LABORATORY INVESTIGATION OF THE
LOADING RATE EFFECTS IN SAND
Authors: N.Q.Huy (1)
Prof. A.F. van Tol (1,2) Dr. P. Hölscher (2)
Date: 24 – 8 - 2006 Version: final
(1): Delft University of Technology, Delft, the Netherlands (2) GeoDelft, Delft, the Netherlands
Report name
LABORATORY INVESTIGATION OF THE
LOADING RATE EFFECTS IN SAND
Authors N.Q.HUY
Geoscience and civil engineering department
Delft University of Technology, Delft, The Netherlands
Supervisors Prof. A.F. van Tol - Delft University of Technology Dr. P. Hölscher - Geodelft
Summary of the report:
In order to improve the interpretation of the quasi-static (e.g. Statnamic) pile load tests, a research project has been started to investigate effects of the loading rate on the bearing capacity of a pile in sand. A series of laboratory tests has been carried out. The testing program consists of a series of triaxial tests for sand and a series of load tests on a model pile embedded in sand in a large calibration chamber.
The research pointed at answering two fundamental questions:
− The effect of loading rate on the strength of sand and on the bearing resistance of a pile in sand;
− The characteristics of excess pore pressure in sand and in the sand near the pile toe during a quasi-static load test.
The results of the triaxial tests are:
− In dry sand, a higher loading rate gives higher shear strength. In the range of applied loading rates, the angle of internal friction of the sand increases up to 2 degrees (strength increases 5-10%).
− During high speed tests on dry sand an excess of pore air pressure is observed. So the dry sand is not in fully air drained condition during these tests.
− The effects of loading rate in dry sand increase with the increase of relative density.
− In saturated sand, the shear strength increases about 5% due to the rate effect. But, the true rate effect may be obscured by cavitation which occurs during the test.
− Before cavitation occurs, the excess pore water pressure is independent of the loading rate. It depends on the relative density of the sand.
The results of the model pile test are:
− Comparison between the dynamic test and the static test shows that the point resistance and sleeve friction are independent of the loading rate in both unsaturated and saturated sand. The stiffness of the soil at pile toe level is higher in the dynamic tests than that in the static tests due to the dynamic effects. − During a dynamic test, a large excess of pore water pressure in the soil around the pile toe leads to
partly undrained behaviour of the sand in that region and to an additional increase of the dynamic stiffness.
Performed tests Performed by
The triaxial tests
The model pile test in unsaturated sand The model pile test in saturated sand
N.Q.Huy J. Dijkstra
Table of contents
Summary 2
Introduction 4
Part I: The laboratory soil test 6
1. Testing program 6
1.1. The type of test 7
1.2. The applied rates of deformation and test conditions 7
1.3. measurement parameters 7
3. Test on dry sand 8
3.1. Specimen preparation and testing procedures 8
3.2. Analysis the testing data 9
3.3. effect of loading rate in dry sand 12
4. Test on saturated sand
4.1. Specimen preparation and testing procedures 14
4.2. Analysis the testing data 14
4.3. Evaluation of rate effects 18
5. Conclusions 18
Appendix A 20
Part II: The model pile test
1. The test setup 22
1.1. The calibration chamber and sand bed 22
1.2. The model pile 23
1.3. The test methods and loading systems 23
1.4. The measurement devices 24
1.5. Notes on the model scaling 25
2. The test results 26
2.1. The tests in unsaturated sand 26
2.1.1. The CPT tests 26
2.1.2. The static load tests 27
2.1.3. The pseudo-static load test 30
2.2. The tests in saturated sand 32
2.2.1. The CPT tests 32
2.2.2. The static load tests 33
2.2.3. The pseudo-static load test 35
3. Evaluation of the rate effects 36
3.1. The rate effects in unsaturated sand 37
3.2. The rate effects in saturated sand 40
3.3. Discussions on the observed rate effects and the role of excess pore pressure 42
4. Conclusions 43
References 45
Appendix B Appendix C
Introduction
Quasi-static pile load tests, such as Statnamic and pseudo-static tests are considered as economic alternative for static test due to the lower costs and faster execution of these tests compared with ordinary static load tests. In practical interpretation of quasi-static tests, rate effects, i.e. an increase in shear strength of soil related to high rate of loading, are taken into account for clay, but generally neglected for sand. There is another approach, which is also related to high rate of loading but neglected, is an excess of pore pressure. Measurements made by Hölscher during a quasi-static pile load test at the testing event of the Forth International Conference on Application of Stress-Wave Theory to Piles (Delft, the Netherlands, 1992) showed that the soil is loaded by a stress wave and a large pore water pressures are generated in the quasi static tests. In order to facilitate the usage of quasi-static pile load tests to improve the quality of design in the Netherlands, the influence of high loading rate such as rate effect and excess pore water pressure must be understood. Therefore, a research project has been started. Because the pleistocene sand layer is essential for the bearing capacity of almost all piles in the Netherlands, the project firstly focuses on sand. There are two tests series are performed in parallel: a triaxial test series and a model pile test series. The results will be presented in this report.
The series of triaxial tests has been carried out in the GeoDelft Geotechnical Laboratory and the series of model pile tests has been carried out in a calibration chamber at the section of Geotechnical Laboratory, DUT to study the two fundamental questions in dry and saturated sand: − The effect of loading rates on strength a sand and on resistance of a pile embedded in sand;
The characteristics of excess pore pressure in the sand specimen and in the sand near the pile toe under different loading rates.
In the triaxial test series, the Constant rate of deformation test has been chosen to investigate the effect of loading rate on strength of the soil in dry and saturated condition. The deformation rate varies from very slow of 0.0125 mm/s to very fast of 600 mm/s.
In the model pile test series, both constant rate of penetration tests and dynamic tests have been performed. The rate of penetration varies from 1 mm/s (static test – STA) to 20 mm/s (CPT test) to investigate the effect of loading rate on point resistance and sleeve friction of the model pile in unsaturated sand and saturated sand. The dynamic test, which is a scaled of the prototype Statnamic test in 1g condition, has been performed on the same model pile to examine the different in pile performance between the static test and the dynamic test. The dynamic effects on resistance of the model pile in unsaturated and saturated sand are also examined. The characteristics of excess pore water pressure during the dynamic test and it effect are of very interest.
PART I: THE LABORATORY SOIL TEST
This section will deal with proper choice of testing regimes to fully meet the purposes of the study. The testing regimes include the test type, the applied loading rates, the test conditions, and the measured quantities.
1.1. The type of test
To fully meet the purposes of this study the tests must be performed with different loading rates in a certain range correlated with static and quasi-static pile load tests, which is determined later. At a loading rate in correlation with static pile load test, the test results are interpreted
straightforward in conventional way. But at high loading rate in correlation with quasi-static pile load tests, there might be dynamic effects such as stress wave phenomenon and inertial force, which will affect the test results. The choice of test type can reduce or even eliminate such
dynamic effects. Therefore, a Constant Rate of Deformation test type is chosen. It will be showed later that even in the test with highest rate of deformation in this test series the dynamic effects are minimized and negligible.
All tests are performed in a triaxial test apparatus with hydraulic loading system available in GeoDelft Geotechnical Laboratory. The loading system is capable of carrying out the tests with different loading velocities.
