6 Test results

6.1 Basic equations

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

where

d_s is the nominal diameter of the pocket. All measurements of the borehole diameter are afterwards referred to d_s. 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 (p_s);

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 E_FDT from shear modulus G_FDT. the following equation shall be applied:

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 Loading test

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 G_FDT is to be determined from Δd and Δp according to Formula (1).

When evaluating flexible dilatometer tests, Δp shall only be selected within a range of any one loading or unloading phase. Whichever is selected determines whether the modulus measured is a loading or an unloading one. Distinction shall be made between the first loading modulus and various reloading moduli (see Figures 4 and 5 and Table C.2). All moduli shall be derived and quoted individually. Modulus values should be quoted to three significant digits.

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 G_L1 from the tangent to the first load loop through the intersection of p_s and d_s (see Figure 4);

— the next first loading modulus G_Li from the slope of the secant between the upper reversal pressure (e.g. p₁ for G_L2) and the final pressure of the loading phase (e.g. p₂), see Figure 4;

— unloading moduli G_Ui, 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 p_1.1 (0 %), see Table 2 and Figure 4;

— reloading moduli G_ri, 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.

First loading	Unloading (30 %—70 %)	Reloading
GL1	GU1	Gr1
GL2	GU2	GR2
GL3	GU3	Gr3

Key for indices: L = loading phase U = unloading phase R = reloading phase 1, 2, 3 = loop number

Key for examples: GLi = shear modulus in loading phase No. i GUi = shear modulus in unloading phase No. i GRi = shear modulus in reloading phase No. i ps =  seating pressure p1, p2, p3 = pressures at reversal points of loops dd = external diameter of the dilatometer

6.2.4 Procedure B

The first loading modulus G_L1 shall be calculated from the tangent to the first load loop through the intersection of p_s and d_s (see Figure 5); the next loading moduli G_L shall be determined from the tangent to the d versus p curve (see Figure 5).

Unloading/reloading moduli G_U shall be calculated for every unload/reload loop by taking the gradient of the line through each individual loop as indicated in Figure 5.

Key for Indices: L = loading phase U = unloading phase R = reloading phase 1, 2, 3 = loop number

Key for examples: GL = Shear modulus in loading phase GUR = Shear modulus in unloading/reloading phase ps = seating pressure ds = nominal diameter of the pocket p1, p2, p3 = pressures at reversal points, loops No. 1, 2 and 3. py = yield pressure of the ground 1 = pressure drop, typically pi/3 2 = membrane collapsing at head of water

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 p_y.

Key

p_y yield pressure of the ground

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

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 k_f 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):

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

d_r as a function of p_r shall be used to plot the uncorrected flexible dilatometer curve:

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

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

where the corrected pocket diameter d is given by

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

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