Corrections on the specimen volume change and axial force in the Wykeham Farrance WF11001/SN: triaxial cell

Transcription

1 Corrections on the specimen volume change and axial force in the Wykeham Farrance WF11001/SN: triaxial cell Georgopoulos Ioannis-Orestis 1 Vardoulakis Ioannis 2 15th December PhD Student, NTU Athens, Greece 2 Professor, NTU Athens, Greece

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3 Contents 1 Introduction 11 2 Cell volume change corrections Volume change due to water compressibility, V water Volume change due to piston movement, V piston Volume change due to nylon flexible pipe expansion, V pipe Volume change due to triaxial cell expansion, V cell Specimen volume change corrections Specimen section area Membrane penetration effect Axial load corrections Standard bush Rotating bush Submersible load cell Conclusions 55 3

4 4 CONTENTS

5 List of Figures 1.1 Wykeham Farrance WF11001/SN: triaxial cell Representation of factors which influence cell volume change measurements: (a) components due to specimen, (b) effects during saturation and consolidation stages, (c) effect of piston penetration during compression ([6]) Automatic volume change apparatus calibration, Automatic volume change apparatus calibration, Automatic volume change apparatus calibration, load Automatic volume change apparatus calibration, unload Automatic volume change apparatus calibration, Automatic volume change apparatus calibration, load Automatic volume change apparatus calibration, unload Automatic volume change apparatus 100kPa, Automatic volume change apparatus 200kPa, Automatic volume change apparatus 300kPa, Automatic volume change apparatus 400kPa, Automatic volume change apparatus 500kPa, Automatic volume change apparatus 600kPa, Calibration of nylon flexible pipe expansion, Calibration of nylon flexible pipe with de-aired water expansion,

6 6 LIST OF FIGURES 2.17 Typical curve of volume change of a triaxial chamber versus cell pressure (Head, K.H., 1986) Section and side/top view of the WF11001/SN: triaxial cell WF11001/SN: triaxial cell calibration WF11001/SN: triaxial cell calibration, b WF11001/SN: triaxial cell calibration, c WF11001/SN: triaxial cell calibration, a WF11001/SN: triaxial cell calibration, b WF11001/SN: triaxial cell calibration, c WF11001/SN: triaxial cell calibration, d Specimen section area due to barreling Membrane penetration effect (after K.H. Head [6]) Membrane penetration error in a typical triaxial test Membrane penetration error as a function of the volumetric strain in an isotropic consolidation test The error in axial load measurement due to ram friction: variation with axial strain in a typical test on a 4-in. diameter sample ([3]) WF11001/SN: triaxial cell bush friction, calibration loading WF11001/SN: triaxial cell bush friction, calibration unloading WF11001/SN: triaxial cell bush 0kPa, calibration loading WF11001/SN: triaxial cell bush 0kPa, calibration unloading WF11001/SN: triaxial cell bush 20kPa, calibration loading WF11001/SN: triaxial cell bush 20kPa, calibration unloading WF11001/SN: triaxial cell bush 100kPa, calibration loading WF11001/SN: triaxial cell bush 100kPa, calibration unloading WF11001/SN: triaxial cell bush 200kPa, calibration loading WF11001/SN: triaxial cell bush 200kPa, calibration unloading WF11001/SN: triaxial cell bush 300kPa, calibration loading

7 LIST OF FIGURES WF11001/SN: triaxial cell bush 300kPa, calibration unloading WF11001/SN: triaxial cell bush 400kPa, calibration loading WF11001/SN: triaxial cell bush 400kPa, calibration unloading WF11001/SN: triaxial cell bush 500kPa, calibration loading WF11001/SN: triaxial cell bush 500kPa, calibration unloading WF11001/SN: triaxial cell bush 600kPa, calibration loading WF11001/SN: triaxial cell bush 600kPa, calibration unloading Wykeham Farrance STALC3-50kN triaxial submersible load cell DBBSE-50kN-A2242 external load cell (Applied Ltd)

8 8 LIST OF FIGURES

9 List of Tables 2.1 Area A of WF17044/SN: and VJT310/SN:0134 automatic volume change apparatus piston calibration table Logarithmic law parameters for nylon flexible pipe (filled with de-aired water) 6/8 mm calibration Logarithmic-linear law parameters for WF11001/SN: triaxial cell calibration WF11001/SN: triaxial cell bush friction coefficient µ calibration

10 10 LIST OF TABLES

11 Chapter 1 Introduction In this report the Wykeham Farrance triaxial cell WF11001/SN: calibration is presented in detail. The main purpose of the calibration is to allow for estimation of precise volume change of specimens, when no on-sample transducers are available or when partially saturated granular media are considered. In these cases, no direct specimen volume change measurement can be performed, thus leading to indirect estimation of the volumetric strain. The WF11001/SN: is a triaxial cell (Ph. 1.1), which may host specimens of diameter up to 105mm and is equipped with a submersible load cell STALC3-50kN, adjusted to its piston. The maximum cell pressure is 1700kPa. More information concerning the triaxial cell can be found in the internal report The Handbook of Wykeham Farrance GeoTriax. 11

12 Figure 1.1: Wykeham Farrance WF11001/SN: triaxial cell. Laboratory of Geomaterials 12

13 Chapter 2 Cell volume change corrections In pp.164 of Manual of soil laboratory testing, Vol.3, K.H.Head states: Measurements of the volume change on the cell pressure line require several corrections and are consequently less accurate than volume change measurements made in the back pressure system. Cell volume change measurements are not required in the test procedures specified in BS 1377:Part 8:1990. However, the movement of water into or out of a partially saturated soil from the back pressure system is not a true measurement of the specimen volume change, and for some soils (e.g.) expansive clays independent measurements based on changes in the cell line are necessary. Factors which affect the movement of water into or out of the cell, and which must therefore be taken into account in the cell line volume change measurements, are as follows. These factors are represented diagrammatically in Figure 2.1 where they are numbered as above. 1. Irregularities on specimen surface 2. Air trapped between specimen and rubber membrane and side drains (if fitted) 3. Expansion of cell due to pressure increase 4. Continued expansion of cell (creep) with time under constant pressure 5. Absorbtion of water into, and mitigation through, cell body 6. Air trapped at top cell 7. Leakage of water - through piston bushing - through membrane and bindings 13

14 Figure 2.1: Representation of factors which influence cell volume change measurements: (a) components due to specimen, (b) effects during saturation and consolidation stages, (c) effect of piston penetration during compression ([6]). - from connecting lines and valves 8. Voids in specimen 9. Change in specimen due to drainage of water (consolidation or swelling) 10. Movement of piston Following Head s suggestions, the main purpose of the triaxial cell volume calibration is to allow the user to estimate with good accuracy the specimen volume change, when no on-sample transducers are available, or when the automatic volume change apparatus cannot be used, due to partially saturated or dry soil. In such cases, it is quite common that the WF17044/SN: automatic volume change apparatus is connected to the cell pressure line (Port 1 or 3) instead of being connected directly to the pore pressure lines (Port 2 or 4). By this way, the automatic volume change apparatus is able to measure the volume of water entering of coming out from the triaxial cell during a test. The measurement of the apparatus is considered to be less accurate, as it contains several errors that have to be withdrawn. These are: Laboratory of Geomaterials 14

15 1. Volume change due to water compressibility, V w 2. Volume change due to piston movement, V piston 3. Volume change due to flexible pipe expansion, V pipe 4. Volume change due to triaxial cell expansion, V cell In the following sections each one of the four corrections will be critically discussed and estimated. 2.1 Volume change due to water compressibility, V water Although water is much less incompressible than air, it still remains a compressible medium. Water compressibility c w depends much on the existence of dissolved air in its mass. In the case of de-aired water, the de-aired water compressibility takes the value of c w0 = /kp a (2.1) Should a volume of de-aired water V w sustain an increase in pressure σ c, the water volume decrease is calculated from eq.2.2 V w = c w0 σ c V w (2.2) 2.2 Volume change due to piston movement, V piston This correction applies to the volume of water displaced or inserted by the loading ram movement, during a triaxial compression or extension test. The volume of water is equal to the volume of the loading ram entering or coming out of the triaxial cell, V piston = πd 2 piston h (2.3) 4 where d piston is the diameter of the loading ram (= 25.1mm) and h is the relative movement of the piston to the triaxial cell. The volume of water displaced by the loading ram in a triaxial compression test must be equal to the volume of water measured by the two automatic volume change apparatus (WF & VJT), connected to the WF11001/ SN: triaxial cell. The water of the cell is allowed to come out or enter the triaxial cell under pressure (cell pressure σ c ). In this way both automatic volume change apparatus are calibrated and the results are given in Table 2.1. The WF17044/SN: and VJT310/SN:0134 automatic Laboratory of Geomaterials 15

16 Vol.ch.app. WF17044/SN: VJT310/SN:0134 Cell Displ.trans. LSC-HS LSC-HS pressure Date A W F (mm 2 ) A V JT (mm 2 ) σ c (kpa) load unload a-load a-unload kPa kPa kPa kPa kPa kPa Table 2.1: Area A of WF17044/SN: and VJT310/SN:0134 automatic volume change apparatus piston calibration table. volume change apparatus are connected to the cell pressure line. Calibration tests were performed under various cell pressures σ c and the area of the internal piston for both apparatus was estimated. From Table 2.1 the propose the following calibration parameters for the WF & VJT automatic volume change apparatus, A (mm 2 ) = { 4164, W F 4261, V JT 2.3 Volume change due to nylon flexible pipe expansion, V pipe One correction that should also be taken into account is the expansion of the flexible pipes, connecting the automatic volume change apparatus with the cell/pore pressure line and the air/water cylinders. Nylon flexible pipes of internal/external diameter (6/8) are used for this reason. They offer relatively high flexibility while their compressibility is rather low. Calibration tests up to 1200kPa in a 3170mm long flexible nylon pipe were performed in order to estimate the compressibility. The total volume change of the flexible pipe filled with de-aired water is given from eq. 2.4 Laboratory of Geomaterials 16

