Rock Mech Rock Eng (2009) 42:585–609 DOI 10.1007/s00603-008-0019-8 ORIGINAL PAPER
Stress Measurement by Overcoring at Shallow Depths in a Rock Slope: the Scattering of Input Data and Results C. Cle´ment Æ V. Merrien-Soukatchoff Æ C. Du¨nner Æ Y. 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. Cle´ment (&) LAEGO-INERIS, Nancy-Universite´, Parc de Saurupt, CS 14234, 54042 Nancy, France e-mail:
[email protected] