The Use of Miniature Soil Stress Measuring Cells in Laboratory Applications Involving Stress Reversals

SOILS AND FOUNDATIONS Japanese Geotechnical Society

Vol. 49, No. 5, 675–688, Oct. 2009

THE USE OF MINIATURE SOIL STRESS MEASURING CELLS IN LABORATORY APPLICATIONS INVOLVING STRESS REVERSALS BITANG ZHUi), RICHARD J. JARDINEii) and PIERRE FORAYiii) ABSTRACT This paper describes the potential use of miniature soil stress measuring cells in model pile tests where normal stresses up to several MPa may be expected, accompanied by unloading and multiple substantial stress reversals. Devices rated in the 0.5 to 7 MPa range are considered and it is shown that they can develop marked cell-action eŠects, including strong non-linearity and hysteresis. A new approach to cell calibration and characteristic modelling is presented. It is shown that measurement errors may only be kept within tolerable limits through complex calibrations involving cells with suitable boundary conditions combined with a multi-stage loading history dependent, data reduction procedure. Key words: calibration, cell action eŠect, curve ˆtting, hysteresis, miniature soil stress cell, non-linearity, pile installation, sand, soil stress, stress reversal (IGC: E4) ing the stress conditions applying in the sand mass under: K0 conditions prior to pile installation, with sº200 kPa The maximum stages of pile installation, when sÀ5 MPa can be expected close to the pile The subsequent steep s reductions expected as the pile tip advances past a given instrument level Further s changes that might take place during insitu ageing over a period of months Pile loading with static and cyclic conditions. Commercially available miniature strain-gauged diaphragm cells were selected that are located carefully within the test sand mass as it is built up by air pluviation. The devices evaluated herein are summarized in Table 1 where they are identiˆed by a code comprising the manufacturer, cell type, rated capacity and number code, such as TML PDA-3 MPa-6048 (where TML signiˆes Tokyo Sokki Kenkyujo Co.) and Kyowa PS/D-7 MPa-0002 (indicates produced by the Kyowa Electronic Instruments Co.). The following sections describe the interactions that take place between such cells and the soil mass within which they operate. A simple approach for calibrating the gauges is set out that addresses the requirements of the authors' pile experiments. It is shown that a nonlinear, load-history dependent, mathematical model is required for strain gauged diaphragm cells of the type considered to capture their key characteristics and reduce potentially large measurement errors to possibly accepta-

INTRODUCTION This paper describes an investigation into the potential use of miniature strain gauged diaphragm cells to measure total soil normal stresses [s] in model pile tests. The work was carried out as part of a laboratory calibration chamber study by Imperial College London and INPG Grenoble of displacement pile installation, ageing and cyclic loading processes. Field research by Chow (1997), Chow et al. (1998) and Jardine et al. (2006) has established that the behaviour of piles driven in sand during installation, ageing in-situ and cyclic loading is inter-related. A new programme of research is being performed in calibration chamber experiments conducted at the Laboratoire 3S-R at INPG Grenoble to understand the physical processes more fully by establishing the ˆelds of radial, circumferential and vertical stresses developed within the sand mass during all stages of a displacement pile's history. Jardine et al. (2009) describe the general approach taken and the development of new mini-ICP instrument systems that are deployed on the test piles, while Foray et al. (2009) give more details of the calibration chamber equipment and test arrangements. Stresses are being measured in the sand mass with small diaphragm cells at up to 40 locations in the calibration chamber, at radial distances of 1 to 10 pile diameters from the test pile axis. We focus in this paper on the steps taken to minimize their measurement errors when followi)

ii)

iii)

Lecturer, Department of Geotechnical Engineering, Tongji University, China (btangzh＠tongji.edu.cn) (formerly Postdoctoral Researcher, Imperial College London, UK). Professor, Department of Civil and Environmental Engineering, South Kensington Campus, Imperial College London, London, UK (r.jardine＠imperial.ac.uk). Professor, Laboratoire Sols, Solides, Structures-Risques, Domaine Universitaire Grenoble, France (Pierre.Foray＠hmg.inpg.fr). The manuscript for this paper was received for review on September 1, 2008; approved on July 27, 2009. Written discussions on this paper should be submitted before May 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month. 675

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676

ble levels. Parallel work is progressing to consider the fundamental particulate mechanics that leads to the observed responses.

displacement piles in dense sand. The main topic of this paper is the measures required to cope with the non-linear responses to the loading paths expected in the authors' model experiment conditions.

BACKGROUND Field soil stress measurements have been made with dams, foundations, underground structures and retaining walls (DunnicliŠ, 1988). Fluid ˆlled hydraulic cells (equipped with pressure transducers) are widely used in both ˆlls and in pushed-in installations. Consideration has to be given to both the stress perturbations caused by cell installation and the subsequent `cell action'. The latter is a consequence of diŠerences between the eŠective stiŠnesses of the stress cell and the soil mass; Bond et al. (1991), Clayton and Bica (1993). If not accounted for, cell action can seriously aŠect the reliability and accuracy of the soil-stress measurements. Weiler and Kulhawy (1982) and DunnicliŠ (1988) reviewed and characterised the factors that in‰uence cell action including: aspect ratio (cell diameter-to-thickness ratio); diaphragm de‰ection; sensing area ratio (sensing area to cell total area); cell orientation; soil behaviour; eccentric or non-uniform loads; lateral stress rotation; lateral stress cross-sensitivity; proximity of other cells or structures, dynamic loading as well as environmental conditions (moisture and temperature). They conclude that calibration with the appropriate soil and ˆeld loading conditions is essential. Theoretical analyses of cell action are sensitive to the constitutive behaviour of the host soil mass. It is common to treat the soil as a simple elastic continuum, which leads to a ˆxed ratio between the measured stress, sm, and the true stress, s, developed in the ground (Ingram, 1965). The latter can only be deˆned under calibration conditions where the applied loads are closely controlled and the ideal `undisturbed' distribution of stresses can be estimated reliably within the soil mass. Unless the strains are kept to very low levels around any embedded sensor, the behaviour of the surrounding soil is likely to be highly non-linear, making cell action potentially strongly hysteretic, pressure dependent and sensitive to loading history. Little has been published on nonlinear stress-sensor behaviour under pressure ranges and load reversals/cycles such as those anticipated around

Fig. 1.