17 Volume change displaced by loading ram and measured by WF automatic volume change 712.6kPa ( ) Volume displaced by piston Volume measured by WF Volume change [mm 3 ] ,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 Time [min] Figure 2.2: Automatic volume change apparatus calibration, Volume change displaced by loading ram and measured by WF automatic volume change 199.6kPa ( ) Volume displaced by piston Volume measured by WF Volume change [mm 3 ] ,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0 Time [min] Figure 2.3: Automatic volume change apparatus calibration, Laboratory of Geomaterials 17

18 Volume change displaced by loading ram and measured by VJT automatic volume change 202.8kPa ( load) Volume displaced by piston Volume measured by VJT Volume change [mm 3 ] ,0 2,5 5,0 7,5 10,0 12,5 15,0 17,5 20,0 22,5 Time [min] Figure 2.4: Automatic volume change apparatus calibration, load Volume change displaced by loading ram and measured by VJT automatic volume change 200.4kPa ( unload) Volume displaced by piston Volume measured by VJT Volume change [mm 3 ] ,0 2,5 5,0 7,5 10,0 12,5 15,0 17,5 20,0 22,5 Time [min] Figure 2.5: Automatic volume change apparatus calibration, unload. Laboratory of Geomaterials 18

19 Volume change displaced by loading ram and measured by WF & VJT automatic volume change 402.9kPa ( ) Volume displaced by piston Volume measured by WF Volume measured by VJT Volume change [mm 3 ] ,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 Time [min] Figure 2.6: Automatic volume change apparatus calibration, Volume change displaced by loading ram and measured by WF & VJT automatic volume change 204.1kPa ( a-l) Volume displaced by piston Volume measured by WF Volume measured by VJT Volume change [mm 3 ] ,0 2,5 5,0 7,5 10,0 12,5 15,0 17,5 20,0 22,5 Time [min] Figure 2.7: Automatic volume change apparatus calibration, load. Laboratory of Geomaterials 19

20 Volume change displaced by loading ram and measured by WF & VJT automatic volume change 198kPa ( a-un) Volume displaced by piston Volume measured by WF Volume measured by VJT Volume change [mm 3 ] ,0 2,5 5,0 7,5 10,0 12,5 15,0 17,5 20,0 22,5 Time [min] Figure 2.8: Automatic volume change apparatus calibration, unload Volume change displaced by loading ram and measured by WF & VJT automatic volume change 97.9kPa ( ) Volume displaced by piston Volume measured by WF Volume measured by VJT Volume change [mm 3 ] ,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 Time [min] Figure 2.9: Automatic volume change apparatus 100kPa, Laboratory of Geomaterials 20

21 Volume change displaced by loading ram and measured by WF & VJT automatic volume change 205.5kPa ( ) Volume displaced by piston Volume measured by WF Volume measured by VJT Volume change [mm 3 ] ,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 Time [min] Figure 2.10: Automatic volume change apparatus 200kPa, Volume change displaced by loading ram and measured by WF & VJT automatic volume change 304.5kPa ( ) Volume displaced by piston Volume measured by WF Volume measured by VJT Volume change [mm 3 ] ,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 Time [min] Figure 2.11: Automatic volume change apparatus 300kPa, Laboratory of Geomaterials 21

22 Volume change displaced by loading ram and measured by WF & VJT automatic volume change 402.9kPa ( ) Volume displaced by piston Volume measured by WF Volume measured by VJT Volume change [mm 3 ] ,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 Time [min] Figure 2.12: Automatic volume change apparatus 400kPa, Volume change displaced by loading ram and measured by WF & VJT automatic volume change 506.7kPa ( ) Volume displaced by piston Volume measured by WF Volume measured by VJT Volume change [mm 3 ] ,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 Time [min] Figure 2.13: Automatic volume change apparatus 500kPa, Laboratory of Geomaterials 22

23 Volume change displaced by loading ram and measured by WF & VJT automatic volume change 607.3kPa ( ) Volume displaced by piston Volume measured by WF Volume measured by VJT Volume change [mm 3 ] ,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 Time [min] Figure 2.14: Automatic volume change apparatus 600kPa, V = V pipe + V w,pipe (2.4) where V is the volume change of the flexible pipe filled with water, measured by the WF automatic volume change apparatus, V pipe is the expansion of the flexible pipe due to increase of pressure and V w,pipe is the compression of water inside the flexible pipe, evaluated from eq. 2.2, where V w,pipe is given from eq. 2.5 V w,pipe = πd 2 int L (2.5) 4 where d int is the internal diameter of the nylon flexible pipe (6.0mm) and L the length of the flexible pipe. In Fig a calibration graph of a nylon flexible pipe filled with deaired water is given. From the data regression curves, we obtain a power law for the flexible pipe expansion in loading-unloading. The volume expansion per unit length of the nylon flexible pipes of internal/external diameter due to internal pipe pressure 6/8mm is given through the following expression, in eq. 2.6, ( ) V pipe /mm = A ln( σ c ) ln(σ c0 ) (2.6) where A (mm 2 /kpa) and σ c0 (kpa) are the parameters of the power law model. The same model applies also for the volume expansion of the flexible Laboratory of Geomaterials 23

