# 6 Test results

## 6.1 Basic equations

The shear modulus of the flexible dilatometer test, GFDT, is

GFDT = Δp [0,5dsd]
(1)

where

ds is the nominal diameter of the pocket. All measurements of the borehole diameter are afterwards referred to ds. It shall be determined as shown in Figures 4 and 5, that is by extrapolating the early linear portion of the expansion graph backwards to meet the horizontal line through the pressure axis at which the pocket expansion first begins (ps);

Δd is the additional diametral displacement of the borehole due to Δp;

Δp is the change of applied pressure above the contact pressure.

To calculate the flexible dilatometer modulus EFDT from shear modulus GFDT. the following equation shall be applied:

EFDT = 2GFDT (1 + v)
(2)

An assumption needs to be made for the Poisson's ratio v

Δd and Δp shall be corrected according to the calibration values obtained before testing (see 5.3.2).

NOTE 1 In many materials the moduli are strain-and path-dependent. A series of secant moduli taken from the pressure versus displacement graph can be used to define this variation.

NOTE 2 Formula (2) yields the Young's modulus for linearly elastic and isotropic materials only.

### 6.2.1 General

For procedures A to C, test data shall be plotted as shown in Figures 4 to 6, in Annex B and in Annex C where results of procedure A tests are shown. The corrected pocket diameter shall be plotted as a function of the corrected applied pressure p. The shear modulus of flexible dilatometer test GFDT is to be determined from Δd and Δp according to Formula (1).

Tests according to procedure D shall be designed for specific purposes. To be able to correctly evaluate the time-dependent ground deformation at constant pressures on the borehole wall when the membrane deformation is large, action shall be taken to keep the corrected pressure constant between t1 and t2.

### 6.2.2 Determination of moduli

G shall be determined using the average value of the pocket diametral displacement measured at least in three diametral directions for a given load cycle. However, if the values differ much from each other indicating anisotropy of the rock or soil mass, the G value shall be determined separately for each direction and reported accordingly.

NOTE This method of evaluation applies to each of the four procedures A to D.

### 6.2.3 Procedure A

The moduli G shall be calculated as follows:

— first loading modulus GL1 from the tangent to the first load loop through the intersection of ps and ds (see Figure 4);

— the next first loading modulus GLi from the slope of the secant between the upper reversal pressure (e.g. p1 for GL2) and the final pressure of the loading phase (e.g. p2), see Figure 4;

— unloading moduli GUi, for every unload path between 30 % and 70 % of the pressure range between upper reversal pressure (p1 or p2 or p3) and full relief pressure p1.1 (0 %), see Table 2 and Figure 4;

— reloading moduli Gri, for every reload path shall be calculated for every unload path between 30 % and 70 % of the pressure range between upper reversal pressure (p1 or p2 or p3) and full relief pressure P1.1 (0 %), see Table 2 and Figure 4.

Table 2 — Moduli of flexible dilatometer tests Figure 4 — Shear moduli GFDT in procedure A

### 6.2.4 Procedure B

The first loading modulus GL1 shall be calculated from the tangent to the first load loop through the intersection of ps and ds (see Figure 5); the next loading moduli GL shall be determined from the tangent to the d versus p curve (see Figure 5). Figure 5 — Shear moduli GFDT in procedure B

### 6.2.5 Procedure C

The loading modulus G1 shall be calculated by taking the gradient between the points corresponding to, for example, p1 and p2 in Figure 6, i.e. at 30 % and 70 % of the pressure range of the linear part of the curve, up to the pressure py. Key

py yield pressure of the ground

Figure 6 — Shear modulus G1 in procedure C

## 6.3 Constant pressure tests (procedure D)

After starting the test with a loading phase followed by a unload/reload cycle, p1 shall be held constant during a given period of time [see Figure 7 a)]. (a) Displacement versus pressure (b) Displacement versus time

Figure 7 — Constant pressure tests

The corrected pocket diameter shall be plotted in semi-log form as a function of elapsed time as indicated in Figure 7 b), the plot showing a nearly linear curve.

The creep parameter kf corresponding to the slope between t1 and f2 characterizing the time-dependent deformation characteristics of the material shall be determined for the given pressure level from Formula (3): (3)

where

• d2 is the corrected pocket diameter at time t2;
• d1 is the corrected pocket diameter at time t1.

## 6.4 Uncorrected and corrected graphs

dr as a function of pr shall be used to plot the uncorrected flexible dilatometer curve:

dr = f(pr)
(4)

d as a function of p shall be used to plot the corrected flexible dilatometer curve:

d = f(p)
(5)

where the applied pressure corrected for membrane pressure loss and stiffness (A.2) is given by

p = pr (dr) – pe (dr)
(6)

where the corrected pocket diameter d is given by

d = dr – apr
(7)

and a is determined by the method described in A.3.

For a variant A dilatometer probe, the membrane compression coefficient a is zero.

ISO 22476-5:2012 Field testing — Part 5: Flexible dilatometer test