CELL CONSTRUCTION

Cells' Properties and Dimensions The miniature diaphragm type strain-gauged cells are shown schematically in Fig. 1, where sm and s respectively are the measured normal stress, and the ideal soil normal stress that would be expected within the soil mass if no gauge was present. Es and ns represent the simplest possible elastic soil model, describing the nominal Young's modulus and Poisson's ratio; dc and tc are the overall diameter and thickness of the cell. A typical ‰at, disk-shaped diaphragm cell is shown in Fig. 1(b). The sensing face incorporates a thin circular metal diaphragm that is restrained by an outer stiŠ ring and has strain gauges mounted on its underside to sense de‰ection under load. The ring supports the diaphragm and isolates it from edge-stress concentrations (Monfore, 1950; Tory and Sparrow, 1967; DunnicliŠ, 1988). The diaphragms are made of beryllium copper with a Young's modulus of around 1.23×108 kPa and Poisson's ratio of about 0.3. The dimensions of the cells and diaphragms are summarized in Table 1, where d and t are the diameter and thickness of the diaphragm, respectively. Four strain gauges are mounted, as shown in Fig. 2. The central pair act in tension and the outer two in compression, allowing the fully active Wheatstone bridge shown in Fig. 3, which oŠers better temperature compensation and sensitivity. The electrical leads exit from the side of the TML PDA cells and at the back of the TML PDB and Kyowa PS/D cells (relative to the sensing face) through a small protuberance. Weiler and Kulhawy (1982) and DunnicliŠ (1988)'s recommendations for minimizing stress measurement errors can be summarised as: (1) Cell aspect ratio, dc/tcÀ5. (2) Diaphragm diameter-to-de‰ection ratio, d/dÀ 2000–5000, where d is the average de‰ection of a thin, circular, rigidly clamped elastic plate (Timoshenko and Woinowsky-Krieger, 1959):

Schematic of soil stress cell in a free ˆeld: (a) installation arrangement and (b) diaphragm cells

THE USE OF MINIATURE SOIL Table 1. Capacity (MPa)

Quantity

TML PDA-500 kPa

0.5

TML PDA-1 MPa

Cell Type

1

677

Characteristics of miniature soil stress cells Cell size

Diaphragm

d 2/d 2c

dc (mm)

tc (mm)

d c / tc

d (mm)

t (mm)

d/d1

1

6.5

1

6.5

5.6

0.14

676

0.74

1

11

6.5

1

6.5

5.6

0.2

985

0.74

TML PDA-3 MPa

3

7

6.5

1.4

4.64

5.6

0.33

1475

0.74

TML PDB-500 kPa

0.5

2

6.5

1

6.5

5.6

0.14

676

0.74

TML PDB-1 MPa

1

4

6.5

1

6.5

5.6

0.2

985

0.74

TML PDB-3 MPa

3

7

6.5

1.4

4.64

5.6

0.33

1475

0.74

Kyowa PS/D-7 MPa

7

12

6

0.6±0.1

10

5.0

0.3

66.7

0.69

Schematic

d is the average de‰ection corresponding to the rated capacity

F＝

Esd 3 Edt 3

(2)

Considering the devices listed in Table 1, the ratios of the diaphragm and mean soil particle diameters exceed 23 in all cases. The aspect ratios, dc/tc also either exceed or fall only marginally below the recommended limit of 5. However, the diaphragm diameter-to-de‰ection ratios (d/d＝67¿1475) and the sensing area ratios (d 2/d 2c＝0.69 or 0.74) fall far short of the above recommendations, suggesting that signiˆcant cell action errors can be expected for these gauges when working at their rated stresses. Fig. 2.

Typical strain gauge arrangement

Gauge Conˆguration and Nominal Calibration Results The manufacturers' speciˆcations are summarised in Table 2, including calibration factors from ‰uid pressure tests. These nominal calibration factors, CFn represents the ``intrinsic'' design stiŠnesses. Air pressure tests by the Authors conˆrmed general conformance to speciˆcation. CALIBRATION IN SAND

Fig. 3.

Strain gauge electrical circuit

d＝

qd 4(1－n2d ) 160Edt 3

(1)

where q＝the uniformly distributed load; Ed and nd are the Young's modulus and Poisson's ratio of the diaphragm material. (3) Sensing area ratio, d 2/d 2cº0.25–0.45. (4) The ‰exibility factor of soil to cell, Fº0.5, deˆned by Tory and Sparrow (1967) as

Calibration Requirements The electrical sensitivity S of pressure cells is generally deˆned as the linear slope of the relative output (expressed Vout/Vin, where Vout and Vin are the output and input voltages, respectively) against pressure and is expressed as mV/V per kPa. Linear calibration factors, CF, are equal to 1/S (giving kPa per mV/V). Any signiˆcant soil cell action eŠects preclude adopting these simple linear approaches. In severe cases, complex models, involving multiple coe‹cients may be necessary. The calibration systems needed to develop such relationships must: 1. Employ the same soil, initial state and stresses as the prototype. 2. Match the anticipated loading history.