24 Nylon flexible pipe expansion, diameter=6/8mm, length=3170mm Test-02/ Test-03/ Test-04/ y = 22,301e 0,002x R 2 = 0,979 y = 20,755e 0,0021x R 2 = 0,9795 Pressure c [kpa] y = 22,019e 0,0021x R 2 = 0, Flexible pipe expansion V pipe [mm 3 ] Figure 2.15: Calibration of nylon flexible pipe expansion, Test-02/ Nylon flexible pipe (filled with de-aired H 2 O) expansion diameter=6/8mm, length=3170mm Test-03/ Test-04/ y = 22,717e 0,002x R 2 = 0,979 y = 21,146e 0,002x R 2 = 0,980 Pressure c [kpa] y = 22,420e 0,002x R 2 = 0, Flexible pipe expansion V pipe [mm 3 ] Figure 2.16: Calibration of nylon flexible pipe with de-aired water expansion, Laboratory of Geomaterials 24

25 Model Parameters A (mm 2 /kpa) σ c0 (kpa) Calibration, (test02) Calibration, (test03) Calibration, (test04) Table 2.2: Logarithmic law parameters for nylon flexible pipe (filled with de-aired water) 6/8 mm calibration. nylon pipes filled with de-aired water and is given by the expression in eq. 2.7, ( ) V pipe&water /mm = A ln( σ c ) ln(σ c0 ) (2.7) where A (mm 2 /kpa) and σ c0 (kpa) are the parameters of the power law model. Comparing Fig and 2.16 shows that the volume expansion of the flexible nylon pipe is much greater than the compression of de-aired water in the nylon flexible pipe, V pipe V w,pipe. Table 2.2 summarises the power law model constants for various calibrations. 2.4 Volume change due to triaxial cell expansion, V cell The last, but not least, volume change correction is the one referring to the WF triaxial cell. Typical curves of cell volume change vs cell pressure are reported by Head, K.H., in Soil Laboratory Testing, Vol.3, 1986 (Fig. 2.17). The WF11001/SN: is a triaxial cell of an almost cylindrical shape. The internal diameter of the triaxial cell is d cyl int = 168.0mm while its height is h cyl = 352.0mm. Figure 2.18 presents in detail the WF11001/ SN: triaxial cell, the triaxial base plate, the top cap and pedestal of the specimen, as well as the submersible load ram & cell. This will later on allow us to roughly estimate the volume of the above triaxial cell items. Next to the rough calculations of the volume of the triaxial items, in parenthesis, the volume of its item will be given, estimated from the Archimedes principle. Laboratory of Geomaterials 25

26 Figure 2.17: Typical curve of volume change of a triaxial chamber versus cell pressure (Head, K.H., 1986). V cell = V cylinder V base plate V load ram&cell V cylinder = πd 2 cyl h cyl = π = 7803 cm V base plate = πd 2 base plate h base plate = π = 220 cm 3 (2.8) 4 4 where V load ram&cell is the volume of the load ram plus the volume of the submersible load cell (STALC3-50kN-24937). As the load ram & cell may freely slide along the triaxial bush, inside the triaxial cell, the volume of the load ram & cell depends on its vertical position. The minimum volume that the load ram & cell occupies in the triaxial cell, is when it is placed in the upper most position, where the load ram is out of the triaxial cell and the load cell is in contact with the lower part of the triaxial cell bush. Should the piston slide into the triaxial cell, the volume the load ram should also be taken into account. In other words, the volume of the load cell & ram is given by eq. 2.9, = πd 2 load ram 4 V load ram&cell = V load ram + V load cell = h load ram + πd 2 load cell h load cell = 4 = πd 2 load ram h load ram cm 3 (150 cm 3 ) (2.9) 4 where d 2 load ram = 25.1 mm and h load ram is the length of the load ram in the triaxial cell. Laboratory of Geomaterials 26

27 Figure 2.18: Section and side/top view of the WF11001/SN: triaxial cell. Laboratory of Geomaterials 27

28 Suppose that the triaxial cell is filled with de-aired water and there is no specimen housed in the cell. Assume also that the load ram & cell is placed in the upper most part of the triaxial cell (thus only the load cell is submerged into the cell and the load ram is outside the triaxial cell). In this case the volume of water in the triaxial cell is according to eq. 2.8, V w,cell = = 7431 cm 3 (7580 cm 3 ) (2.10) The volume in parenthesis is the volume of water needed to fill the triaxial cell. The difference between the two values lies in the fact that the triaxial cell is not a perfect cylinder of diameter d and height h, while the triaxial base plate has also small openings and pipes where water may enter. For this reason the volume of de-aired water needed to fill the triaxial cell is greater than the rough estimate. The calibration setup, which will allow us to estimate the triaxial cell expansion as a function of the cell pressure, will follow the calibration setup of the two automatic volume change apparatus (described in previous section), but for the fact that the cell pressure line will be closed. In other words, the triaxial cell will be filled with de-aired water, the loading ram will be forced to reach its upper limit, thus only the loading cell will be in the cell at the beginning of the calibration test and the increase of the cell pressure will be monitored from cell pressure line port 1. As the loading ram slides inside the triaxial cell, keeping all cell valves closed, cell water pressure is increased. The total volume change V total of the triaxial cell filled with de-aired water will be equal to the volume of the loading ram entering the cell. By denoting V WF cell the volume change attributed to the triaxial cell expansion and V WF cell water the volume change due to de-aired water inside the triaxial cell, the WF triaxial cell expansion is calculated from eq. 2.11, V total = V W F cell + V W F cell water (2.11) where V total = πd 2 piston h piston 4 A logarithmic-linear law is applied to the experimental data (see Fig. 2.20, Fig. 2.21, Fig. 2.22, Fig. 2.23, Fig and Fig. 2.25), leading to the following analytical expression for the WF triaxial cell expansion due to pressure, V W F cell = c 1 ln( σ c σ c0 ) + c 2 (σ c σ c0 ) + c 3 (2.12) where the values of c 1, c 2, c 3, σ c0 are given in Table 2.3 In the case of specimen s presence in the triaxial cell, eq has to be modified as follows, Laboratory of Geomaterials 28

29 WF11001/SN: triaxial cell expansion, GIO/GeoLab Cell pressure c [kpa] b / Vw=7450 cm^ c / Vw=7450 cm^ a / Vw=7480 cm^ b / Vw=7480 cm^ c / Vw=7160 cm^ d / Vw=7160 cm^ Cell expansion V cell [mm 3 ] Figure 2.19: WF11001/SN: triaxial cell calibration. Cell pressure c [kpa] Experimental data Model curve loading Model curve unloading WF11001/SN: expansion (base plate, load ram, V w =7.450cm 3 ) Loading ram, GIO/GeoLab/ b Cell expansion V cell [mm 3 ] Figure 2.20: WF11001/SN: triaxial cell calibration, b. Laboratory of Geomaterials 29

30 Cell pressure c [kpa] Experimental data Model curve loading Model curve unloading WF11001/SN: expansion (base plate, load ram, V w =7.450cm 3 ) Loading ram, GIO/GeoLab/ c Cell expansion V cell [mm 3 ] Figure 2.21: WF11001/SN: triaxial cell calibration, c. Cell pressure c [kpa] Experimental data Model curve loading Model curve unloading WF11001/SN: expansion (base plate, load ram, V w =7.480cm 3 ) Loading ram, GIO/GeoLab/ a Cell expansion V cell [mm 3 ] Figure 2.22: WF11001/SN: triaxial cell calibration, a. Laboratory of Geomaterials 30

31 Cell pressure c [kpa] Experimental data Model curve loading Model curve unloading WF11001/SN: expansion (base plate, load ram, V w =7.480cm 3 ) Loading ram, GIO/GeoLab/ b Cell expansion V cell [mm 3 ] Figure 2.23: WF11001/SN: triaxial cell calibration, b. Cell pressure c [kpa] WF11001/SN: expansion (base plate, load ram & dummy cylinder, V w =7.160cm 3 ) Loading ram, GIO/GeoLab/ c Experimental data Model curve loading Model curve unloading Cell expansion V cell [mm 3 ] Figure 2.24: WF11001/SN: triaxial cell calibration, c. Laboratory of Geomaterials 31

32 Cell pressure c [kpa] WF11001/SN: expansion (base plate, load ram & dummy cylinder, V w =7.160cm 3 ) Loading ram, GIO/GeoLab/ d Experimental data Model curve loading Model curve unloading Cell expansion V cell [mm 3 ] Figure 2.25: WF11001/SN: triaxial cell calibration, d. Model c 1 c 2 c 3 σ c0 parameters (mm 3 ) (mm 3 /kpa) (mm 3 ) (kpa) b-loading b-unloading c-loading c-unloading a-loading a-unloading b-loading b-unloading c-loading c-unloading d-loading d-unloading Table 2.3: Logarithmic-linear law parameters for WF11001/SN: triaxial cell calibration. Laboratory of Geomaterials 32

33 V total = V W F cell + V W F cell water + V pipe + V specimen (2.13) where V WF cell is calculated according to logarithmic-linear law, V WF cell water is the volume of de-aired water in the cell, V pipe is the volume expansion of the pipes between the cell pressure line of the triaxial cell and the automatic volume apparatus and V specimen is the volume of the specimen. Laboratory of Geomaterials 33