1.2. The applied rates of deformation and test conditions
The applied rates of deformation in the test series are chosen as close as possible to the rates, at which the soil is experienced during a conventional static and quasi-static pile load tests. In reality, the rates of deformation in the soil during such pile load tests are very difficult to
determine but the pile velocity are supervised so the choice of testing rates will be based the pile velocity. Because there is no stipulation for the pile velocity in a static pile load test, the lowest rate of deformation representative for a static test is chosen as slow as 0.0125 mm/s. The peak pile head velocity during a quasi-static pile load test is from 0.5 m/s up to 1 m/s, so the rate of deformation chosen for this test series as fast as 0.6 m/s (maximum velocity of the loading system). Some tests with intermediate rates of deformation are also performed for verification of the rate effect results.
The test conditions except the loading rate should be kept the same for all tests because the rate effects will be pointed out from any difference in the results from different loading rates tests. Those are the effective confining pressure of 100 kPa is applied in all test; all specimens are sheared to failure during a test by a vertical displacement of top loading plunger up to 3 cm (about 20% of axial strain).
Details of the applied deformation rates and test conditions for the tests on dry and saturated sand will be given in particular sections
1.3. Measurement parameters
The measurement parameters during a test are: − The applied force on specimen;
− The downward displacement at the top of specimen; − The applied confining pressure;
− The pore pressure during a test at the bottom of specimen;
All measurement quantities are measured as a function of time. In some tests the applied force is measured at both ends of specimen to examine the dynamic effects as explained later.
2.1. Characteristics of the sand
The sand used in this study is named Itterbeck sand. The grain size distribution (figure 1) and classification parameters (table 1.1) for the Itterbeck sand are determined in TUDelft Geotechnical Laboratory according to the procedures described in Head (1986).
Figure 1.1: Grain size distribution curve. Table 1.1: Classification parameters of Itter-beck sand
Property Value
Specific gravity, ρ s Max. dry density, ρmax Min. dry density, ρ min Mean grain size, d 50
Uniformity coefficient, D60/D10 2.613 ton/m3 1.731 ton/m3 1.415 ton/m3 0.165 mm 1.7 2.2. Testing system
The overview of the testing system is shown in figure 2. The testing system includes four parts: the triaxial cell; the hydraulic loading system with control box; the data acquisition system; and a desktop computer for visualizing the testing data.
The triaxial cell
The triaxial cell was designed as conventional triaxial cell for testing the soil sample with 6.6cm in diameter and 14cm in height. The only difference is an immersible load cell is placed at the bottom plate to measure the axial force at bottom end of specimen. This load cell was used in several tests.
The hydraulic loading system and loading control box
To apply a desired loading velocity patterns on the specimen, a hydraulic loading system was used. The hydraulic loading system is operated by a flow of high pressure oil. The oil flow is controlled by the loading control box. Maximum designed loading velocity of the loading system is 0.6 m/s and the minimum loading velocity is in magnitude of 10 -5 m/s. Another load cell was mounted at the tip of the loading plunger to measure the axial load. The capacity of this load cell is … and used in all tests. An internal displacement transducer also incorporated with the loading plunger to measure the axial displacement.
The loading control box is used to control the oil flow, consequently control the downward velocity of the loading plunger. The velocity of oil flow is automatically interpolated from the input pre-determined loading velocity, which can be changed manually. Each specific loading velocity correlates to a running program in the loading control box.
Figure 1.2: Overview of testing and data acquisition system. 3. Tests on dry sand
3.1. Specimen preparation and testing procedures
The preparation of dense sand specimen and testing procedure are closely followed the
conventional standard laboratory triaxial test procedures as described in Head (1998) in order to avoid any unexpected error. Details of the procedures will be presented below.
3.1.1. Specimen preparation
Before use, the sand is dried in an oven for at least 12h and cooled at room temperature. All specimens are prepared with the same dimensions of 6.6 cm in diameter and 15 cm in height. The amount of sand for each specimen is calculated from a desired relative density of the specimen and contented in a box.
A dense specimen is prepared in a cylindrical mold by the method of multi-stage vibration, which was acceptable in routine laboratory triaxial test. The vibration is applied on the mold by a
tamping hammer and a vibration machine. During vibration, the mold is kept in full of sand until all the amount of sand is in. Then, the surface of specimen is careful flatted and closed. A
vacuum is applied to the specimen through the drainage connection to help the specimen stay stable when the mold is removed. After the removal of the mold, the specimen dimensions were careful measured at the vacuum of -20 kPa and recorded. Initially, the dimension measurements are made with 2 vacuum values, i.e. a stay stable value of -20 kPa and the confining effective pressure of -100 kPa, but the different is very small and negligible.
Before shearing, the air confining pressure is applied to a prepared specimen as follow. The cell pressure is increased to 50 kPa first, then the vacuum in the specimen is released and the cell pressure is increased again to the desired effective confining value of 100 kPa. The loading plunger is then lowered to a space of about 2 mm above the top of the specimen. This space is intended to minimize the inertial effect of the loading plunger on testing results.
The tested specimen is shearing at constant rate of deformation up to 20% of axial strain. All measurement data are recorded by the data acquisition system (figure 2). The sampling rate of the data acquisition system is appreciate set for each test (usually is 1 kHz for a dynamic test and 1 Hz for a static test).
3.2. Analysis the testing data
The analysis of testing data includes the verification of actual rate of deformation in a test; the evaluation of the dynamic effects in high rate tests; the calculation of actual relative density in tested specimen; and the calculation of shear strength value.
3.2.1. Verification of the rate of deformation
The typical recorded displacement – time diagram in a rapid test is in figure 3. The desired velocity of deformation for the test is 0.6 m/s and the desired displacement – time diagram is also in figure 3. The recorded velocity is different from the desired velocity and must be adjusted. It was determined by an iterative process, in which various values are trying until the calculated diagram fits the measured diagram. In this case, the determined true velocity of deformation is about 0.525 m/s. For the static tests, the actual rate of deformation is as the same as desired value (figure 4).
The reason for this difference is the oil pressure in the loading system is not large enough to speed up the loading plunger to the desired value in the high rate tests. For the result in figure 3, the oil pressure is set to 120 bars. When the oil pressure was increased to 200 bar, the actual rates of deformation was very close to the desired values (around 0.59 m/s).
This procedure to point out an actual rate of deformation was applied for the high rate tests.
0 5 10 15 20 25 30 0 0.01 0.02 0.03 0.04 0.05 0.06 time(sec) d is p .( m m ) measured v=0.525 m/s v=0.6 m/s 0 5 10 15 20 25 30 0 500 1000 1500 2000 2500 tim e (s) d is p .( m m ) measured v=0.0125m/ s
Figure 1.3: Displacement-time diagram Figure 1.4: Displacement-time diagram in a high rate test. in a static test.
3.2.2. Evaluation of the dynamic effects
the recorded data from the top load cell includes inertial force from accelerating the loading plunger and specimen to the desired loading rates; at steady-state of deformation these inertial forces will disappear. As results, at beginning of a high rate test the load at top load cell will be bigger than the load at bottom load cell. As result, the existence of such dynamic effects can be verified from any different of the recorded load at both ends of specimen.
v=0.580 m /s -20 0 20 40 60 80 100 120 0 0.02 0.04 0.06 0.08 0.1 0.12 Tim e (s) F o rc e ( k g f) top bottom A Detail A -20 0 20 40 60 80 0 0.002 0.004 0.006 0.008 0.01 Tim e (s) F o rc e ( k g f) top bottom
Figure 1.5: Load – time diagram from Figure 1.6: Detail A (at beginning of the test) top and bottom load cells.