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Table 2.

Speciˆcations of miniature soil stress cells

Type

PDA/B-500 kPa

PDA/B-1 MPa

PDA/B-3 MPa

PS/D-7 MPa

Capacity

0.5 MPa

1 MPa

3 MPa

7 MPa

Rated output Calibration factor Non-linearity Hysteresis Temperature eŠect on zero Temperature eŠect on span Compensated temperature range Temperature range Input/output resistance Recommended exciting voltage Allowable exciting voltage 1

－6

1 mV/V (2000×10－ 6 strain) 8.343 kPa per mV/V 1z RO 1z RO 0.2z RO/9C 0.2z/9C 0¿509C －20¿＋709 C 350 Q 1¿2 V AC or DC Less than 3 V AC or DC

1 mV/V (2000×10 strain) Dependence on each cell 1z RO1 1z RO 1z RO/9C 1z/9C －10¿609 C －20¿＋709 C 350 Q Less than 2 V AC or DC 5 V AC or DC

RO＝the rated output

Table 3.

Mineralogy and index properties of Fontainebleau sand

Coe‹cient of Grain SiO2 Speciˆc d10 d50 d60 non-uniformity emax emin (mm) (mm) (mm) angularity (z) gravity Uc ( G s) Sub-angular 99.7

Fig. 4.

2.65

0.15 0.21 0.23

1.53

0.90 0.51

Stress cell calibration arrangement

3. Apply a stress ˆeld that would lead, in the absence of any sensor, to a soil normal stress s at the sensor position that can be estimated with reasonable accuracy. In practical terms the calibration system must employ boundary conditions that minimise stress non-uniformity and uncertainty in the region where the sensor is to be placed. It is recognised that the local stress ˆeld is inevitably modiˆed by local cell-action within a certain `zone of in‰uence' when the gauge is present. The Authors' calibrations were performed in the `tall oedometer' arrangement shown in Fig. 4. In order to minimize side friction, the inside cylinder wall was lubricated with silicone grease and a latex membrane, which was ˆxed to the base pedestal with an O-ring. Trial tests indicated that wall friction was eŠectively eliminated over the 90 mm thickness positioned above the stress cell, while friction developed below this level should not have any eŠect on the calibrations. The axial load was exerted through a computer-controlled electro-pneumatic valve

Fig. 5.

Gradation curve of NE34 Fontainebleau sand

and Bellofram cylinder acting onto a rigid platen. As described later, reference to linear and non-linear theoretical analyses indicated the degree of sand cover that would be required to ensure acceptably uniform stress conditions at the location; checks were made by calibration runs involving a range of embedded depths. The pressure control system was calibrated by means of a high quality load cell that had itself been dead-weight calibrated up to 18.7 kN. The maximum vertical soil stress developed at the sensor location was just under 3 MPa. The laboratory was temperature controlled to run at 219 C.

Sand Properties As the pile tests, the calibration tests involve NE34 Fontainebleau sand, a well known ˆne to medium sized test sand. As indicated in Table 3 and Fig. 5, it is uniform, subangular and composed of pure (99.7z) sili-

THE USE OF MINIATURE SOIL

ca. The peak and critical state friction angles of the sand with a relative density of 72z respectively were 35.29and , measured from direct shear tests under normal 32.89 stress ranging from 50 to 500 kPa.

Test Procedures and Program Exploratory tests led to a four-step procedure: (1) Connect the cell to the signal conditioning, including a high noise-rejection 16 bit data logger. (2) Fill the `oedometer' with eight 25 mm layers up to the desired stress-cell level. Tamp to achieve the mass density (1.64 kg/m3) and relative density (about 72z) as the pile tests. (3) Gently place the cell with a horizontal orientation (to measure vertical load) at the centre of the cylinder, providing an all round radial clearance of about 7dc. Continue to ˆll the sand in the same manner up to the required ˆnal level, running the cell lead wires along the inner wall of the cylinder and out from the annular gap between the loading platen and the cylinder. (4) Apply air pressure changes under automatic control to increase or decrease the vertical stress, adopting a rate of 117 kPa/min (for the 0.5 and 1 MPa capacity stress-cells) or 234 kPa/min for the 3 and 7 MPa cells. The applied pressure, stress cell output, input voltages and elapsed times were registered every two seconds, leading to one read-

Fig. 6.

679

ing per 3.9 to 7.8 kPa of soil stress change, depending on cell capacity. The main calibration series' involved 4 `two minute hold' points at the maximum or minimum pressure involved in each loading or unloading test for the 0.5 and 1 MPa cells, with 6 similar `hold' points being allowed for the 3 and 7 MPa cells. Five diŠerent Types of calibrations were conducted as outlined in Fig. 6 to give the 52 individual calibrations detailed in Table 4. The preliminary Type 1 tests involved a single load-unload cycle; multiple loading, unloading and reloading stages were applied in the Type 2 to 5 tests to match the objectives listed in Table 4.