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35 Chapter 3 Specimen volume change corrections During a drained or undrained triaxial compression/extension test, the specimen deforms. Such deformation inevitably leads to a change its geometrical dimensions. The calculation of the axial stress or strain should take into account the deformed configuration of the specimen. 3.1 Specimen section area During a triaxial compression/extension test the cylindrical specimen deforms and the its cross section (perpendicular to the primary axis x 1 ) increases/decreases. Let us assume that the initial cylindrical configuration of the specimen is given by its height h 0 and its diameter d 0. The initial volume of the specimen is given by the eq.3.1 V 0 = πd h 0 (3.1) In the case of undrained triaxial compression/extension, where the volume change of the specimen is zero ( V = 0) and the specimen remains cylindrical, the following expression holds for the initial and final specimen volume, V 0 = V πd 2 4 h = πd h 0 d = d 0 h0 h (3.2) In this case, the area of any section perpendicular to a vertical axis of the specimen will be given by A = πd 2 4 h = A 0 h 0 h (3.3) 35

36 In the case of a drained test, the above expressions can be modified to take into account the change of the volume due to drainage. By denoting the volumetric strain ɛ vol = V/V 0 (positive if water comes out of the specimen, that is compression positive) and ɛ ax = h/h 0, we get: V = V 0 V V V 0 = 1 ɛ v Ah = A 0 h (1 ɛ vol ) A = A 0 1 ɛ vol 1 ɛ ax (3.4) During triaxial compression tests barreling of the specimen may also occur. The specimen ceases to deform as a cylinder and the cross section of the specimen perpendicular to the vertical axis is not constant. This is the case where the friction in the top cap and pedestal is high enough so it does not allow the specimen to freely expand. Barreling may fully or partially appear. In the first case the diameter of the specimen as a function of the vertical distance from the pedestal is given by eq. 3.5 A = π 4 (d 0 + 2a sin πz h )2 (3.5) while for the case of partial barreling eq. 3.6 holds, A = π 4 (d 0 + 2a cos πz 2h )2 (3.6) The volume of the specimen for each of the two above cases is given by integration of eq. 3.5 and 3.6 in respect to the height of the specimen, that is respectively, V = and h 0 Adz = h 0 [ π 4 (d 0 + 2a sin πz h )2] dz = πd 2 0 h + 2ahd 0 + πa2 h (3.7) 4 2 V = h 0 Adz = h 0 [ π 4 (d 0 + 2a cos πz 2h )2] dz = πd 2 0 h + 2ahd 0 + πa2 h (3.8) 4 2 Inserting eq. 3.7 and 3.8 into eq. 3.4 the parameter a can be evaluated and thus the section A of the specimen along the vertical axis is known. 3.2 Membrane penetration effect In the triaxial test on a granular soil a volume change measurement made as a result of an increase in confining pressure will be influenced by the penetration of the membrane enclosing the specimen into the voids between Laboratory of Geomaterials 36

37 Figure 3.1: Specimen section area due to barreling the particles at the interface. This is known as the membrane penetration effect, illustrated in Figure 3.2. It can affect volume change measurements in both the back pressure line and the cell pressure line. The effect has been shown to depend mainly on particle size, and to a much lesser extent on the state of packing (i.e. density) and particle shape, as well as on the membrane thickness and stiffness. It applies to materials of medium sand size and upwards, having a 50% particle size, D 50, exceeding 0.1mm, and is of greatest significance with large diameter specimens. The effect is negligible for fine-grained soils. Newland and Allely (1959) studied the effect using lead shot, and Roscoe, Schofield and Thurairajah (1963) investigated it using Ottawa sand. A graphical method of estimating the effect in sandy silts, based on the 50% size D 50, was given by Frydman, Zeitlen and Alpan (1973). Corrections of the same order of magnitude were derived theoretically by Poulos (1964) using measured elastic properties of membrane material. Most recent investigations were made by Molenkamp and Luger (1981). This correction is unlikely to by significant in routine testing. Baldi and Nova ([1]) investigated theoretically and experimentally the membrane penetration effects in triaxial testing. They found that membrane penetration depends strongly on the diameter of the grain (expressed by d 50 ), the value of the mean effective stress σ 3 and the diameter of the specimen d specimen. According to their analysis, a semiempirical relation (eq. 3.9) allows for a quantitative membrane penetration correction in a typical triaxial test. Laboratory of Geomaterials 37

38 Figure 3.2: Membrane penetration effect (after K.H. Head [6]) V m = d g 2d spec V 0 3 σ 3 d g E m t m (3.9) where V m is the volume reduction of the specimen due to membrane penetration effect, d g is the grain mean diameter, d spec is the diameter of the specimen, V 0 is the volume of the specimen, σ 3 is the lateral effective stress (σ 3 = σ 3 u), E m is the membrane Young modulus and t m is the membrane thickness. In Figure 3.3 the error of the membrane penetration effect to the initial volume of the specimen is calculated for a cylindrical Hostun Sand HS 28 specimen of 100mm in height and diameter placed in a Geotest elastic membrane of 0.025in thickness, while in Figure 3.4 the membrane penetration effect error to the volumetric strain of the specimen in an isotropic consolidation test is given. Laboratory of Geomaterials 38

