stress measurement by overcoring at shallow depths in a rock slope

ORI GIN AL PA PER

Stress Measurement by Overcoring at Shallow Depthsin a Rock Slope: the Scattering of Input Dataand Results

C. Clement Æ V. Merrien-Soukatchoff Æ C. Dunner ÆY. Gunzburger

Received: 28 March 2008 / Accepted: 13 October 2008 / Published online: 3 December 2008

� Springer-Verlag 2008

Abstract This paper describes a field experiment of stress measurement using the

overcoring method performed in a rock slope, called Rochers de Valabres (located

in France’s Southern Alps Region), a field laboratory site prone to rockfalls. Six

measurements were conducted at shallow depths from the surface, moving deeper

along a sub-horizontal borehole. The experiment was conducted in heterogeneous

and anisotropic gneiss, with the overcored rock elastic properties, as evaluated by

biaxial and uniaxial tests, being widely scattered. Since stress calculations are

sensitive to all input data uncertainties, strain inversion was, thus, performed using

an experimental device and Monte Carlo simulations. The experimental device

allows the assessment of rather broad confidence intervals for both stress magnitude

and orientation. The results indicate that the stress state in the surface area is quite

heterogeneous and may be correlated with topography. The measurements show a

nonlinear stress distribution with distance to the free surface, along with high values

of principal stresses, despite the vicinity of the surface. Although influenced by local

topography, orientations of the principal computed stresses are characterized by a

high turnover due to local heterogeneities. The results are roughly in accordance to a

2D finite element model of the site.

C. Clement (&)

LAEGO-INERIS, Nancy-Universite, Parc de Saurupt, CS 14234, 54042 Nancy, France

e-mail: [email protected]

Present Address:C. Clement

ANTEA, 1, rue du parc de Brabois, 54500 Vandoeuvre, France

V. Merrien-Soukatchoff � Y. Gunzburger

LAEGO, Nancy-Universite, Parc de Saurupt, CS 14234, 54042 Nancy, France

C. Dunner

Institut National de l’Environnement Industriel et des Risques (INERIS),

Parc de Saurupt, CS 14234, 54042 Nancy, France

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Rock Mech Rock Eng (2009) 42:585–609

DOI 10.1007/s00603-008-0019-8

Keywords Stress � Overcoring � Rock slope � Uncertainty � Numerical modeling �Experimental device

1 Introduction

Rock slope stability is governed by several factors, including slope topography,

fracture network, groundwater pressure, seismic activity, and in situ stress

conditions. This last factor, yielding, for example, an unbalanced stress concen-

tration, can produce phenomena such as rockfalls and slipping (Amadei and

Stephansson 1997, p. 51). Panthi and Nilsen (2006) revealed that very anisotropic

stresses near the topographic surface exert a significant impact on both present and

future slope stability. Similarly, Obara et al. (2000) demonstrated that the horizontal

stress component plays a key role in estimating rock slope stability.

Even though the stress state constitutes an important factor of slope stability, it

remains difficult to grasp in the case of an irregular ground surface. As opposed to

studies on tunnels and ground-related problems, few analytical solutions of initial

stresses are available, and these are limited to smooth surfaces (Ling 1947;

Akhpatelov and Ter-Martirosyan 1971; Pan and Amadei 1994). For irregular and

complex three-dimensional topographies, numerical computations provide the best

alternative for computing in situ stresses, yet, input data are required. Stress

measurements on slopes also prove to be rare, particularly close to the surface.

Some such efforts have been performed on manmade cuts, e.g., open-pit mines and

dumps (Obara et al. 2000; Bozzano et al. 2006; Demin et al. 2003; Kang et al.

2002). However, these measurements were conducted on slopes with regular and

simple topographies and not on natural slopes.

Under these complex conditions, in situ stress measurements, by use of the

overcoring method, were performed within the experimental zone of a natural slope

called Rochers de Valabres.

Although not directly linked to instability evaluations, the stress measurement

analysis described herein is intended to:

• Offer an order of magnitude for the stress state at shallow depths, as necessary

for conducting a stability evaluation. It was decided to investigate and monitor

the surface zone of the slope (first few meters of depth) inasmuch as rockfalls

begin with a slip of the surface block (5–10 m wide). This subsurface area is

also particularly sensitive to the topographic surface, fracturation, and thermal

stresses, all of which produce a more heterogeneous and complex stress state

than for stresses inside the rock mass (Haimson 1979; Amadei and Stephansson

1997, p. 14, 108).

• Compare stress-to-stress variations due to thermal effects, which are partially

measured by a strain cell network at the Rochers de Valabres rock slope

(Merrien-Soukatchoff et al. 2007; Clement et al. 2008).

• Compare in situ measurements and their uncertainties with analytical and

numerical computations.

• Contrast measurement data with the a priori assumptions adopted for the stress

state on the rock slope. As an example, it is generally assumed that stresses close

586 C. Clement et al.

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to the surface are smaller, since the shallower part of the slope may be less

compressed than the deeper part, due to the presence of open discontinuities and

weathering near the topographic surface (Comite Francais de Mecanique des

Roches 2004, p. 350). It may also be considered that the vertical normal stress

equals the weight of the overlying rock for horizontal topography; in the case of

hilly terrain, this evaluation would involve the orientations of the major

principal stresses lying in the plane of the slope, with the minor stresses being

normal to the slope and equal to zero. Similarly, these stresses approach zero

where the rock slope is convex upward, but increase where the slope is concave

upward (Goodman 1980, pp. 104–105, see Fig. 1).