EŠect of Embedment Depth Three factors aŠect the burial depth required to achieve reliable calibrations. Firstly non-uniform stresses are known to develop in test specimens beneath rigid loading platens. Bishop and Henkel's (1962) analyses of triaxial tests suggest that vertical stresses remain non-uniform across the sample down to depths of around 2/3 of the loading platen diameter, or 50 mm in this case. Secondly, a su‹cient depth is required to encompass fully the zone where stresses are aŠected by cell-action; Selig (1980). Non-linear analyses of rigid pad foundations (Jardine et al., 1986) suggest that an additional all-round thickness of at least ˆve sensor diameters (or around 35 mm) will be required, giving an overall depth to sensor requirement

Loading schemes of calibration tests: (a) for Type 2 and 3, (b) for Type 4 and (c) for Type 5

Table 4. Test type

Cell's code

Sand cover (mm)

Load scheme

1

PDA-3MPa-6048

25, 75, 90, 120

Testing program Features

Objective

0ªmaximumª0

DiŠerent burial depths for one cell

EŠect of burial depth EŠect of stress reversals, nonlinearity and hysteresis behaviours EŠect of sand density EŠect of the stress location (on or below the loading branch) from which unloading starts EŠect of the maximum prior stress on reloading

2

All 44 cells

90

See Fig. 6(a)

A series of load-unload-reload and unload-reload-unload process

3

PDB-3MPa-6019

90

See Fig. 6(a)

4

PDA-3MPa-6046

90

See Fig. 6(b)

5

PDA-0.5MPa-6307

90

See Fig. 6(c)

DiŠerent sand densities for one cell After the maximum stress, reload from diŠerent stresses to the same stress of 2345 kPa and then unload Reload from the same stress with diŠerent maximum prior stresses

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680

À85 mm. Finally, even the minimized friction developed on the `lubricated oedometer' walls induce ˆnite vertical stress `losses' that increase with soil cover depth, so the sensor should be placed no deeper than is necessary to achieve good stress uniformity. Trials were run to establish the optimum depth with a TML PDA-3MPA gauge (No. 6048) positioned, in successive tests, at depths of 25 mm, 75 mm, 90 mm and 120 mm. Figure 7 indicates the resulting calibration relationships. While the characteristics are strongly hysteretic, the (upper) loading branches of the tests indicated practically linear relationships, with apparently almost constant calibration factors CFm for loading at each depth. The factor found with 25 mm cover fell 40z below the other loading curves, showing that greater cover was required to achieve stress uniformity. However, there was relatively little diŠerence between the 70 mm depth test and the two deeper cover cases, which gave practically the same loading results. A standard depth of 90 mm (or 13.8 dc) was adopted for all further tests as being su‹ciently

Fig. 8.

deep to both eliminate loading platen eŠects and allow cell action to develop fully without inviting excessive wall friction losses.

Fig. 7.

EŠect of embedment depth on calibration results

Typical responses of cells with various rated capacities: (a) 0.5 MPa cells, (b) 1 MPa cells, (c) 3 MPa cells and (d) 7 MPa cells

THE USE OF MINIATURE SOIL Table 5.

Typical ˆtting errors for each cell type during ˆrst loading, unloading and reloading stages TML PDA type

Cell type

Loading (L) Unloading (U) Reloading (R)

681

Error (kPa) z RO (z) Error (kPa) z RO (z) Error (kPa) z RO (z)

TML PDB type

Kyowa PS/D-7 MPa

0.5 MPa

1 MPa

3 MPa

0.5 MPa

1 MPa

3 MPa

－7 ¿ 7 －1.4¿1.4 －37¿7 －7.4¿1.4 －31¿11 －6.3¿2.1

－18¿9 －1.8¿0.9 －28¿45 －2.8¿4.5 －24¿15 －2.4¿1.5

－25¿41 －0.8¿1.4 －18¿31 －0.6¿1.0 －66¿31 －2.2¿1.0

－10¿6 －1.9¿1.2 －14¿27 －2.8¿5.3 －14¿12 －2.8¿2.3

－15¿11 －1.5¿1.1 －56¿11 －5.6¿1.1 －23¿15 －2.3¿1.5

－34¿35 －1.0¿1.1 －21¿51 －0.7¿1.7 －22¿22 －0.7¿0.7

Cells' Behaviour Associated with Stress Reversals (Test Type 2) Calibrations were performed with all 44 cells following the scheme shown in Fig. 6(a). The `loading-branch' of the calibration involved a series of four-to-six (depending on the sensor's rated capacity) full load-unload cycles with peak loads that gradually ascended up to the appropriate maximum for the particular cell. These cycles deˆned the cells' `ˆrst' loading (L), full unloading (U) and reloading (R) characteristics. The following `unloading branch' started from the maximum calibration load and involved a similar number of partial unloadingreloading-unloading cycles, each involving a gradually descending peak load. These tests were designed to match the load cycling characteristics expected with the model pile experiments, matching the most severe loading cycles developed by the discrete jack strokes applied to install the pile, with the tip ˆrst descending towards the instrument level (the loading branch) and then passing by it (the unloading branch). Although the number of pile jack strokes exceeds the number of calibration cycles applied, the general features of the stress history imposed by pile installation are well captured by this procedure. Cells of the same design generally exhibited similar responses, and typical examples are presented in Fig. 8. The features to note include: (1) The ˆrst `fresh' loading (L) responses, as typiˆed by the envelope to the segments from L1¿L4 in Figs. 8(a) and (b) or L1¿L6 in Figs. 8(c) and (d) show a nearly linear response for the 3 and 7 MPa devices, while the 0.5 and 1 MPa cells showed slight curvature. (2) The unloading (U) traces showed clear hysteresis. The relatively widths of the hysteresis loops correlate inversely with the stress-cells' rated capacities. Indeed, the outputs from the 0.5 and 1 MPa cells failed to close completely, remaining signiˆcantly above their initial `zero' values after full unloading. The 3 and 7 MPa cells gave better characteristics and almost recovered their initial `zero' readings, regardless of the manufacturer or cell type. (3) The hysteresis may be attributed to both arching eŠects and variations between the non-linear and pressure dependent soil stiŠnesses developed under `virgin' loading and unloading. (4) Reloading (R) stages applied to the 0.5 and 1 MPa cells led to output characteristics that lay between

－25¿28 －0.4¿0.4 －17¿55 －0.2¿0.8 －40¿20 －0.6¿0.3

the loading and unloading curves, and re-joined the `virgin' loading curve once the previous maximum load had been exceeded. Reloading tests on the 3 and 7 MPa cells gave curves that nearly rejoined the `virgin' loading curve at an earlier stage of reloading.