39 Membrane penetration effect Hostun Sand HS 28, Geotest membranes 0.025in 0,300% Ratio of membrane penetration to initial volume V m /V 0 [-] 0,250% 0,200% 0,150% 0,100% 0,050% 0,000% Lateral effective stress ' 3 [kpa] Figure 3.3: Membrane penetration error in a typical triaxial test 50% Membrane penetration effect error in isotropic consolidation test CD-HS (e o =1.044), Geotest membrane t m =0.025in 45% Error of membrane penetration in isotropic consolidation test [-] 40% 35% 30% 25% 20% 15% 10% 5% 0% Lateral effective stress ' 3 [kpa] Figure 3.4: Membrane penetration error as a function of the volumetric strain in an isotropic consolidation test. Laboratory of Geomaterials 39

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41 Chapter 4 Axial load corrections 4.1 Standard bush The correction to the measured axial force due to friction of the piston in the cell bushing can be allowed for by running the compression machine, with the cell under pressure, at the rate of displacement required for the test, but with the piston not in contact with the specimen top cap. If this is done immediately before starting a compression test and the load ring dial gauge is set to read zero, no further correction will be necessary at that machine speed so long as the lad remains truly axial. If there are no lateral forces, the friction loss for a piston and bush in good condition should be small if oil is inserted at the top of the cell as a lubricant. Bishop and Henkel quoted errors of about 1 3% of the axial force, increasing with axial strain. Tests on 100mm diameter specimens in a cell with a 19mm diameter piston indicated that the correction of about 1% of the axial force should be deducted for every 5% strain. When a specimen fails by slipping along a single plane, lateral forces are introduced which can appreciably increase the bush friction. Under these conditions Bishop and Henkel suggested that the error could rise to about 5% of the axial force. The correction needed would also depend on the axial strain, and a deduction of about 1% of the measured force for every 2% strain from the start of slip seems appropriate. The nominal corrections suggested above are accurate enough for most practical purposes. If the frictional force is likely to exceed about 2% of the measured axial force it is better to measure the force with a device mounted inside the triaxial cell (submerged load cell/ring). In Figures 4.2, 4.3 the normal and shear stress applied on the bush, as well as the friction coefficient µ are given, 41

42 Figure 4.1: The error in axial load measurement due to ram friction: variation with axial strain in a typical test on a 4-in. diameter sample ([3]). 1,60 WF11001/SN: triaxial cell bush friction GeoLab/GIO/ /loading/ =1,76 o 1,40 1,20 y = 0,0308x R 2 = 0,9968 Shear stress [MPa] 1,00 0,80 0,60 0,40 0,20 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.2: WF11001/SN: triaxial cell bush friction, calibration loading Laboratory of Geomaterials 42

43 WF11001/SN: triaxial cell bush friction GeoLab/GIO/ /unloading/ =1,86 o 1,60 1,40 1,20 y = 0,0324x R 2 = 0,9972 Shear stress [MPa] 1,00 0,80 0,60 0,40 0,20 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.3: WF11001/SN: triaxial cell bush friction, calibration unloading 1,50 WF11001/SN: triaxial cell bush 0kPa GeoLab/GIO/ /loading 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.4: WF11001/SN: triaxial cell bush 0kPa, calibration loading Laboratory of Geomaterials 43

44 WF11001/SN: triaxial cell bush 0kPa GeoLab/GIO/ /unloading 1,50 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.5: WF11001/SN: triaxial cell bush 0kPa, calibration unloading 1,50 WF11001/SN: triaxial cell bush 20kPa GeoLab/GIO/ /loading 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.6: WF11001/SN: triaxial cell bush 20kPa, calibration loading Laboratory of Geomaterials 44

45 WF11001/SN: triaxial cell bush 20kPa GeoLab/GIO/ /unloading 1,50 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.7: WF11001/SN: triaxial cell bush 20kPa, calibration unloading 1,50 WF11001/SN: triaxial cell bush 100kPa GeoLab/GIO/ /loading 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.8: WF11001/SN: triaxial cell bush 100kPa, calibration loading Laboratory of Geomaterials 45

46 WF11001/SN: triaxial cell bush 100kPa GeoLab/GIO/ /unloading 1,50 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.9: WF11001/SN: triaxial cell bush 100kPa, calibration unloading 1,50 WF11001/SN: triaxial cell bush 200kPa GeoLab/GIO/ /loading 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.10: WF11001/SN: triaxial cell bush 200kPa, calibration loading Laboratory of Geomaterials 46

47 WF11001/SN: triaxial cell bush 200kPa GeoLab/GIO/ /unloading 1,50 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.11: WF11001/SN: triaxial cell bush 200kPa, calibration unloading 1,50 WF11001/SN: triaxial cell bush 300kPa GeoLab/GIO/ /loading 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.12: WF11001/SN: triaxial cell bush 300kPa, calibration loading Laboratory of Geomaterials 47