The recorded loads on a test with highest rate of 0.580 m/s is shown in figure 1.5; the details recorded loads at beginning of the test are shown in figure 1.6. From these figures it is clear that there is no difference between the loads at top and bottom load cells; only a different in time lag. This time lag relates to the compression wave velocity in the specimen. The height of specimen is about 15 cm; the time lag in figure 6 is about 0.001s and the wave velocity will be 150 m/s. This value is reasonable for dry sand (Hölscher, 1995). The dynamic effects are negligible in this case and it can be assumed if the dynamic effects do not exist in this highest rate test, it would not exist in other lower rate tests.
The measured load by top load cell is used in calculation stress on specimens.
3.2.3. Calculate density of specimens
From the measured dimensions and mass of a prepared specimen, the actual relative density (Head, 1996) can be determined as:
I D = D max , D min , D max , D min , D D ρ ρ . ρ ρ ρ ρ In which: I D : relative density (%)
ρD, max. : maximum volumetric mass of the sand (= 1.731 g/cm3) in densest state emin
ρD, min. : minimum volumetric mass of the sand (= 1.415 g/cm3) at loosest state emax
ρD : actual volumetric mass of the specimen (g/cm3) =
m V m: mass of sand in the specimen (g)
V: measured volume of the specimen (cm3).
Since the dimensions of a specimen are measured by hand, a certain deviation is unavoidable. An uncertainty analysis from the measurement deviations is given in Appendix A. With the assumption of 0.5 mm inaccuracy in the height measurement and 0.2 mm for diameter, the inaccuracy in relative density (I D) will be about ±4.5%.
The axial strain is calculated as: 1 0 u h
ε = .100%
Vertical stress is calculated as:
(
1 3)
m F Aσ −σ =
In which:
u : the measured vertical displacement (m); h 0 : the initial height of specimen (m);
F : measured vertical force by top load cell (kN);
A m is modified cross section area of specimens due to axial strain (m2).
A m can be determined if the volume of specimen is known at every moment during the test. But
in this case, the volume change is not measured. So A m will be calculated as we assumed the
Poisson’s ratio (ν) is equivalent to 0.2 (Head, 1986). Then: A m = A 0.(1+ν ε. 1)
2
The internal friction angle is calculated from Mohr cycle as: sinϕ = 1 3 1 3 ' ' σ σ σ σ − +
3.2.5. Results of the tests
The tests results are summarized in table 1.2. Total 22 tests have been done in dry sand. Of which, 9 tests are static and 13 tests are dynamic tests with different loading velocity. The range of specimen relative density is from 63% to approximately 85%. Details of stress-strain diagrams for every test are in Appendix 2.
Table 1.2: Results tests in dry sand
18 (0909-1419) static 79.4± 4.4 100 388.44 41.7 ± 0.1 2.9
19 (0909-1536) 0.480 75.8 ± 4.4 102 401.42 41.6 ± 0.1 4.8
20 (0910-1257) static 70.2 ± 4.5 100 367.25 40.3 ± 0.1 3.1
21(0910-1418) 0.195 69 ± 4.5 102 372.00 40.2 ± 0.1 3.4
22 (0910-1515) static 63.1 ± 4.6 100 319.51 38.0 ± 0.1 3
“static” is the tests with loading rate of 0.0125 mm/s
3.3. Effect of loading rate in dry sand
3.3.1. Loading rate effect on internal friction angle
In order to determine the effect of loading rates on shear strength of the dry sand, the test results in table 1.2 are divided into three groups. Group 1 is all the static tests namely “static”; group 2 is all the rapid tests with the loading velocities around 0.2 m/s namely “v=0.2 m/s”; group 3 is all the tests with loading velocity from 0.55 m/s up to 0.595 m/s namely “v=0.55 m/s”. Diagram of internal friction angle vs. relative density of the three groups is shown in figure 1.7 together with the trendline of each group. The results in figure 1.7 show an increase in internal friction angle of the dry sand is about 0.5 degree at 65% of relative density sand and up to 2 degree at 83 % of relative density sand. The loading rate does effect on shear strength of the dry sand and magnitude of rate effect increases as the relative density of specimen increases. This result agrees with the previous findings of Casagrande and Shannon (1948), Seed and Lundgren (1954), Whitman and Healy (1962) and others (Huy, 2003)
36 38 40 42 44 46 60 65 70 75 80 85 90 Relative density Id (%) F ri ct io n a n g le ( d eg .) static v=0.2 m/s v=0.55 m/s
Figure 1.7: Rate effect on internal friction angle of dry sand.
3.3.2. Rate effect on stress-strain relation and characteristic of excess pore air pressure
This paragraph will consider the stress-strain relation and the excess of pore pressure of the tests at about 83% of relative density since the rate effect appears to be large at that density. This consideration is preferred because of three tests closely the same with that relative density were sheared in three different loading velocities. The stress-strain diagrams of the three tests are shown in figure 1.8. The relative density of the static test is 84.6%; that of v=0.195 m/s test is 83.5%; and that of v=0.590 m/s test is 83.3%. The excess pore pressure of the three tests is shown in figure 1.9 as function of axial strain and in figure 1.10 as function of time.
deviator stress is effected by loading rates. The maximum increase in shear strength is about 20%.
The excess of pore air pressure during the rapid tests observed in figures 1.9 & 1.10 confirms the fact that during the rapid loading, even the air does not have enough time to drain fully, i.e. the sand behavior during the rapid loading is not in fully drained condition. Certainly, the faster shear the specimen results in the bigger rate of excess pore pressure (figure 1.10). A slightly lower of excess air pore pressure might reveal that in the faster test, the dense specimen dilates a bit bigger. The effect of excess pore pressure on the strength is negligible since the value of excess pore pressure at failure is about -5kPa, very small compare to the isotropic stress at failure of more than 230 kPa.
0 100 200 300 400 500 0 2 4 6 8 10 12 14 16 Axial strain (%) D ev ia to r st re ss ( k P a) v=0.195 m/s v=0.590 m/s v=static
Figure 1.8: Stress-strain relations with different loading rates.
-14 -12 -10 -8 -6 -4 -2 0 2 0 2 4 6 8 10 12 14 16 18 20 Axial strain (%) P o re p re s s u re ( k P a ) v=0.195m/s v=0.590m/s v=static
-14 -12 -10 -8 -6 -4 -2 0 2 0 20 40 60 80 100 time [ms] p o re p re s s u re [ k P a ] V=0.195 m/s V=0.590 m/s
Figure 1.10: Excess pore air pressure-time with different loading rates.
4. Tests on saturated sand
4.1. Preparation of specimen and testing procedures
4.1.1. Preparation of saturated specimen
The preparation process of a saturated specimen includes the preparation of dry specimen with desired relative density and the saturation of the specimen. The former was described in previous part, the later is presented here.