The Loading (L) Response The ˆrst `fresh' loading curves provide constant `backbone' curves that can be described by a single set of calibration coe‹cients for each device. For accurate stress reduction, a power law function is appropriate: s＝a(Vout/Vin)b

(3)

where a and b are the ˆtting parameters. For simplicity the output ratio Vout/Vin is denoted as V hereafter. Typical ˆtting errors for each type of cell are outlined in Table 5 and fall systematically with cell capacity from around 2 z of Rated Output (RO) for the 0.5 MPa cells with nonlinear ˆtting (and 6z with the linear approximation) down to just 0.4z RO when either approach is applied to the 7 MPa cells. The errors were largest over (i) the curved low-load portions of the curves and (ii) the sections of subsequent loading segments (L1 to L6) that apply just after rejoining the `virgin' loading curves. Noting that b＝1 indicates a linear response, the full range reported is 0.961ÃbÃ1.342 and linear approximations s＝A＋CFmV can be made1, especially for the higher capacity cells, that are useful for evaluation of cell action eŠect. Irrespective of the cell supplier and type, the CFm values correlate closely with cell capacity, or the nominal calibration factor, CFn as shown in Fig. 9(a). The 7 MPa cells show some scatter because two diŠerent designs were considered that employed diŠerent strain gauges and cable lengths. The ratio, CFm/CFn indicates the degree of cell action applying to ˆrst-time `fresh' loading and this is plotted against CFn and gauge capacity for all cells in Fig. 9(b). Cell action leads to a large stress `under-registration' of 60 to 70z with the softest low capacity (0.5 MPa) gauges, which falls systematically as cell capacity (and stiŠness) rises to give an under-registration of around 10z with the 7 MPa devices. The experimentally established decay of CFm/CFn with CFn is similar in form to 1

Noting that in this case the ˆtting coe‹cient A results only from the system ’s divergence from ideal linearity over the stress range of interest: A would be zero for a perfectly linear instrument.

ZHU ET AL.

682

Fig. 9.

Relationship of CFm with CFn: (a) CFm versus CFn and (b) CFm/CFn versus CFn

Fig. 10. Typical normalized unloading data of cells with various rated capacities: (a) 0.5 MPa cells, (b) 1 MPa cells, (c) 3 MPa cells and (d) 7 MPa cells

that predicted in elastic solutions (e.g., Tory and Sparrow, 1967): the greater the cell stiŠness, the weaker is the cell action.

The Unloading (U) Response The unloading characteristics all depended on prior loading history. However, the unloading curves could be collapsed into a narrow band by dividing each stress point considered by the maximum prior loading stress.

The normalized characteristics found for each cell type are illustrated in Fig. 10, where it can be seen that the procedure was most successful with the higher capacity (3 and 7 MPa) devices. Good ˆts were obtained for all normalized unloading data of each cell by applying the following family of exponential functions:

s/smax＝y0＋A1e (V/V

－ x0)/t1

max

＋ A 2e ( V/V

－ x0)/t2

max

(4)

Where s and smax are the current and maximum prior

THE USE OF MINIATURE SOIL Table 6.

Absolute Error (kPa) z RO (z)

Fig. 11.

Potential maximum errors of general load conditions during unloading TML PDA type

Cell type

683

TML PDB type

Kyowa PS/D-7 MPa

0.5 MPa

1 MPa

3 MPa

0.5 MPa

1 MPa

3 MPa

±15.2 ±3.04

±36.1 ±3.61

±46.5 ±2.59

±28.3 ±5.66

±29.8 ±2.98

±49.2 ±1.64

±36.5 ±0.52

Typical normalized reloading data of each type of cell: (a) 0.5 MPa cells, (b) 1 MPa cells, (c) 3 MPa cells and (d) 7 MPa cells

stresses and V and Vmax are the electrical signals corresponding to s and smax cases respectively. Note that six calibration coe‹cients are required: y0, x0, A1, t1, A2 and t2 for each unloading branch and thus 24 coe‹cients for 0.5/1 MPa cells and 36 coe‹cients for 3/7 MPa cells. Considering as an example cell TML PDA-0.5 MPa-6307 unloading from smax＝117.2 kPa, the coe‹cients are y0＝ －0.614, x0＝－0.073, A1＝0.423, t1＝1.325, A2＝0.001 and t2＝0.165. To save space the full sets are not presented here for all 44 cells. The ˆtting errors found for each cell type are summarised in Table 5. As with the loading branches, the errors were far smaller (in proportion to RO) for the higher capacity cells. The families of 4 to 6 unloading curves ˆtted from each sensor's calibration data lead to diŠerent degrees of error under more general conditions, when unloading could start from a maximum stress that falls between the values

imposed during calibration. The potential errors are greatest for paths that fall midway between the calibration data sets, and can be evaluated by comparing predictions made for such intermediate positions by (i) the curve ˆtted to the next data set above and (ii) the curve ˆtted to the data set below. Table 6 gives the potential maximum errors evaluated by this approach. As before, the errors reduce as the sensor capacity increases.