48 WF11001/SN: triaxial cell bush 300kPa GeoLab/GIO/ /unloading 1,50 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.13: WF11001/SN: triaxial cell bush 300kPa, calibration unloading 1,50 WF11001/SN: triaxial cell bush 400kPa GeoLab/GIO/ /loading 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.14: WF11001/SN: triaxial cell bush 400kPa, calibration loading Laboratory of Geomaterials 48

49 WF11001/SN: triaxial cell bush 400kPa GeoLab/GIO/ /unloading 1,50 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.15: WF11001/SN: triaxial cell bush 400kPa, calibration unloading 1,50 WF11001/SN: triaxial cell bush 500kPa GeoLab/GIO/ /loading 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.16: WF11001/SN: triaxial cell bush 500kPa, calibration loading Laboratory of Geomaterials 49

50 WF11001/SN: triaxial cell bush 500kPa GeoLab/GIO/ /unloading 1,50 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.17: WF11001/SN: triaxial cell bush 500kPa, calibration unloading 1,50 WF11001/SN: triaxial cell bush 600kPa GeoLab/GIO/ /loading 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.18: WF11001/SN: triaxial cell bush 600kPa, calibration loading Laboratory of Geomaterials 50

51 WF11001/SN: triaxial cell bush 600kPa GeoLab/GIO/ /unloading 1,50 1,25 Shear stress [MPa] 1,00 0,75 0,50 0,25 0,00 0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00 Normal stress [MPa] Figure 4.19: WF11001/SN: triaxial cell bush 600kPa, calibration unloading 4.2 Rotating bush Where the effect of piston is significant, such as with very soft soils and stiff soils that fail along a slip surface, a cell fitted with a rotating bush reduces the friction to a negligible amount, if oil is used in the top of the cell. provided that the piston and the bush are in good condition, the effect of lateral thrust caused by slip-plane failure can be neglected. 4.3 Submersible load cell The effect of friction between piston and cell bush can be eliminated altogether if a submersible force measuring device can be mounted inside the triaxial cell. Electrical devices of this kind, known as submersible load transducers, are now often used in place of externally mounted rings in commercial testing, especially for the use with automatic recording and dataprocessing systems. Laboratory of Geomaterials 51

52 Calibration friction coef. aver. shear stress cell pressure date µ ( 0 ) τ (MPa) mathrmσ c (kpa) (loading) (unloading) (load & unload) (load & unload) (load & unload) (load & unload) (load & unload) (load & unload) (load & unload) (load & unload) Table 4.1: WF11001/SN: triaxial cell bush friction coefficient µ calibration. Figure 4.20: Wykeham Farrance STALC3-50kN triaxial submersible load cell Laboratory of Geomaterials 52

53 Figure 4.21: DBBSE-50kN-A2242 external load cell (Applied Ltd) Laboratory of Geomaterials 53

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55 Chapter 5 Conclusions The main purpose of this short report was to calibrate the WF11001/ SN: triaxial cell in order to be able to measure with fairly good accuracy the volume change of the specimen during a test in the case of partially saturated or dry material, in absence of on-sample transducers. From the above analysis it is clearly stated that in order to measure as precise as possible the volume change of a specimen through the cell pressure line with an automatic volume change-like apparatus, four main aspects have to be taken into account: The triaxial cell, nylon flexible pipes and volume change apparatus are flushed with de-aired water. The volume of de-aired water inside the cell is well-known. The nylon flexible pipes used to connect the triaxial cell with the automatic volume change apparatus and the pressure pump are properly calibrated. The initial position and movement of the load ram during the test is monitored. The method of measuring the volume change of a specimen indirectly inserts by default many errors, which most of the times can not be traced down. For this reason, in cases when other methods of measuring the volume change of the specimen are available (optical ones), a first preliminary comparison of the results would avoid possible hidden errors. 55

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57 Bibliography [1] Baldi, G. and Nova, R. (1984). Membrane Penetration Effects in Triaxial Testing, ASCE, Journal of Geotechnical engineering, Vol. 110, No.3, Paper No [2] Bardet, J.P. (1997). Experimental Soil Mechanics, Prentice Hall, pp.582. [3] Bishop, A.W. and Henkel, D.J. (1957). The Measurment of Soil Properties in the Triaxial test, 2nd ed., Edward Arnold, London, pp.228. [4] Frydman, S., Zeitlen, J.G., and Alpan, I. (1973). The membrane effects in triaxial testing of granular soils. Journal of Testing and Evaluation, ASTM, Vol.1, pp [5] Georgopoulos, I.O. and Vardoulakis, I. (2005). The Handbook of Wykeham Farrance GeoTriax, internal laboratory report, pp.296. [6] Head K.H. (1992). Manual of soil laboratory testing, Volume 3: Effective stress tests, second edition, John Wiley & Sons, New York, pp.428. [7] Newland, P.L. and Allely, B.H. (1959). Volume changes in drained triaxial tests on granular materials. Géotechnique, Vol.9, pp [8] Steinbach, J. (1967). Volume change due to membrane penetration in triaxial tests on granular materials. Thesis presented to Cornell University, at Ithaca, in 1967, in partial fullfillment of the requirements for the degree of Master of Science. 57