to 6.37 into Equation 6.34 the
distribution of shear stress can be obtained as follows:
2
23
)(3
1
)(2)(3
ra
grrr
a
grr
rr
a
grr
r
r
o
ooo
r
soil
om
r
soil
om
om
r
soil
om
o
or

r
⎭
⎬
⎫
⎩
⎨
⎧
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠

⎞
⎜
⎜
⎝
⎛
−
−
=
γ
γγ
τ
τ


ra
grr
r
o
r
soil
om
m
⎭
⎬
⎫
⎩
⎨
⎧
⎟
⎟

⎠
⎞
⎜
⎜
⎝
⎛
−
−
γ
)(2
(6.38)