After a dry specimen is prepared, the cell pressure is increased to about 30kPa to keep the specimen stable during saturation process. Firstly, CO2 gas at low pressure (less than 5kPa) is
slowly pumped into the specimen in about 5 minutes to replace the air in the void of specimen. Then, the specimen is slowly saturated by de-air water till no gas bubble are seen in the drainage connection. Lastly, the pore water pressure and cell pressure are step by step increased to 300 kPa and 400 kPa respectively by a routine laboratory back pressure procedure. At every step of cell pressure increasing, the values of cell pressure and pore water pressure are recorded to calculate the Skempton’s factor (B), i.e. verify the degree of saturation of the specimen. When the pore water reaches 300 kPa of back pressure, any remaining gas in the void will be dissolved, the Skempton’s factor closes to unity, i.e. the specimen is considered as 100% saturated. At the end of the back pressure procedure, the cell pressure of 400 kPa and the pore pressure is 300 kPa results in an effective confining pressure of 100 kPa applied to the specimen.
4.1.2. Testing procedures
In general, the test procedures are the same as in the dry test series but there are some differences in the applied loading velocities and the test conditions due to limitations of the testing system. The static tests are performed with a constant loading velocity of 0.0125 m/s as in dry tests. The dynamic tests are performed with a constant loading velocity of 0.4 m/s because of a problem with the loading system as explained later. In addition, some tests are carried out with an intermediate loading velocity of 1 mm/s.
All tests are performed in undrained condition to avoid any effect of the testing system to the excess of pore water pressure behavior.
4.2. Analysis the testing data
The bottom load cell was damaged during the time of the test series and no replacement is available so the verification dynamic effects are impossible. But the dynamic effects would also negligible in this case due to the fact that the wave velocity is faster in saturated sand, i.e. the stress wave can travel back and forth more times, and the uniform stress state can be reached easier.
4.2.1. Determination of the actual deformation rate
In the first test, the loading velocity is set at the highest capacity of the loading system (0.6 m/s) to check the operation of testing system in saturated tests. The result of displacement as function of time is in figure 1.11. At the first about 15 cm of displacement, the velocity is approximately 0.44 m/s then, perhaps the failure in specimen happens, it increases suddenly to about 0.75 m/s. These actual velocities are different from the desired velocity. After several times trying, it was found out that a high applied loading rate is required to make a fast deformation of specimen but the oil pressure in the hydraulic loading system can not support such a high rate. The maximum supplied rate is only about 0.44 m/s. That is the reason for the choice of maximum velocity of 0.4 m/s for the dynamic tests on saturated specimen.
In other tests, the true loading velocity is determined as the same as in dry tests.
0 5 10 15 20 25 30 35 40 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 time (s) D is p . (m m ) Measured Verif ied v=0.44 m/s v=0.75 m/s
Figure 1.11: Displacement-time in the preliminary test 4.2.2. The existence of cavitation phenomenon
The tests are in dense sand specimen, where a strong volume expansion is expected. The volume change in undrained condition will result in large decrease in pore water pressure. When the pore water pressure reaches its vapor pressure (usually around -100 kPa) the cavitation phenomenon happens in the specimen. Once the cavitation occurs, the specimen is free to dilate as it would be. So the condition of constant volume in undrained tests and the measurement of pore water
pressure are and no longer valid because of the existence of pore air. As results, the effective stress is unknown unless the pore air pressure is measured. Therefore the verification of cavitation phenomenon for the test series is necessary.
Typical change of pore water pressure during a test is shown in figure 1.12. At beginning of a test, a specimen is isotropic compressed, the pore water pressure increases a bit; then the
supplied force but fortunately, the data is enough to verify the cavitation phenomenon. The total change in pore water pressure (Δu) in figure 1.12 is about 400 kPa while that of the special test in figure 1.14 is about 600 kPa at 3.5% of axial strain. If specimens have the same relative density and tested in the same condition, the degree of dilatancy wills more or less the same, i.e. the total change in pore water pressure must be the same. The different in these figures confirmed that the cavitation has occurred; the vapor pressure in the test condition is around -80 kPa.
Because the cavitation occurs in the tests on saturated sand, the effective stresses are unknown and the effective internal friction could not be determined. The only possibility to consider the rate effects in the test series is the deviator stress – strain relationship and the peak compression strength, i.e. the maximum value of (σ1 – σ3). The consideration is presented in the next section.
-100 -50 0 50 100 150 200 250 300 350 0 2 4 6 8 10 12 14 16 18 Axial strain (%) P o re p re s s u re ( k P a ) 62.47%-0.0125 62.95%-1 63.8%-375
Figure 1.12: Pore pressure vs. ε1 with different rates
0 1 2 3 4 5 6 7 0 150 300 450 600 Tim e (s) D is p . (m m ) 0 100 200 300 400 500 600 700 0 2 4 6 8 10 Strain (%) P o re p re s s u re ( k P a )
Figure 1.13: Displacement – time diagram Figure 1.14: Excess pore pressure – strain in the special test diagram in the special test
4.2.3. Calculation of relative density and peak compress strength
The calculation is the same as in dry test series. Only different is the calculation of a modified cross section of specimen due to axial strain before the cavitation occurs since the tests are in undrained condition up to that time, the volume of specimen is constant through the test. The modified cross section area is calculated as:
Am = ε = − 0 0 0 1 . .100 100 m A h A h Where:
A m is modified cross section area of specimens due to axial strain (m2).
h m = h 0 – u
h 0 is the initial height of specimen (m)
u is vertical displacement (m) ε 1 is axial strain (%)
After the cavitation occurs, the assumption value of Poisson’s ratio (ν) must be applied to calculate the modified cross section.
The compression strength s u is taken as maximum deviator stress in stress – strain diagrams. 4.2.4. Results of the tests
The test results are summarized in table 1.3. There are total 10 tests: three static tests; three intermediate velocity tests; and four rapid velocities tests. Calculated stress and measured pore water pressure as function of axial strain for these tests are shown in figures from 1.15 to 1.20.
Table 1.3: Results tests in saturated sand
Test No. (mm:dd-hh:mm) V (mm/sec) I D (%) 3 ' σ (kPa) Max. (σ - 1 σ ) 3 (kPa) φ (deg.) ε1-max (%) 1 (1004-1502) static 62.47 x 1293 N/A 6.5 2 (1003-1149) 1 62.95 x 1284 N/A 7.5 3 (1004-1206) 375 63.8 x 1328 N/A 9 4 (929-1115) static 71.3 x 1442 N/A 6.5 5 (0928-1506) 1 71.5 x 1420 N/A 7.5 6 (0929-1508) 380 71.2 x 1421 N/A 7 7 (1003-1530) 0.7 75 x 1450 N/A 7 8 (0829-1157) static 80.5 x 1553 N/A 6.5 9 (0831-1115) 350 80.3 x 1647 N/A 5.5 10 (0823-1129) 440 80.9 x 1648 N/A 6.5
“static” is the tests with loading rate of 0.0125 mm/s
0 200 400 600 800 1000 1200 1400 0 2 4 6 8 10 12 14 16 18 Strain (%) S tr e s s ( k P a 62.47%-0.0125 62.95%-1 63.8%-375 -100 -50 0 50 100 150 200 250 300 350 0 2 4 6 8 10 12 14 16 18 Axial strain (%) P o re p re s s u re ( k P a ) 62.47%-0.0125 62.95%-1 63.8%-375
0 200 400 600 800 1000 1200 1400 1600 0 2 4 6 8 10 12 14 16 18 Strain (%) S tr e s s ( k P a ) 71.3%-0.0125 71.5%-1 71.2%-380? 71.5%-370 -100 -50 0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 12 14 16 18 Strain (%) P o re p re s s u re ( k P a ) 71.3%-0.0125 71.5%-1 71.2%-380 71.5%-370
Figure 1.17: Stress – strain in different rates Figure 1.18: Pore pressure – strain in (Id ≈ 71%) different rates (Id ≈ 71%) 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 14 16 18 Strain (%) S tr e s s ( k P a ) 80.5%-0.0125 80.3%-350 80.9%-440 -100 -50 0 50 100 150 200 250 300 350 0 2 4 6 8 10 12 14 16 18 Strain (%) P o re p re s s u re ( k P a ) 80.5%-0.0125 80.8%-350 80.9%-440
Figure 1.19: Stress – strain in different rates Figure 1.20: Pore pressure – strain in (Id ≈ 80%) different rates (Id ≈ 80%)
4.3. Evaluation of rate effects
The evaluation of loading rate effect on behavior of the saturated sand will be based on the results presented in figures 1.15 to 1.20. Because of the effects of cavitation phenomenon, the evaluation of the rate effects is only valid before the occurrence of the cavitation, i.e. less than 3% of axial strain.