• Evaluate the feasibility of stress measurements using the overcoring test in a

rock slope. The field experiment is, indeed, intended to apply the overcoring

technique to investigating other fractured rock slopes.

This paper will initially present the laboratory site and provide a description of

the experimental setup. A description of the drilling campaign and acquisition of

anisotropic rock properties will be described next. In order to evaluate the impact of

uncertainties and quantify errors in the estimation of in situ principal stresses, a

procedure relying upon reliability analysis (or an ‘‘experimental device’’) will be

suggested. Lastly, the stress measurement results will be detailed, discussed, and

compared with the output from a simple 2D finite element model.

2 Site Description

The Rochers de Valabres is a large fractured rock slope located in the Tinee Valley

(in France’s Southern Alps region). The slope overhangs a road, its viaduct, and a

hydroelectric power plant (Fig. 2).

Two rockfalls occurred, respectively in May 2000 (involving some 2,000 m3 of

material) and October 2004 (roughly 30 m3 of material).

Since 2002, this slope has been investigated as a laboratory site by the Laego and

Ineris Institutes (Gunzburger 2004; Gunzburger et al. 2005; Merrien-Soukatchoff

et al. 2005; Dunner et al. 2007) and the Geosciences Azur and Geosciences

Fig. 1 Estimated initial stresses in the case of a valley side, according to Goodman (1980, pp. 104–105)

Stress Measurement by Overcoring at Shallow Depths in a Rock Slope 587

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Besancon laboratories. Beginning in 2006 and within the framework of a French

national program (entitled STABROCK), these research organizations, along with

new partners, have been concentrating their efforts on field observations,

monitoring, and numerical modeling. The scientific investigations have sought to

better understand the effect of climatic variations on rock slope stability, as well as

to test and introduce new equipment and monitoring techniques (Senfaute et al.

2006). Instrumentation technologies, such as microseismic networks, mechanical

measurements using tiltmeters, and deformations cells, have been installed in a zone

denoted the experimental area (Fig. 3). Stress measurements have been carried out

beneath this area, thanks to the presence of a former access road.

This experimental zone ranges in elevation from 700 to 900 m, with an average

dip of around 50–70�. The top of the slope actually culminates at more than

2,000 m, while the bottom of the valley lies at an altitude of 600 m.

The site is cut into hard migmatic gneiss, which displays significant foliation,

generally oriented N110�–140�E. The fracture network cuts the rock mass into

many blocks potentially capable of sliding towards the valley by means of plane

sliding (Gunzburger 2004; Gunzburger et al. 2005).

3 Stress Measurements Using the Overcoring Test

3.1 Description of Field Experiments

Overcoring methods are commonly applied with success in mine settings (Lahaie

et al. 2003), natural gas storage (Glamheden and Curtis 2006), and radioactive waste

storage research (Heusermann et al. 2003). This technique enables measurement of

the full 3D stress tensor from a single measurement; in the case of several tests

along a profile, both the stress gradients and local heterogeneous stress fields can be

detected. The scale of rock volume covered by such measurements amounts to

Fig. 2 Location of the Rochers de Valabres experimental site in the Southern French Alps


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around 10-2–10-3 m3 (Amadei and Stephansson 1997 p. 96; Bertrand 2001). The

overcoring test, thus, yields a fine level of stress tensor detail.

In November 2005, in situ stress measurements were performed by INERIS along

a sub-horizontal borehole drilled towards the north on the former road beneath the

monitored area (Dunner et al. 2007). The stress field was determined by overcoring

CSIRO Hi 12 stress cells on six locations at the following depths from the free

surface: 2.45, 4.35, 6.35, 10.25, 15.75, and 18.35 m (Fig. 4). These locations

correspond to overlying rock extending between 15 and 45 m.

Each cell comes equipped with 12 gauges (Worotnicki 1993): two axial gauges

(ez), five tangential gauges (eh), and five inclined strain gauges (e45 and e135).

During the measurement procedure, a CSIRO strain cell placed in a small-diameter

pilot hole (38 mm) is overcored by drilling a large-diameter borehole (146 mm).

The overcored sample becomes totally isolated and relieved of the surrounding

stress. The 12 strain gauges then record deformations as a result of the volume

increase in the sample created by the stress relief (Amadei 1983). The stress tensor

is calculated, using inversion methods, from the strain response and elastic

Fig. 3 Description of the experimental area of the Rochers de Valabres study slope


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properties of the overcored sample, which are typically evaluated using biaxial tests.

The strain responses of the CSIRO cells were recorded by a SYTGEO� system and

the inversion was performed with the SYTGEOstress� software developed by

INERIS.

The stress measurement depths were chosen by virtue of the local geological

setting, i.e., fracturation rate. The first several meters of rocks from the borehole

were too heavily fractured and constrained the initial measurement conducted at a

depth of 2.5 m.