The Reloading (R) Response The full reloading stages (R1, R2, R3 and R4) applied to the 0.5 and 1 MPa cells, starting from around 0 kPa, led to a family of curves that were nearly parallel to each other, and steeper than their respective ˆrst loading curves (L1, L2, L3 and L4), only joining the latter as the loads approached the prior maximum. However, the high capacity devices (3 and 7 MPa), generated reloading curves that practically overlapped the ˆrst `virgin' load-

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ing characteristic. Reloading from stress levels other than zero was examined by the Type 5 calibrations described later. As shown in Fig. 6(a), the unloading branches of the Type 2 calibrations involved partial unload-reload cycles of similar magnitude but with gradually falling starting loads. Figure 11 shows the typical normalized reloading data of each cell type in the unloading branch, although the ˆnal reloading data in the loading branch are also shown in the ˆgures. The main features are: (1) Stepwise unloading from the maximum load gave practically the same curve as the full unloading (U) cycle of the `loading branch' calibration, as shown in Fig. 8. Curve U can be viewed as a `backbone' for all parts of the unloading-reloading-unloading response since the prior maximum had been applied. Equation (4) was adopted to ˆt this `unloading backbone curve, with the ˆtting procedures described above. (2) The partial reload-unload loops imposed during the `unloading branch' calibrations led to narrow, almost linear, closed loops, especially for the cycles starting at higher stress levels. The slopes of these near linear sections changed systematically with the starting stress level. The simple normalized relationship given in Eq. (5) was found to give appropriate ˆts.

s＝smin＋Sr(V－Vmin)smax/Vmax

(5)

where smax and smin are the maximum prior stress and the minimum stress since the application of smax; Vmax and Vmin are the electrical signals corresponding to the smax and smin, respectively; Sr＝the slope of the linear ˆtting for the normalised reloading data corresponding to the smin. The corresponding error assessment is also tabulated in Table 5. The absolute errors are generally in the same range, although the higher capacity cells oŠer lower errors as a fraction of their Rated

Output (RO). For the general case where reloading curve starts from a level smin between those of the four or six reloading branches, the slope, Sr can be approximated by ˆtting the known values of Sr using a polynomial function

Sr＝C1(smin/Pa)3＋C2(smin/Pa)2 ＋C3(smin/Pa)＋C4

(6)

where C1, C2, C3 and C4 are ˆtting parameters for each device and Pa＝atmosphere pressure.

EŠect of Sand Density (Type 3 Test) Type 3 calibrations were undertaken to assess how sand state at placement aŠects cell-action. Data from the loading branch of the Fig. 6(a) scheme are presented in Fig. 12 considering a TML PDB-3 MPa device which was installed ˆrst in the standard dense sand (1.64 g/cm3, Dr＝ 72.1z), and then again in the same sand placed with 1.48 g/cm3, Dr＝28.1z. The resulting `virgin' near linear loading curves are shown in Fig. 12(a) where the slope (CFm) for the loose sand test fell about 8.6z below the standard case. The normalized unloading curves were almost insensitive to the sand's initial state, as shown in Fig. 12(b). It is clearly important to match the test sand states during calibrations, but small variations should not impact too greatly on the results obtained. EŠect of Minimum and Maximum Stress Locations on Unloading and Reloading The Type 4 and Type 5 calibrations aimed to extend the `unloading branch' investigations included in the Type 2 scheme and investigate more general unload-reloading behaviour. The Type 4 calibrations applied the scheme illustrated in Fig. 6(b), where the system was reloaded back to a constant maximum level (2345 kPa) from ˆve gradually falling `unloading branch' start points: 1876, 1403, 935, 460 and 224 kPa respectively.

Fig. 12. Calibration curves for TML PDB-3 MPa-6019 in dense and loose sands in Type 3 tests: (a) unique loading curve and (b) normalized unloading curves; maximum stresses from which unloading took place are annotated in the legend

THE USE OF MINIATURE SOIL

The results obtained with TML PDA-3 MPa-6046 in the standard set-up are shown in Fig. 13, where the `virgin' loading (L) and full unloading (U) curves are represented by the ˆnal (R5, L6 and U5, U6) stages of the `loading branch' stage of the Type 4 sequence outlined in Fig. 6(b), with which they were coincident. As in earlier calibrations the L and U curves deˆned backbone limits to the possible outputs. The ˆrst three reloading stages gave responses that were broadly similar to those seen in the (relatively small loops) applied in the Type 2 calibrations and could be ˆtted using the linear function (Eq. (5)) outlined above. However, the latter two cases with larger loops, in which the reloading rejoined the `virgin' loading branch prior to unloading, had clearly non-linear unloading stages that migrated towards the full unloading curve U; the reloading stages branches were approximately linear and could be using Eq. (5). Type 5 calibrations investigated further aspects of the reloading response. As outlined in Fig. 6(c), these tests checked the consequences of applying diŠerent levels of

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maximum pre-load. Figure 14 shows the response of TML PDA-0.5 MPa-6307, set up with the standard sand, which was loaded ˆrst to 352 kPa, and then subjected to three unloading stages, each of 117 kPa magnitude, that reduced down to zero loads. The system was then reloaded to 469 kPa and subjected to four further similar unload-reload loops, three of which started from the same minimum stress levels. As can be seen in Fig. 14, and proven by closer analysis, the reloading curve slopes depend principally on the minimum (starting) stresses and are practically independent of the maximum stress applied. This implies that the slope of any reloading curve can be modelled adequately by applying reloading relationships derived from tests with diŠerent maximum prior stresses; the key is matching the reloading stress.