Through pictures 1.15, 1.17, 1.19, the loading rate has no effect on the stress – strain relation of the saturated sand specimens. There is a bit increase in peak shear strength (the maximum increasing is in very dense specimen but only about 5% - figure 1.19) but the true loading rate effect may be obscured by the cavitation.
5. Conclusions
Based on the results of test series of the fast triaxial test, conclusions about rate effects on the dense sand are drawn.
For dry sand:
− The angle of internal friction of dry sand increases as the loading rate increases. This increase depends on the initial relative density of the sand. For the range of relative density from 60% to 80%, the angle of internal friction ( ) increases from 0.5o to 2 o. This means that the strength (defined by tan( ) ) increases about 5-10%.
− There is an excess pore air pressure during a high rate of loading test on dry sand. However, the excess pore air pressure is very small compared to the isotropic stress at failure. It shows that the behavior of sand at the high loading rate is not in fully air drained condition.
For saturated sand:
− The rate effects on the peak strength of saturated sand are small (about 5% increase of the strength). This conclusion may be effected by cavitation that occurs in the specimens during the tests. Due to cavitation it is not possible to calculate the angle of internal friction from the saturated tests. From the test results up to cavitation, the loading rate has no effect on the stress-strain relation of the sand.
APPENDIX A: UNCERTAINTY ANALYSIS
1. List of symbols:
D 1: measured diameter at bottom of specimen.
D 2: measured diameter at middle of specimen.
D 3: measured diameter at top of specimen.
D 0: mean diameter of specimen (reference is 6.59 cm).
D’0: measured mean diameter of specimen.
H : measured height of specimen (reference is 15.05 cm) A’: measured area of cross section of specimen.
A : area of cross section of specimen V : volume of specimen.
m : mass of specimen.
I D: relative density of specimen; =
D max , D min , D max , D min , D D ρ ρ . ρ ρ ρ ρ . 100% (1) ρD: dry density of specimen; = m/V
ρDmax : maximum dry density of the sand; = 1.731 g/cm 3
ρDmin : minimum dry density of the sand; = 1.415 g/cm 3 2. Suppositions:
The measurement of force, displacement, cell pressure, mass of sand are accurately. So, uncertainties in relative density and mobilized friction angle should come from dimensional measurement. The height of specimen is measured by the standard ruler with 1 mm accuracy so a deviator measurement should 0.5 mm. The diameter of specimen is measured by “pi” string with 0.1mm accuracy so a deviator measurement should 0.2 mm. From that values. The uncertainty is analyzed. 3. Analysis: - Uncertainty in diameter: ± 0.02 cm D’0 = 1 2 3 2. 4 D + D +D D 0 = 1 0.02 2.( 2 0.02) 3 0.02 4 D ± + D ± +D ± = ' 0 0.02 D ± - Uncertainty in height: ± 0.05cm
- Uncertainty in cross section: ± 0.2 cm2
A’ = (pi/4). (D’0) 2 A = (pi/4). 2 0 D = (pi/4).( ' 0 0.02 D ± ) 2 ≈ A’ ± 0.2 cm2 - Uncertainty in stress calculation:
' 0.2 F F A A σ = = ±
V’ = A’ . H
V = A . (H ± 0.05) = (A’ ± 0.2).( H ± 0.05) ≈ V’ ± 4.8 cm3
- Uncertainty in dry density of specimen: ± 0.015 g/cm 3
m V ρ= = ' 4.8 m V ± ≈ ρ ’ ± 0.015 g/cm 3
- Uncertainty in relative density:
1. The test set up
The model pile tests series are performed by means of 1g model test in a calibration chamber at the Geo – Engineering Department of Delft University of Technology. The schematized view of the test set up is shown in figure 2.1. Details of the tests set up are presented in Dijkstra, 2004 and summarized this section.
1.1. The calibration chamber and sand bed
1.1.1. The calibration chamber
This is a rigid steel wall calibration chamber with 1.9 m diameter and 3.23 m height. It is equipped with two steel beams on the top as a support frame for the pile driving system. At the bottom, a number of drains are embedded in a filter bed and connected to a pumping system, which are used to saturated the sand bed from below and fluidize the sand. A couple of vibrators, attached to the sides of the chamber (figure 2.1), are used to densify the sand while draining the water.
Given the design of the calibration chamber, it differs from most of calibration chambers worldwide at several points (Broere, 2004). First and most noticeable is the lateral and bottom rigid boundaries but its effects on the test results are minimized by the large chamber – to – cone diameters ratio, Rd = 56; the top boundary is free. Secondary, the sand bed is not prepared by the
common used pluviation method, but by the method of fluidization and vibration, which will lead to less uniform densification of the sand bed. For the purposes of this study, this effect can be minimized by executing different tests in the same sand bed preparation and test location, i.e. the test conditions are the same, any different in results is caused by the loading rates.
Figure 2.1: The sketch of test set up Figure 2.2: Grain size distribution of the sand 1.1.2. The sand bed
The calibration chamber was filled with a sand bed of approximately 1.6 m in height. The sand was quite coarsely grain river sand with grain size distribution shown in figure 2.2. The mean grain size, D50, is 0.27 mm; the maximum and minimum volumetric masses are 1788 kg/m3 and
1467 kg/m3.
The sand bed was prepared by fluidization and vibration procedures. Firstly, the sand bed was saturated and fluidized with a water flow from bottom of the chamber to the top by the pumping system. In this way, the sand grains redistribute to loose state and a sufficiently homogeneous sand sample is expected after 1.5 hours of fluidization. Right after the fluidization, the chamber was vibrated by two vibrators while water was draining to obtain a greater compaction. The vibration time is usually from 5 minutes to 20 minutes. After the vibration, the remaining water can be drained to create an unsaturated sand bed condition or kept for partially saturated sand bed condition.
1.2. The model pile
The model piles are actually a Dutch standard penetration cone (CPT) for the test series in unsaturated sand and a piezometer cone (CPTu) for the test series in saturated sand. The cones have the diameter of 36 mm, the point surface is 10 cm2 and the friction sleeve is 150 cm2. The total length is 2.65 m of which 1.3 m is embedded in the sand. The rod above the sand bed surface is equipped with strain gauges, an acceleration transducer and a displacement sensor (linear stroke potentiometer). For the piezometer cone, the pore pressure sensor is located between the tip and friction sleeve.