Strain curves recorded during overcoring Tests 1–6 are shown in Fig. 5, which

plots measured strain versus time. All strain curves reveal a gradual elongation and

the various types of gauges are well distinguished.

3.2 Geological Setting of the Boreholes

All 18-m samples from the borehole were investigated and described in order to

survey fractures, foliation orientation, and weathering zones. The foliation

orientation actually constitutes an input data element for strain inversion, and the

fractured or weathering zones may influence the in situ stress state. Moreover, thin

sections were prepared from each overcored sample and then investigated under the

microscope.

Fig. 4 Location of the six stress measurements within the horizontal borehole over a cross-section


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The discontinuities display a perpendicular direction with respect to the drilling

direction, varying from approximately N70� to N110�, with a dip in the 50–70%

range. This fracturation system shows good agreement with the main fracture sets,

as described on the slope scale (Gunzburger et al. 2005). These natural

discontinuities present rough, weathered, and oxidized surfaces; some discontinu-

ities contain calcite filling.

The petrological description reveals that the borehole was drilled through a

migmatic paragneiss formation, belonging to the Alpine Hercynian basement. The

rock is composed of quartz, feldspar, and mica (mostly biotite). At the slope scale,

foliation is oriented 110�–140�NE, with a dip of 65�N. On the drilling scale

however, foliation layers are undulating and often discontinuous, with quartz-

Fig. 5 Response curves observed during overcoring Tests 1–6. The dark curves with squares correspondto transverse gauges, the gray curves with triangles to inclined gauges, and the gray curves with circles toaxial gauges


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feldspar lenses included in the host gneiss. Consequently, gneiss samples of each

overcoring test appear to be heterogeneous, and it is difficult to accurately display

the main foliation orientations of each sample. This difficulty will exert a certain

impact on stress calculations, as will be discussed further below.

Although the borehole samples exhibit numerous heterogeneities, it is still

possible to separate the drilling length into five sections (see Fig. 6) as follows:

• First section—between 1 and 8.5 m: zone with undulating foliation layers,

quartz-feldspar lenses, and quartz veins.

• Second section—between 8.5 and 11.5 m: zone with regular and thin foliation

layers dipping towards the southeast. Higher proportion of mica.

• Third section—between 11.5 and 15.5 m: zone with considerable open

fracturing, plus calcified and rough surfaces. Quartz-feldspar lenses are larger

and numerous. The foliation orientation is, therefore, imperceptible.

• Fourth section—between 15.5 and 16.5 m: known as the breccia area. Gneiss

stones are enclosed by a chlorite matrix.

• Fifth section—between 16.5 and 18.5 m: a zone similar to the first section.

3.3 Overcored Rock Mechanics Properties

The stress tensor is calculated from the strain response recorded during the

overcoring test and from the elastic parameters of overcored rock.

Since the rock fabric is clearly anisotropic, mechanical behavior will be assessed

by means of transversely isotropic theory (Amadei 1996), which requires defining

five elastic parameters: E1 and E2, Young’s moduli in the direction normal to the

plane of transverse isotropy and in the parallel direction; v12 and v23, Poisson’s ratio;

and G12, the shear modulus.

If anisotropy were to be neglected, a major error in the calculated principal

stresses would be introduced (Amadei and Stephansson 1997, pp. 108–109). Hooker

and Johnson (1969) derived an error of approximately 25% in magnitude and 25� in

orientation, while Amadei (1996) and then Lahaie (2005) demonstrated that

anisotropy can introduce 33 and 40% error, respectively.

Fig. 6 Location of overcoring tests and the petrological sections


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Elastic parameters are typically obtained from biaxial testing applied directly on

the overcored sample. In our case however, biaxial tests were not sufficient to

estimate the entire transversely isotropic elastic matrix. It proved necessary to use

uniaxial testing for a full determination of anisotropic properties. Given that the

rock is clearly anisotropic and heterogeneous and that various types of laboratory

tests were employed, the elastic parameters are widely scattered and affected by

uncertainties, as will be shown below.

3.3.1 Biaxial Testing

In this paper, the so-called biaxial test designates the test directly performed on the

overcored sample using a biaxial chamber. A radial and increasing confining

pressure is to be applied, although no prescribed load or displacement is applied on

the sample axis.

Only two overcored samples (120 mm diameter and 600 mm long), retrieved

from a depth of 2.45 m (Test 1) and 15.75 m (Test 5), were usable for the biaxial

tests. Indeed, the length of the overcored samples extracted from Tests 2, 3, 4, and 6

were too short to be introduced in the biaxial chamber.

The Test 1 sample clearly exhibits a foliation plane, hence, an anisotropic

fabric, while the second sample (Test 5) is composed of breccia and will be

considered as isotropic. Two loading–unloading cycles were introduced on each

sample.

Nevertheless, biaxial testing can only establish the apparent elastic parameters,

i.e., Young’s modulus (Eeq) and Poisson’s ratio (veq), with the assumption of an

isotropic material. The results are shown in Table 1.

Table 1 shows low Poisson’s ratio values, especially for Test 5, and a scattering

of the apparent Young’s modulus values, which may be caused by both anisotropy

and heterogeneity at the sample scale.