Stress Calculation Involving Stress Reversals The observations made from the Type 2, 4 and 5 calibrations led to the following three rules relating the current stress, s, (that would be acting in the soil if the gauge was absent) to the cell's output V. The approach accounts for the maximum prior stress smax that has been applied since the sand-cell system has been set up and the minimum stress smin since the application of smax, and the corresponding outputs Vmax and Vmin. (1) If VÆVmax, Eq. (3) is used to calculate the stresses; (2) If VÃVmin, the `full' unloading Eq. (4) s＝( y0＋ A1e (V/V －x )/t ＋A2e (V/V －x )/t )smax is applied where y0, x0, A1, t1, A2 and t2 are the calibration coe‹cients corresponding to the normalized unloading deˆned by the maximum stress smax; (3) If VminºVºVmax, there are two cases, i.e., reloading and unloading, which are deˆned according to the sign of the rate dV/dt. For reloading, the stress is taken as the minimum of Eqs. (3) and (5). For unloading, Eq. (5) is applied unless unloading continues from a point already existing on the L curve, max

Fig. 13.

Calibration curves for TML PDA-3 MPa-6046 in Type 4 test

Fig. 14.

0

1

max

0

2

Calibration curves for TML PDA-0.5 MPa-6307 in Type 5 test: (a) overall response and (b) local reloading curves

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in which case Eq. (4) applies. The above test procedures and modelling rules oŠer a practical approach for improving the reliability of stress measurements in sands that were applied successfully to seven diŠerent diaphragm stress sensor models. It is suggested that the approach may be applied generally in cases where loading, un-loading and re-loading stress measurements need to be taken. The coe‹cients ˆtted to Eqs. (3) to (6) will inevitably vary with sensor type, test sand and initial placement density but their general forms should remain applicable. While the approach outlined allows the degree of measurement error to be both quantiˆed and minimized, but the potential uncertainty in measurement is best reduced by adopting stiŠ, high capacity, devices. PERFORMANCE DURING PILE INSTALLATION The application of the above procedures is demonstrated by presenting examples of measurements interpreted from a model pile installation made in the calibration chamber with dense Fontainebleau sand surcharged vertically to 150 kPa. The 36 stress cells deployed were orientated to measure radial, vertical and circumferential stresses at three depths, adopting a series of radial distances from the pile axis. Pile installation was by jacking with each stroke advancing the pile by 1 cm until reaching a ˆnal penetration of 92 cm; the jack was unloaded to zero load between strokes, imposing a total of 92 load cycles. Figure 15 illustrates the installation process while the tip arriving at the sand surface, the middle level of the stress cells at 55 cm depth and the ˆnal position. The corresponding relative height, h/R of the middle cells' level is －30.6, 0 and 20.6, where h is the height of the middle level above the pile tip and R is the pile radius of 18 mm. Figure 16 presents data from a single 7 MPa radial stress gauge set 18 mm from the ˆnal pile perimeter at the middle level, reporting two measurement envelopes that match: (i) the maxima applying at the end of each stroke and (ii) the minima associated with the end of each zeroloaded pause. The radial stress was about 64 kPa under initial K0 conditions (h/RÃ30.6), and the stresses cycled with each jack stroke once pile installation commenced, trending upwards to reach the maximum load of around 6 MPa (around h/R＝0) and cyclic amplitudes exceeding 1 MPa as the tip approached the instrument level, before reducing sharply as it advanced further (hÀ0), reaching ˆnal values in the 200 to 300 kPa range at h/R＝20.6. These general features conform to Chow's (1997) ˆeld ICP observations made in dense sand and those seen in looser sand by Lehane et al. (1993). Independent Cone Penetration Test (CPT) measurements allowed the ˆnal ratios of radial stress (sr) to local CPT tip resistance stress (qc) to be established, showing values around 1.0¿1.4z, which match those expected to apply close to the pile shaft by recent CPT based design methods, such as those outlined by Jardine et al. (2005) or Lehane and White (2005). Applying the data reduction rules outlined above led to results that are both fully credible and com-

Fig. 15. Experiment setup for a model pile installation with the calibration chamber

Fig. 16. Envelopes for the radial stresses recorded by Kyowa PS/D-7 MPa-0002, distinguishing the maxima and minima recorded at the ends of each stroke and pause respectively

patible with the independent measurements made in the same test on the mini-ICP shaft. Despite the extreme conditions imposed, repeated calibration chamber tests by the Authors indicate that the stress trends recorded at particular positions are repeatable and consistent to within ¿15z. CONCLUSIONS An assessment has been made of whether commercially available miniature stress-cells can be used to measure soil stresses in model displacement pile experiments where a very wide range of soils stresses (50 kPa to 6

THE USE OF MINIATURE SOIL

MPa) are applied in multiple load cycles. It has been shown that calibration needs careful consideration. It is essential to (i) eliminate non-uniformities due to external boundary conditions; (ii) allow full soil-sensor cell action to develop, (iii) involve the correct test sand and state, and (iv) follow stress histories that capture the prototype problem appropriately. All of the stress cells tested developed strong cell action eŠects under the anticipated loading regimes and very careful calibrations and data reduction models were essential to obtaining meaningful data. The paper has presented a calibration and modelling approach that should prove applicable to other compliant diaphragm stress sensors and diŠerent test sands, although similarly detailed calibrations will be required for each individual case. More detailed points include: (1) The transducers all gave nearly linear `virgin loading' L curves, despite the highly non-linear behaviour of the host sand. These L curves provided one of the backbones required for transducer data interpretation. When power functions (with exponents between 0.96 and 1.4) were applied to obtain best ˆtting relationships the typical errors amounted to between 7 and 40 kPa with the devices investigated, depending on transducer capacity and type. (2) Substantial diŠerences were seen between the equivalent linear Calibration Factors (CF) measured during `virgin' loading calibrations and the nominal manufacturers' values. The ratios fell from ¿2.5 (for the 0.5 MPa) to ¿1.1 for the 7 MPa devices, re‰ecting the latters' greater structural stiŠness. (3) Non-linearity and hysteresis were seen in unloadreload stages applied to the lower capacity cells, which diminished as the stress cell rated capacity increased. (4) The full unloading U curves could be normalized by their maximum loading stage values to provide a second backbone function that could be modelled with reasonable accuracy by a two-part exponential function. Analysis indicates potential errors of 15 to 60 kPa with the devices considered, depending on the transducer type and loading history. (5) Reloading behaviour can be ˆtted by applying simple linear relationships in common with the L and U backbone curves that can again to subject to errors in the 10 to 60 kPa range with the present devices. (6) Variations in the initial density of the test sand also aŠect the system response, but to a much lesser degree than the transducer range, type and loading history. (7) Even when the recommended multi-parameter approach to calibration and modelling is applied, the possible error bands may amount to between 50 and 150 kPa, depending on cell type and stress history. Such errors can often be reduced (at the expense of sensitivity) by adopting devices with Rated Capacities higher than the expected soil stresses. (8) It is possible that still larger errors may accumulate