1.3. The test methods and loading systems
1.3.1. The test methods
Since the main objective of this research is to study the effect of loading rate on either the bearing capacity of a pile or the response of pore water pressure near the pile toe, the tests with different loading rates must be applied on a pile in the same soil condition. The same soil condition is supposed by the same sand bed preparation, i.e. the same fluidization and vibration time; and test location. Three different loading rate tests are employed for the test series, namely CPT test, static test, and pseudo-static test.
• The CPT test is the installation of the cone (the model pile) into sand bed. Penetration rate of the pile is kept constant of 20 mm/s, which is standard rate of the CPT test in the Netherlands. During the last ≈160 mm of penetration the cone resistance and sleeve friction are recorded.
• The static test is performed in the same manner as the CPT test but the rate of penetration is 1 mm/s. This penetration rate is hard to get right since the operation is manually done, resulting in slower or faster rates. In a static test, the model pile displacement reaches about 20 mm (more than 50% of the model pile diameter).
• The pseudo-static test in this study is performed by dropping a heavy mass from a certain height onto the model pile head. A series of steel disc springs is installed between the drop mass and pile head to extent the duration of the blow. The number of disc springs is pre-determined to create a loading pulse on the model pile head with duration of about 22 ms. The test is a dynamic test, the loading pulse is considered as the Statnamic loading for the model scale (Dijkstra, 2004).
1.3.2. The loading systems
Two loading systems are used to load the model pile with different rate, a constant loading rate apparatus and a dynamic loading apparatus. The constant rate of loading system is a hydraulic rig (figure 2.3), which is used to install the model pile into the sand bed with a constant rate of 20 mm/s (normal rate of the CPT test in the Netherlands) as well as to perform static tests with a constant velocity of 1 mm/s. The dynamic loading apparatus is used to perform a high loading rate test on the model pile as shown in figure 2.4. It consists of a 64 kg steel drop mass and an aluminum guidance tube to guide the drop mass hits to the pile head. A series of disk springs are attached to the drop mass to lengthen the loading duration.
Figure 2.3: The constant rate of loading apparatus Figure 2.4: The dynamic loading devices 1.4. Measurement devices
The measured parameters during a test are: the point resistance and sleeve resistance of the cone, the applied force on the pile head, the displacement and acceleration of pile head. The pore water pressure is also measured during the tests in saturated sand. These parameters are measured with the following devices:
• The point and sleeve resistance as well as pore water pressure are measured by built-in sensors of the cone.
• The applied force on the pile head is measured by a strain gauge attached to the pile head (figure 2.5). It is used in the static tests and quasi-static tests.
• The pile head acceleration is measured by an acceleration transducer installed on a mounting steel plate (figure 2.6). It is used only in the pseudo-static tests.
Figure 2.5: The strain gauge
Figure 2.6: The acceleration transducer Figure 2.7: The displacement gauge 1.5. Notes on the model scaling
This paragraph deals with the scaling aspects of the model pile embedded in sand bed at 1-g condition. Scaling factors are chosen for the similarity of behaviors between the model pile load test and the prototype pile load test. In this study, a prototype quasi-static pile load test had been performed in the model scale and mentioned as the pseudo-static test. The similarity conditions are considered in next paragraphs.
The first similarity aspect is the wave propagation phenomena, which is specified by relative loading duration (tr). According to the recommendation of many authors from the second
international conference of Statnamic pile load test (Statnamic pile load testing, 1998), a pile is considered as quasi – static loaded if the relative loading duration is larger than 10. The relative loading duration is defined as the length of the loading pulse (T.c) divided by double length of the pile (2.L). For this model, the length of pile is 2.65m and the wave velocity in the pile rod is about 5200 m/s, leads to the required loading duration of:
T ≥ 10 *2 *L 0.010s
c ≈
It was theoretical and practical fulfilled by attached a number of disk spring on the drop mass (Dijkstra, 2004). The actual measured loading durations range from 0.013 s to 0.024 s. In
comparison with the typical loading duration of prototype quasi-static pile load test from 0.1 s to 0.22 s, it is reasonable to choice the time scale parameter n t =
p
m t
t = 10 (subscript m stands for
model; p for prototype). This is the basis scaling parameter, from which other quantities related to the model pile are scaling as well. For example, the scaling of pile dimension can be derived from the equal of relative loading duration between model and prototype:
t rp = t rm = . 2. p p p t c L = . 2. m m m t c L
Since wave velocity (c) is identical in prototype and model pile; the time scale n t = 10, leads to
n L = 10
p p
m m
L t
L =t =
The second similarity aspect involves the excess of pore pressure during the test. Since the permeability of the sand are not scaled, the excess of pore pressure is different between the model test and the prototype test. From the governing equation of consolidation, the time scale parameter can be derived by equaling of dimensionless time factor T:
T p = 2 . p vp p t c d = T m = 2 . m vm m t c d è p m t t = 2 2 . p vm vp m d c c d = nt 2 . vm vp c c
where dis length of drainage path; c v is coefficient of consolidation
This time factor must coincide with nt, which is derived from wave propagation phenomena, the
coefficient of consolidation in prototype must be n times larger than that in model, c vp = nt.c vm.
The coefficient of consolidation related to the soil permeability by c v =
. . v k m g ρ , in which other
parameters except permeability k are similar between prototype and model, results in the
permeability of the prototype sand (kp) is n times larger than the permeability of the sand used in
the model test (km). It implies that the present sand is the model of prototype sand whose
permeability is 10 times larger than the permeability of present sand.
The third similarity aspect is the soil stress state. It is a well-known severe handicap of model pile test at1-g condition, the soil stress state of the model is scaled in the same order with the dimension. As results, the unit point resistance and sleeve friction of the pile are scaled by the same factor as dimensions (nL).
2. The test results
Results of the tests in unsaturated sand bed and saturated sand bed are presented in this section. At first, representatives of the measuring quantities during these tests are presented in together with the usage of these measurements to determine the pile resistance. Then, the overall results will be summarized for later evaluation of the loading rate effects.
2.1. The tests in unsaturated sand
Since the set up of the model, a lot of tests have been done to verify the consistence of sand bed preparation procedure, the effects of test location… but they are not included in this report. Only the tests in the same soil condition and are tested with the different loading rate tests are of interest in this report. There are total eight tests are ready to investigate the effect of loading rates on bearing capacity of the model pile in unsaturated sand (Dijkstra, 2004). The sand bed
preparation is the same for these tests, i.e. 1,5 hours of fluidization and 10 minutes vibration. Three different loading rate tests are applied in each test with the sequence of (1) the CPT test (CPT); (2) the static test 1 (STA1); (3) the pseudo – static test (PS); (4) the static test 2 (STA2). The static test is performed before (STA1) and after (STA2) the pseudo-static test to examine the possibility of soil resistance changes due to the pseudo-static test. The representative results of the tests are shown from figure 2.8 to figure 2.17. The results of all these tests are presented in Appendix C.
2.1.1. The CPT tests
sand bed; large increasing gradient is caused by the change in soil property with depth. At time of point A, the CPT test stops, the pile shifts from loading phase to unloading phase cause a sudden change in pile resistance. As the pile stops moving downward, the soil resistance at point of the cone stops mobilizing results in a sudden decrease of the point resistance; the remaining applied force transfers to sleeve friction results in a sudden increase of the sleeve friction. The elastic rebound of the soil makes the values nearly constant for a while before drop to zero.