In the case of the Test 1 sample however, i.e., for an anisotropic sample, biaxial

testing is not sufficient to estimate all of the transversely isotropic parameters (E1,

E2, v12, v23, and G12), since this testing is not being performed in the plane of

foliation or normal to it and since, to the best of our knowledge, no analytical

solutions have actually been proposed for such a complete determination by means

of biaxial testing.

Table 1 Apparent elastic parameters calculated during biaxial testing

Apparent elastic parameter Minimum Maximum Mean Standard deviation

Test 1

Eeq: Young’s modulus (GPa) 18.2 33.6 27.5 5.6

veq: Poisson’s ratio 0.06 0.19 0.12 0.07

Test 5

Eeq: Young’s modulus (GPa) 23.1 42.1 29.7 7.8

veq: Poisson’s ratio 0.05 0.06 0.05 0.003


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3.3.2 Uniaxial Testing

In order to estimate the transversely isotropic parameters, uniaxial compression tests

were conducted on specimens cut at different angles with respect to the plane of

transverse isotropy. Two samples were collected from the borehole at depths of 2.88

and 15.5 m, and then cut into eight specimens (38 mm in diameter and 76 mm long)

and instrumented with strain gauges. All of the specimens displayed foliation layers

and were considered to be anisotropic.

The five independent elastic properties (i.e., E1, E2, v12, v23, and G12) were

determined from the linear portion of stress–strain curves via several loading–

unloading cycles. The results from uniaxial compression tests indicate a clearly

anisotropic fabric with an anisotropy factor (R = E2/E1) of about 1.4. The entire set

of transversely isotropic parameters, measured at a point 2.88 m deep, is presented

in Table 2.

3.3.3 Choice of Mechanical Parameters

Two kinds of laboratory tests were conducted on Valabres samples at two different

scales; this approach has served to raise the problem of parameter value choice

inherent in this study.

Biaxial testing can only determine the apparent elastic parameters, i.e., Young’s

modulus (Eeq) and Poisson’s ratio (veq), under the assumption of an isotropic

material. Biaxial testing does, however, yield an order of magnitude for

mechanical parameters at the scale of the overcoring test, given that the samples

are directly extracted from the in situ experiment and correspond to the scale of

the studied volume (i.e., around 10-2–10-3 m3, Bertrand 2001) and its state of

heterogeneities. These apparent elastic parameters must be kept to follow up with

the study.

On the other hand, uniaxial tests are carried out on smaller specimens, which do

not correspond to the scale of the studied rock volume. They are, however, useful in

quantifying rock anisotropy by being performed with reference to the plane of

transverse isotropy.

Consequently, we decided to deduce the transversely isotropic parameters E1 and

E2 using apparent parameters from biaxial testing (due to their scale), along with the

anisotropic factor R from uniaxial testing. We also decided to maintain the

anisotropic Poisson’s ratio.

Table 2 Transversely isotropic parameters calculated from uniaxial testing at a point 2.88 m deep

Transversely isotropic

parameter

Minimum Maximum Mean Standard

deviation

Number

of values

E1 (GPa) 32.2 48.50 41 5.2 7

E2 (GPa) 56.20 60.37 58 1.5 4

v12 0.09 0.15 0.13 0.02 7

v23 0.12 0.17 0.15 0.02 4

G12 (GPa) 20 1


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4 Stress Computations with the Experimental Device

4.1 Understanding and the Handling of Uncertainties: use of the Experimental

Device

Stress computations by means of strain inversion require input data, such as

mechanical parameters and (two-angle) foliation orientation in the case of a

transversely isotropic material. If these parameters are known, then the

knowledge of strain after overcoring will lead to determining the stress tensor

by inversion and least-squares minimization. In our case, the determination of

these input data was complex and involved several sources of uncertainties, as

detailed below:

• Uncertainties on foliation layer orientation, due to undulating foliation.

• A scattering of mechanical properties, which could be caused by the

considerable heterogeneity of the gneiss sample, as revealed during the

petrological description of the borehole.

• Uncertainties on anisotropic elastic properties, due to the use of two kinds of

laboratory tests at various scales.

• Uncertainties on elastic properties of overcoring Tests 2, 3, 4, and 6. Biaxial

and uniaxial testing was performed at just two locations (overcoring Tests 1

and 5), and their elastic rock properties will be extrapolated to the other

points.

The first two points correspond to the natural spatial variability of the rock, while

the last two correspond to measurement uncertainties.

Stress computations however, are sensitive to all input data uncertainties, which

cannot be overcome, though it is possible to quantify their impact by displaying

results with a confidence interval evaluation.

In our specific case, we have decided to perform a reliability analysis (also called

‘‘experimental device’’). Both mechanical and geometric input data are treated as

random variables, according to Monte Carlo analysis techniques, and their influence

on the output random variable will be examined.

This process can be detailed as follows (see Fig. 7):

• Input data are mechanical parameters and geometric characteristics (azimuth

and dip of the foliation layer); they are generated using Monte Carlo

simulations. The random intervals are chosen with respect to variations deduced

from laboratory testing and sample observation.