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if large numbers of cycles are applied during pile installation. However, examples of the measurements made with the miniature cells along with other results obtained in the calibration chamber tests, indicate that the stresses within the sand mass may be still established to within ¿15z with the systems deployed. (9) It is normal in soil element testing to aim for stress or pressure measurements that are accurate to within 1z, or better. However, to achieve soil stress measurements that can be relied upon to within even 15z is clearly di‹cult in displacement model pile tests. Theoretical studies are currently underway to assess whether DEM solutions can explain the experimental non-linear cell action observations, which may prove di‹cult to reproduce through other simpler treatments. ACKNOWLEDGEMENTS The above research was funded by Shell U.K. Limited, the UK Health and Safety Executive, the UK Engineering Physical Sciences Research Council, and Total, France. Their support is gratefully acknowledged. The authors would like to thank Mr. Steve Ackerley and Dr. Zhongxuan Yang for assistance in the development of the experimental apparatus and calibration testing. REFERENCES 1) Bishop, A. W. and Henkel, D. J. (1962): The measurement of soil properties in the triaxial test, Edward Arnold, London, Second Edition. 2) Bond, A. J., Jardine, R. J. and Dalton, J. C. P. (1991): The design and performance of the Imperial College instrumented pile, ASTM Geotech. Test. J., 14(4), 413–424. 3) Chow, F. C. (1997): Investigations into displacement pile behaviour for oŠshore foundations, Ph.D. Thesis, Department of Soil Mechanics, Imperial College, London, UK. 4) Chow, F. C., Jardine, R. J., Brucy, F. and Nauroy, J. F. (1998): EŠects of time on capacity of pipe piles in dense marine sand, ASCE J. of Geotech. and Geoenvir. Engrg., 124(3), 254–264. 5) Clayton, C. R. I. and Bica, A. V. D. (1993): The design of diaphragm-type boundary total stress cells, Geotechnique, 43(4), 523–535. 6) DunnicliŠ, J. (1988): Geotechnical Instrumentation for Monitoring Field Performance, John Wiley and Sons, New York. 7) Foray, P., Zhu, B. T. and Jardine, R. J. (2009): Extensive instrumentation of a calibration chamber for investigation of pile-soil interaction (in preparation). 8) Ingram, J. K. (1965): The development of a free-ˆeld soil stress gage for static and dynamic measurements, Instruments for Soil Mechanics, ASTM STP 392, ASTM International, West Conshohocken, PA, 20–34. 9) Jardine, R. J., Potts, D. M., Fourie, A. B. and Burland, J. B. (1986): Studies of the in‰uence of non-linear stress-strain characteristics in soil-structure interaction, Geotechnique, 36(3), 377–396. 10) Jardine, R. J., Chow, F., Overy, R. et al. (2005): ICP design methods for driven piles in sands and clays, Thomas Telford. 11) Jardine, R. J., Standing, J. R. and Chow, F. C. (2006): Some observations of the eŠects of time on the capacity of piles driven in sand, Geotechnique, 56(4), 227–244. 12) Jardine, R. J., Zhu, B. T., Foray, P. and Dalton, C. P. (2009): Experimental arrangements for investigation of soil stresses developed

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around a displacement pile, Soils and Foundations, 49(5), 661–673. 13) Lehane, B. M., Jardine, R. J., Bond, A. J. and Frank, R. (1993): Mechanisms of shaft friction in sand from instrumented pile tests, J. of the Geotech. Engrg. Div., Proc. ASCE, 119(1), 19–35. 14) Lehane, B. M. and White, D. J. (2005): Lateral stress changes and shaft friction for model displacement piles in sand, Can. Geotech. J., 42(4), 1039–1052. 15) Monfore, G. E. (1950): An analysis of the stress distribution in and near stress gauges embedded in elastic soils, Structural Report No. SP 26, U.S. Bureau of Reclamation, Denver, Colorado. 16) Selig, E. T. (1980): Soil Stress Gage Calibration, ASTM Geotech.

Test. J., 3(4), 153–158. 17) Timoshenko, S. and Woinowsky-Krieger, S. (1959): Theory of Plates and Shells, 2nd edition, McGraw-Hill Book Co., Inc., New York, N.Y. 18) Tory, A. C. and Sparrow, R. W. (1967): The in‰uence of diaphragm ‰exibility on the performance of a soil stress cell, J. of SCI. Instrum., 44, 781–785. 19) Weiler, W. A. and Kulhawy, F. H. (1982): Factors aŠecting stress cell measurements in soil, J. of the Geotech. Engrg. Div., Proc. ASCE, 108, 1529–1548.