There is a notice for the measurement values of sleeve friction in figure 2.9, two types of measurement are observed (namely type I and type II). Type II, the measurement is as the same as that of the ordinary CPT test, the sleeve friction step increase to a certain value at beginning of the test due to the existence of soil friction at a depth then gradually increase to the final value (point A). This happens in some tests but for other test, the measurement is of type I and unlike the measurement in an ordinary CPT test, the sleeve friction is almost linear increase to the final value. The reasons for this are under examination and not clear at this time.
Since these measurements are the mobilized soil resistance against the penetration of the cone at that depth, the values at time of point A are considered as the unit point resistance and sleeve friction of the model pile during the CPT test. For the case shown in figure 2.8 and figure 2.9 – type I, the unit pile toe resistance is 10.5 MPa and the unit shaft friction is 0.05 MPa. The pile resistance of the 8 CPT tests is summarized in table 2.1.
-2 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Time (s) R e s is ta n c e ( M P a ) A -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 2 4 6 8 10 12 14 16 18 20 Time (s) F ri c ti o n ( M P a ) Type I Type II A
Figure 2.8: The measured point Figure 2.9: The measured sleeve friction resistance in a CPT test in a CPT test
2.1.2. The static load tests
The measurements during static load test STA1 and STA2 as functions of time are shown in figure 2.10 to figure 2.13. Results of the STA2 show a strange measurement because of an interruption during the test. The model pile is first loaded then the load stops increasing for some reasons in about 2 seconds before continue increasing. As results, the pile displacement increases a bit and remain constant for nearly 2 seconds at beginning of the test (figure 2.13); and there is a step change in the measured pile head force and point resistance value. The STA1 is performed continuously as shown in the results. The following points will be discussed from the result of measurements: the actual penetration rate of the model pile; the quality of measured pile head force; the value of point resistance and sleeve friction; and the comparison between the results of STA1 and STA2.
The pile head displacement is only measured in some static test (test 6; test 7 and test 8 – table 2.10) and indicates the same trend.
The measured pile head force by the strain gage is shown in figure 2.12. Consider the static equilibrium of the model pile, the pile head force must be equal to the sum of the point resistance and sleeve friction forces (total soil resistance). Of which, the point resistance force is calculated by:
Fpoint = qc. Apoint = qc . π. r2 = qc. 0.001 (kN)
The sleeve friction force is calculated by supposing the uniform distribution of the measured sleeve friction along the pile shaft (the case of maximum sleeve friction force) as:
Fsleeve = fs . Csleeve = fs . 1.3. π. 2. r = fs . 0.147 (kN)
Where qc and fs are measured point resistance and sleeve friction; Apoint and Csleeve and r are the
area of the toe and circumference of the shaft and the diameter of the model pile. Then the total soil resistance (Fsoilmax) is calculated as:
Fsoilmax = Fpoint + Fsleeve
Comparison of the calculated soil resistance and measured pile head force is in figure 2.14. The measured pile head force is about 5 kN (~30%) larger than the maximum total soil resistance and this discrepancy holds more or less the same in other tests. Since the cone sensors was calibrated regularly but the strain gage was calibrated only one before the first used, the cause would be the strain gage (may be installation problem or data conversion factor or something else). For that reason, the point resistance and sleeve friction will be utilized for pile resistance instead of the total bearing capacity derived from the measured pile head force in evaluating the loading rate effect.
The variation of point resistance and sleeve friction with time during a static test shown in figure 2.10 and 1.11 are very similar to those in the CPT test; the above mentioned point A (when the pile changes from loading phase to unloading phase) can be seen. The value of point resistance and sleeve friction at time of point A is considered as maximum soil resistances during the static test and taken as static resistance of the model pile as in CPT test. The first peak value of sleeve friction in figure 2.11 is not of interest since it is caused by the dry friction effect not the intrinsic soil-pile friction. The results of static tests are summarized in table 2.1.
Table 2.1: Summarized results from CPT and static load tests in unsaturated sand
Test No 1 2 3 4 5 6 7 8
Date (dd-mm-2004) 20-7 27-7 17-8 19-8 19-8 8-9 8-9 10-9
Location ii i i i ii i ii iii
Point (MPa) 14.73 N/A 16 13.38 14.24 11.17 10.6 14.69
CPT
Sleeve (MPa) 0.064 N/A 0.064 0.021 0.054 0.043 0.051 0.068
Head (kN) 23.26 28.21 29.6 25.05 26.53 22.8 20.6 27.57
Point (MPa) 10.6 11.77 13.12 11.25 12 9.56 9.25 12.44
Sleeve A (MPa) 0.067 0.072 0.055 0.031 0.055 0.042 0.047 0.069
u (mm) N/A N/A N/A N/A N/A 12.7 18.25 N/A
STA1
v (mm/s) N/A N/A N/A N/A N/A 0.81 2.44 N/A
Head (kN) 20 27.52 27.3 23.13 25 22.77 21.8 26.78
Point (MPa) 9.8 11.02 12.89 10.5 11.88 9.59 9 12.4
Sleeve A (MPa) 0.064 0.07 0.05 0.045 0.055 0.043 0.049 0.066
u (mm) N/A N/A N/A N/A N/A 18.18 15.14 17.92
STA2
Notes:
- “location” : position of the model pile in calibration chamber (see figure 2)
- “point” : measured point resistance (MPa)
- “sleeve A” : measured sleeve friction at point A (MPa)
- “head” : measured force at pile head (kN)
- “u” : measured maximum pile head displacement (mm)
- “v” : average pile head velocity (mm/s)
- N/A : not available
In considering the possibility of change in soil condition due to the pseudo-static test, the results from static test 1 (STA1) and static test 2 (STA2) are compared in figures 2.10; 2.11; 2.12. There is not much different between the two measurements, the measurements are almost the same and this is true for all tests (see Appendix C). Statistical analysis of all the static test measured values by Dijkstra, 2004 confirmed that the results from the static tests are the same with 95% of
confidence limit values. Thus, the soil condition is unchanged during the pseudo – static load test; the values of the static test 1 (STA1) are representative for the static pile resistance in evaluation of the rate effect.
-2 0 2 4 6 8 10 0 2 4 6 8 10 12 14 16 Time (s) R e s is ta n c e ( M P a ) STA1 STA2 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0 2 4 6 8 10 12 14 16 Time (s) F ri c ti o n ( M P a ) STA1 STA2
Figure 2.10: The measured point resistance Figure 2.11: The measured sleeve friction in static load test in static load test
-5 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Time (s) H e a d f o rc e ( k N ) STA1 STA2 -4 0 4 8 12 16 20 24 0 2 4 6 8 10 12 14 16 Time (s) D is p . (m m ) STA1 STA2
-5 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Time (s) F o rc e ( k N ) Fhead Fpoint Fsleeve Fsoilmax Figure 2.14: Fhead vs. Fsoil
2.1.3. The pseudo – static load tests
The measurements during a pseudo – static load test are shown from figure 2.15 to figure 2.19. The pile head velocities shown in figure 2.20 are integrated from the measured acceleration and differentiated from the measured displacement. In the next paragraphs, some comments on the quality of measurement results will be given first, and then the determination of pile resistance will be presented.
The first high peak value in figure 2.15; 2.17 and 2.18 are the results of metal to metal impact when the drop mass hits the pile head and out of concern. The comments are concentrated on the quality of the measured pile head force and pile head acceleration. The pile head force measured by strain gage may have problem as the same as mentioned in section 2.1.2 but the verification is more difficult in this case of pseudo-static test since the test is a dynamic event, the inertial force does play a role and must be removed from measured pile head force for the comparison with the total cone resistance (Fsoilmax = Fpoint + Fsleeve). Value of inertial force is hardly determined exactly
because the movement mass does not precisely know, i.e. the drop weight could be an added mass before rebound. By simplified taking into account only the mass of pile, the soil resistance can be calculated by subtracting the inertial force of pile mass from the measured pile head force, i.e. (F(t) – m*a(t)). The derived load – time diagram (Fsoil – t) is shown in figure 2.15 in
combination with the total cone resistance (Fsoilmax) calculated as in 2.1.2. There is still different
between the soil resistance and the total cone resistance; the different is small in the loading phase (about 2 kN) then become larger in the unloading phase (about 8 kN). The same problem as during static test in measuring the pile head force does exist.
In additional, the pile motion is not consistence from the measured pile head acceleration and the measured pile head displacement. Comparison between the pile velocities derived from the measured acceleration and displacement in figure 2.20, a relative agreement in the trend of pile velocity is achieved till the maximum displacement is reached; then the agreement disappears. The derived velocity from the measured acceleration indicates a continuously moving upward at nearly constant velocity of the pile when rebound, which is impossible. The values of derived pile velocity are different since the integration of pile acceleration is largely depend on the initial values of the measured acceleration but these values contain a big noise from the impaction of metal to metal. In combination with the results from other tests (Appendix C), it can be
concluded that the measured displacement is more reliable than the measured acceleration; the pile velocity should be derived by differentiated the measured displacement for later evaluation of the rate effect.
bearing resistance of the model pile. For the point resistance, the maximum value is quite clear in figure 2.17 since the noise of recorded signal is small in comparison with the value of point resistance. In case of sleeve friction, lots of peak values are created since the noise of signal is quite large in comparison with the value of sleeve friction. In figure 2.18, the first peak value (1) is caused by the metal to metal impact; the second peak values (2) are caused by dry friction effect; the average value at third peaks (3) is chosen as sleeve friction of the model pile during a pseudo-static test. Results of the 8 pseudo-static tests are summarized in table 2.2.
-5 0 5 10 15 20 25 30 35 0 0.005 0.01 0.015 0.02 0.025 Time (s) F o rc e ( k N ) F(t) F(t)-m*a(t) Fsoilmax 0 2 4 6 8 10 12 14 0 0.005 0.01 0.015 0.02 0.025 Tim e (s) D is p l. ( m m ) Figure 2.15: Measured pile head force Figure 2.16: Measured pile head displacement in a pseudo-static load test in a pseudo-static load test
-2 0 2 4 6 8 10 0 0.005 0.01 0.015 0.02 0.025 Time (s) R e s is ta n c e ( M P a ) -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0 0.005 0.01 0.015 0.02 0.025 Time (s) F ri c ti o n ( M P a ) 1 3 2
Figure 2.17: Measured point resistance Figure 2.18: Measured sleeve friction in a pseudo-static load test in a pseudo-static load test
-1000 -500 0 500 1000 1500 0 0.005 0.01 0.015 0.02 0.025 Time (s) A c c . (m /s 2 ) -1 -0.5 0 0.5 1 1.5 2 0 0.005 0.01 0.015 0.02 0.025 Time (s) V e lo c it y ( m /s ) From a From u
Figure 2.19: Measured pile head acceleration Figure 2.20: Pile head velocity in a pseudo-static load test in a pseudo-static load test
Table 2.2: Summarized results of pseudo-static load tests
Date (dd-mm-2004) 20-7 27-7 17-8 19-8 19-8 8-9 8-9 10-9 Location ii i i i ii i ii iii # disc springs 1 1 6 6 5 5 5 6 Drop height (cm) 18.5 20.9 29.9 30 32.5 29.3 32 27.5 u (mm) 5.4 3.5 >5.9 >3 6.5 >6 13 >9 Pulse width (ms) 13 14 23.5 23 22 21 22 22.5 v (m/s) 1.5 1* 0.7* >0.4* 1.25 1.1* 1.6 2.2* Point (MPa) 11.84 12.37 11.17 10.22 11.84 8.7 9 11.39 Sleeve (MPa) 0.068 0.065 0.057 0.03 0.057 0.052 0.050 0.074 Notes:
- In test 3, 6, 8 the pile head displacement is not fully measured because the transducer reaches its
limit.
- The displacement in test 2 shows a strange behavior (App. C) by unknown reason.
- The measurement of displacement in test 4 is fail.
- “*” : the value is estimated
2.2. The tests in saturated sand
There are total 8 tests with the same order of applied load test methods (CPT – STA1 – PS – STA2) have been performed. All tests are performed at central point of the calibration chamber (location i). The saturated sand bed is prepared with 1.5 hours of fluidization and 5 minutes of vibration. The measurements are included the value of pore water pressure near the pile toe. The typical results for the tests in saturated sand bed will be introduced in this section from figure 2.21 to figure 2.28. Details of measurement results for all tests can be found in Appendix D. 2.2.1. The CPT test
For the CPT tests in saturated sand bed, the results are recorded in the last 40 cm penetration of the cone and shown in figures 2.21; 2.22 and 2.23. The measurement of point resistance and sleeve friction are very similar to those of the tests in unsaturated sand. The excess of pore water pressure increases due to the penetration of the pile and quickly decreases as the cone stop penetrating.
The pile resistance is taken the values at point A as the same as in the CPT test in unsaturated sand bed. Summary of the results is in table 2.3.
-1 0 1 2 3 4 5 6 7 8 0 5 10 15 20 25 30 Time (s) R e s is ta n c e ( M P a ) A -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0 5 10 15 20 25 30 Time (s) F ri c ti o n ( M P a ) A
-0.002 0 0.002 0.004 0.006 0.008 0.01 0 5 10 15 20 25 30 Tim e (s ) E x c e s s p p . (M P a )
Figure 2.23: Excess pore water pressure in a CPT test
2.2.2. The static test
During a static test, the pile is penetrated about 20 mm into the saturated sand bed with the intended velocity of 1 mm/s but the true velocity is often slower. The measurements during a static test are shown from figure 2.24 to figure 2.28. The measured pile head force and cone resistance are very similar to those of the test in unsaturated sand; the point A where the model pile change from loading phase to unloading phase is seen.
Differentiated with time from the measurement of pile head displacement in figure 2.27 indicates the pile velocity in STA1 and STA2 are 0.5 mm/s and 0.44 mm/s consequently. Results from other tests show the nearly the same value (Table 2.3)
There is an excess of pore pressure during the static test (figure 2.26) but its value are very small compare to the cone resistance. As the pile starts moving, the loading rate is large; the pore pressure sharply increases to the maximum value. When the pile steady penetrates, the loading rate slowdown, the pore pressure decreases and remains at an almost constant value.
In figure 2.28, the comparison between measured pile head force and total pile resistance is shown. The total soil resistance is calculated from the measured point resistance and sleeve friction as explained in the unsaturated case. The discrepancy of about 1.3 kN appears; review from other tests in appendix D show the range of discrepancy is from 1 kN to 3 kN. Results from these static tests are summarized in table 2.3, in which the sleeve is taken at the point A as the same as that of the static tests in unsaturated sand; the point resistance is taken at the time when the displacement equal to the maximum displacement of the correlated pseudo – static test. The reason will be explained later (section 3.2.1).