• Output data are stress tensors, i.e., magnitude, azimuth, and dip angle. Using

random input data, the strain data inversion produced 500 stress tensors for each

Fig. 7 Summary diagram of the experimental device


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measurement point. Such an inversion was performed using the SYTGEO-

Stress� software application (Lahaie and Renaud 2005).

• The impact of uncertainties may be assessed both qualitatively with response

surface models and quantitatively with multiple regression operations.

• The stress estimation can then be presented, together with confidence intervals,

and interpreted more accurately.

Such statistical techniques, e.g., least-squares method and Monte Carlo

analysis, have already been used successfully by Cornet and Valette (1984) and

by Walter et al. (1990); they may be applied to stress determination using

hydraulic fracturing. These methods produce a variation domain and, with it,

confidence intervals on the magnitude and orientation of the mean principal

stresses. The level of confidence assigned to stress determination will then provide

an order of magnitude for the resolution needed when performing numerical

modeling.

4.2 Random Input Data Intervals

The quality and precision of the experimental device depends on the choice of

random input data intervals; in our case, the input data will depend on mechanical

behavior, i.e.:

• For an isotropic material, i.e., for overcored Test 5, only two input data are

necessary: E, Young’s modulus; and v, Poisson’s ratio.

• For a transversely isotropic material, i.e., for overcored Tests 1, 2, 3, 4, and 6,

five mechanical properties (E1, E2, v12, v23, and G12) and two geometric

parameters (azimuth [A] and dip [D] of the foliation layers) need to be

introduced. These five mechanical properties have been reduced to three

(R = E2/E1, v12, v23) using:

• A Saint-Venant approximation (Amadei 1996):

1

G12

¼ 1þ 2v12

E1

þ 1

E2

ð1Þ

• A fixed value of Eeq (i.e., 27.5 GPa) and an assumption between E1 and E2,

the anisotropy factor R, and Eeq.

Furthermore, since only two measurement points (Tests 1 and 5) were

characterized using laboratory results, it proved necessary to extrapolate rock

properties to the other measurement points. Transversely, isotropic parameters

obtained during Test 1 have, thus, been applied to Tests 2, 3, 4, and 6, which reveal

anisotropic behavior and apparent foliation layers. Only Test 5 is considered to be

isotropic.

The mechanical parameter random intervals for each overcored test are listed in

Table 3. The intervals for each mechanical parameter have been deduced from the

maximum and minimum values yielded by laboratory testing.


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Foliation layers (two parameters: azimuth [A] and dip [D]) are also random. Their

intervals depend on the irregularity observed in borehole samples.

4.3 Results: Application of the Experimental Device on Overcored Test 1

The experimental device will be detailed first on overcored Test 1 in order to clarify

the method. Explanations will focus on the major principal stress (r1). The aim here

is to bound the major principal stress magnitude (m_r1), trend (tr_r1), and plunge

(pl_r1), all of which depend upon random input data by use of regression analysis. A

polynomial equation connecting the output (m_r1, tr_r1, and pl_r1) with five input

variables (R, v12, v23, A, and D) can be derived according to the following equation:

y ¼ b0 þ b1Rþ b2v12 þ b3v23 þ b4Aþ b5D ð2Þ

where y is one of the output parameters (m_r1, tr_r1, or pl_r1) and b0, b1, b2,... are

the regression coefficients, which may be considered as a weighting of the influence

from each input parameter.

Let’s note that the multiple linear regression analysis is performed on a

standardized database (i.e., with a reduced centered variable).

In order to ensure model adequacy, the multiple determination coefficient (R2) is

calculated for each regression analysis using the following expression:

R2 ¼Pn

i¼1 yi � �yð Þ2Pn

i¼1 yi � �yð Þ2ð3Þ

where �y; yi, and yi are the mean, the real values, and the predicted values of the

output response (y), respectively. R2 lies between 0 and 1, with a value close to 1

indicating that the majority of the variability in y is explained by the regression

analysis. Table 4 presents, for each output data element, the regression coefficient

for each input parameter and the corresponding R2 values.

The above table reveals that the variation in output response stems from a

complex combination of input data, i.e.:

• The magnitude of r1 is more heavily influenced by mechanical parameters.

Anisotropy factor R is especially influential.

• The variation in r1 trend is bounded with anisotropy factor R and foliation layer

dip D. v23 also exerts a significant impact.

Table 3 Random mechanical

parameter intervalsMechanical parameter Minimum Maximum

Tests 1, 2, 3, 4, and 6 (transversely isotropic)

R = E2/E1 1.16 1.9

v12 0.06 0.19

v23 0.12 0.17

Test 5 (isotropic)

E (GPa) 23.1 42.1

v 0.05 0.06


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• The variation in plunge r1 depends on both v23 and the geometric parameters (Aand D).

• The high R2 values suggest good model approximation.

Furthermore, the response surface representation may be used to analyze

response variability versus the random input parameters. Figure 8 depicts the

variability in r1 magnitude versus both anisotropy factor R and Poisson’s ratio v12.

It can be observed that the magnitude of r1 increases with higher R values and then

decreases with higher v12 values.

Moreover, application of the experimental device on Test 1 has produced an

estimation of r1, along with its variability and, hence, its confidence interval:

• The mean magnitude of r1 is 6.3 MPa, with a standard deviation of ±0.8 MPa.

• The mean trend of r1 is 290�N, with a standard deviation of ±15�. In comparison

with the potential trend range (360�), this variability becomes minor.

• The mean plunge of r1 is 56�, with a standard deviation of ±15�.

The directions of the three principal stresses calculated for overcoring Test 1,

using the experimental device, have been plotted on the lower-hemisphere polar

stereographic projection (OX: north, OY: upward vertical, OZ: east) in Fig. 9.

Fig. 8 Response surface for a magnitude of r1 versus both v12 and R

Table 4 Results from the linear regression analysis: calculation of regression coefficients

Constant R = E2/E1 v12 v23 A D R2

m_r1 -0.11 0.62 20.46 0.30 -0.13 0.02 0.98

tr_r1 0.49 20.39 -0.04 20.15 -0.02 20.80 0.96

pl_r1 -0.13 0.01 -0.05 20.29 0.20 20.36 0.89

Bold values are corresponding to the most important values


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One of the first key results to notice in Fig. 9 is the vertical W–E plane created by

the entire set of simulations of r1 and r2. A significant variability in plunge, coupled

with a minor variability in trend and a small difference in magnitude between r1 and

r2, has produced an isotropic plane in which stresses are nearly uniform. This

diagram clearly shows a plane containing the two major stresses, yet, their

respective orientations in this plane are less distinguishable.

4.4 Results: Application of the Experimental Device to the Full Stress Profile

In order to generate the stress profile (overcoring Tests 1 through 6) along with its

confidence interval, the experimental device was applied on each overcoring test;

the corresponding results are listed in Table 5 and Fig. 10. The principal stress

directions are plotted on the upper part of Fig. 10 using a polar stereographic

projection, while principal stress magnitudes are plotted on the lower part of Fig. 10

using curves with BoxPlot (Tukey 1977).

5 Interpretation and Numerical Modeling

5.1 General Interpretation: Effect of Topography and Heterogeneities

The computed stress profile (see Table 5; Fig. 10) leads to the following general

considerations:

Fig. 9 Polar stereographic projection of the principal stress directions and stress magnitudes fromovercoring Test 1 performed at a depth of 2.45 m (lower hemisphere)


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• The magnitudes of the major principal stresses, ranging from 5.5 to 11.8 MPa,

are sizable for data collected close to the surface; they are 10 times higher than

the estimated vertical overburden weight (0.3–1.1 MPa for an overburden

weight at 15–45 m, see Fig. 4), but the order of magnitude still agrees with

numerical modeling results, as will be shown subsequently.

• The maximum principal stress r1 is not influenced by the direction of the ‘‘large

slab’’ (i.e., 40–50�N, 50–70�SE) overhanging the borehole (Fig. 4).

• The evolution in stress magnitude is not linear: a shift is observed in stress

magnitude during Test 4, with a strong gradient and then a surprising decrease in

Test 5.

The stress profile is described in detail below (Fig. 11).

5.1.1 Stress Tensor for Tests 1, 2, and 3

At the locations of Tests 1, 2, and 3, the stress field magnitude shows no gradient.

The minimum principal stress r3 lies horizontally (Fig. 10) in a direction normal to

the free surface at the borehole location (Fig. 4). Moreover, a consistent propensity

can be detected for both the major r1 and intermediate r2 stress directions to lie in a

vertical plane, tending towards the E–W direction. Due to trend and plunge

variability, these two principal stresses overlap in this plane, where the magnitudes

Table 5 Stress measurement results: average values and standard deviations

Principal stress Magnitude (MPa)/standard deviation Trend (�N) Plunge (�)

Test 1 r1 6.3/0.8 290/15 56/15

r2 5.3/0.6 90/10 32/16

r3 2.2/0.2 184/5 9/6

Test 2 r1 5.5/0.7 265/30 58/12

r2 4.5/0.6 86/7 32/12

r3 1.3/0.2 176/6 2/2

Test 3 r1 6.6/0.9 272/16 51/16

r2 5.2/0.6 107/11 38/16

r3 1.9/0.2 12/3 6/4

Test 4 r1 10/1.2 80/4 37/4

r2 7.1/1.0 301/23 42/10

r3 4.4/0.5 203/40 24/9

Test 5 r1 7.6/1.3 284/0.1 37/0.01

r2 6.3/1.1 100/0.03 53/0.01

r3 2/0.3 193/0.05 2/0.01

Test 6 r1 11.8/1.4 89/18 66/5

r2 9.5/1.3 230/46 19/9

r3 5.9/0.6 301/71 9/6


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are nearly equivalent. Such an ‘‘isotropic’’ vertical plane can be correlated with the

influence of the free vertical surface.

5.1.2 Stress Tensor for Test 4

In contrast, the principal stresses as calculated for Test 4 are quite different from

Tests 1, 2, and 3. First of all, we have observed an increase in stress values (r1

increases from 6.6 to 10 MPa). Secondly, the stress directions are changing: the

directions of both the intermediate r2 and minimum r3 principal stresses reveal

significant variations that lead to a plane tending in the N–S direction, while the

maximum principal r1 stress features a more fixed trend of 80� with a plunge of 37�.

This particular tensor does not correspond to any discontinuities or rock slab

orientations.


Test 5 displays no real stress orientation variation, due to its particular type of

processing (i.e., as an isotropic material). We can observe a shift in stress magnitude

during Test 5, which may be explained by the influence of both the fractured zone

(third section, see Fig. 6) and the breccia zone (fourth area) that produced a local

anomaly. As a result of this geological disturbance and given that Test 5 presents

isotropic behavior and, hence, requires specific processing, it has been considered as

an anomaly in the stress state.


For Test 6, the principal stress orientations become lithostatic (or far-field stresses),

i.e., with vertical and horizontal directions. The direction of r1 has, indeed, trended

Fig. 10 Stress profile (overcoring Tests 1 through 6). Upper part principal stress directions plotted on apolar stereographic projection. Lower part principal stress magnitudes plotted by curves with BoxPlot.The box plots are constructed using the lower quartile (Q1 = 25%) and upper quartile (Q3 = 75%) ofeach data set, which serve to create the middle box. The curves cross the median values. Constructionextremities are limited by the interquartile range


123

Fig. 11 Summary depiction of stress measurements and the geological and geometric setting


123

vertically, while r2 and r3 overlap and lie within a horizontal plane. We have

assumed that Test 6 corresponds to depths from which the stress state becomes more

homogeneous and topographic influences diminish. Moreover, the location of the

fractured and breccia areas could insulate this measurement point from the surface

area, which is influenced by topography.

As expected for stress measurements conducted at shallow depths, the calculated

stress state is strongly affected by topography and geological heterogeneities.

Topography has a truly major effect: on Tests 1, 2, and 3, a vertical isotropic plane,

in alignment with the local vertical free surface, contains r1 and r2, while r3 is

normal to this plane. Such a finding confirms that stress near the slope surface tends

to be characterized by the maximum principal stress running along the ground

surface and by the minimum principal stress lying normal to it (Goodman 1980).

Furthermore, for Test 6, stress tensor orientation becomes close to that of lithostatic

stresses, which agrees with the assumption that topographic influence decreases

with depth. Finite element modeling, performed before the field experimentation,

had determined that, at a depth corresponding to twice the topographic roughness,

topographic influence is no longer perceptible (Merrien-Soukatchoff et al. 2006).

This depth corresponds, for the Rochers de Valabres site, to 20 m from the surface,

which approximately complies with Test 6 conducted at 18 m. Such an estimation

corresponds with what was found by Haimson (1979) and Cooling et al. (1988), who

measured stresses at shallow depths in alignment with the topography, as well as by

Savage et al. (1985), who expressed the distance for topography-induced stresses to

become far-field stresses.

The effect of heterogeneities can be observed on Test 5, which highlights

minor stress magnitudes and, hence, a jump in the stress profile. It is generally

considered that the presence of geological heterogeneities can significantly

disturb the distribution and magnitude of in situ stresses and, therefore, result in

measurement scattering (Amadei and Stephansson 1997, p. 45). Many cases of

measured stress field disturbance in the vicinity of heterogeneities have, indeed,

been reported in the literature (Ask 2006; Stephansson 1993). In our particular

case, a large fractured zone is located in front of Test 5 (see Fig. 6), and the test

was performed in a breccia area considered to be an isotropic material. If we

cannot express a precise relationship between this local geological disturbance

and the shift in stress magnitudes, we can then presume that these phenomena

are exerting a real effect on our data and, consequently, must be taken into

account.

5.2 Comparison Between Measurement Results and Modeling Output

In order to better explain stress measurement magnitude and orientation, we have

conducted some simple plane strain finite element computations using the

CESAR-LCPC� software. We chose, as a first step, not to introduce any fracture

network.

The geometry was constructed using both a digital elevation model (DEM)

obtained by Lidar Technology, as shown in Fig. 12 close to the experimental area,

and national geographic information for the far-field construction. From this 3D


123

model, we extracted four cross-sections passing through the exact location (cross-

section B) or near the borehole (cross-sections A, C, and D) used for the overcoring

test. The cross-sections are 1,400 m high and 800 m wide (Fig. 13) and include both

the mountain crest (elevation: 1,400 m) and valley floor (elevation: 650 m).

Since the mountain peak and valley floor are considered as axes of symmetry, the

horizontal displacements were fixed on the side boundaries and vertical displace-

ments on the bottom boundary (Fig. 13). The calculation was performed under

plane strain assumptions, due to the large slope extension, and the rock was assumed

to be a linearly elastic material.

The rock mass mechanical parameters were deduced from rock mass assessments

made using the geological strength index (GSI) (Hoek and Brown 1988, 1997). The

rock mass deformation modulus Erm was estimated from the empirical expression

defined by Hoek and Diederichs (2006), i.e.:

Erm ¼ Ei 0:02þ 1� D=2

2þ e 60þ15D�GSIð Þ=11ð Þ

� �

ð4Þ

where:

E The Young’s modulus value for intact rock (Ei = 46.6 GPa).

GSI The geological strength index value for the rock mass (Hoek 2006). We have

determined that GSI = 65, which corresponds to a rock mass formed by three

intersecting discontinuity sets under good surface conditions.

D The disturbance factor value, which is another qualitative index that depends

on the degree of blast damage and/or stress relaxation. For slopes, D varies

from 0.7 for a good blasting to 1 for a poor one (Hoek 2006). We have set

D = 0.7.

Fig. 12 Digital elevation model (DEM)—close-up of the experimental area for altitudes ranging from700 to 900 m. A, B, C, and D are the cross-section references. Cross-section B is positioned at theborehole location


123

All of the elastic properties associated with the rock mass are given in Table 6.

The initial stress state was estimated by applying gravity loading on the four

models. The stress tensors were extracted from lines extending from the former road

until the area 20 m deep. Computed stresses (both magnitude and orientations) at

cross-section B are shown in Fig. 14.

In order to compare measurement and modeling results, the magnitudes of the

major principal stress, deduced from these four models, are presented with the six

stress measurements in Fig. 15.

Figure 15 reveals that the magnitudes of major principal stresses extracted from

finite element modeling vary between 6 and 8 MPa and feature a low gradient

with depth (0.8 and 1.2 for cross-sections C and A, respectively). The order of

magnitude for the computed stresses agree with overcoring Tests 1, 2, 3, and 5;

however, the computations do not explain the increase in magnitude beginning

with Test 4.

Fig. 13 Mesh and boundary conditions at cross-section B

Table 6 Elastic rock mass parameters used for the numerical modeling exercise

Parameter Value Source

Erm: Young’s modulus of the rock mass (GPa) 10 GSI characterization

v: Poisson’s ratio 0.24

p: relative density (kg m-3) 2,700 Laboratory measurements on samples


123

Furthermore, orientations of the major and minor stresses, as computed by the

2D finite element model (Fig. 14), show a significant topographic effect. For the

first 2 m, the major stress plunge is aligned with the local vertical free surface

(plunge: 90�), while the minor stress is horizontal. This first area corresponds

with the first overcoring test. On the other hand, from a depth of 2 m and

extending deeper, the computed major stresses tend to align with the mean dip

of the ‘‘large slab’’ (50–70�) until reaching a greater depth (around 300 m),

where the major stresses become vertical. The measured stresses show a more

scattered orientation, and the major stress plunge becomes vertical during Test 6

(18 m deep).

Numerical tests have, nonetheless, highlighted that the entire slope weight leads

to high stress magnitudes at the foot of the slope, a finding that complies with stress

measurements, even though anisotropy has not been taken into account in the

modeling set-up. However, the fact that stress magnitudes increase with depth, as

Fig. 14 Magnitudes and orientations of computed major principal stresses on cross-section B

Fig. 15 Measurements and modeling results for the major principal stress profile. The continuous linesrepresent numerical computations of major principal stresses for cross-sections A, B, C, and D.Overcoring Tests 1 through 6 are depicted using box plot squares (over the lower quartile Q1 = 25% andupper quartile Q3 = 75% of the data). The curves cross the median value points


123

well as with orientation, has not been fully understood by this 2D computation. This

particular stress profile is obviously influenced by 3D topography, stress history, the

discontinuity network, and network heterogeneities. Further calculations, such as

those associated with 3D modeling, are foreseen.

6 Conclusion: Contributions Foreseen by this Study

Within the framework of multidisciplinary investigations at the Rochers deValabres rock slope site, the shallow stress field has been determined experimen-

tally at the foot of the slope composed of anisotropic gneiss.

Stress computations were performed using an experimental device and Monte

Carlo simulations. This process enabled us to highlight confidence intervals on the

stress module and orientation, in correlation with input data uncertainties. For the

studied case, the influence of anisotropy proved to be particularly acute, even

though the undulating foliation and mechanical dispersion remain significant.

Knowing the dispersion of these input data, the average standard deviations on

stress magnitude range between ±0.5 and ±0.9 MPa, which corresponds to 15–25%

of the stress quantity. This order of magnitude must be kept in mind for further

comparison with numerical modeling exercises or for all other conclusions drawn

from these stress measurements.

Moreover, these unusual stress measurements have provided us with information

on the stress field within the subsurface slope area. The measurements undertaken

have revealed that:

• The magnitudes of principal stresses are high, which complies with the simple

2D computation. Both computed and measured stresses have the same order of

magnitude, which corresponds to the overburden weight of the entire slope,

including the mountain crest.

• The subsurface area is heterogeneous and characterized by a high turnover of

the principal orientations and magnitude scattering. The initial measurements,

taken close to the surface and down to a depth of 7 m, are heavily influenced

by topography. Yet, topography is not the sole influential factor, as stress

history, the discontinuity network, and network heterogeneities have all been

hypothesized to explain stress heterogeneities, which indicates that a sizable

share of stress remains unpredictable and inaccessible due to a lack of

knowledge.

In conclusion, the stress measurements carried out as field experiments, through

the use of the overcoring test, have proven the feasibility of the overcoring

technique under rock slope conditions. Nevertheless, the results may not be

transposed to reach general assessments, as these investigations are characteristic of

the given site and depend on the particular stress determination techniques.

Acknowledgments This work program has been performed thanks to the financial support provided by

the French Ministry of Ecology and Sustainable Development. All authorizations and assistance from the

Mercantour National Park and the national EDF electric utility are gratefully acknowledged.


123

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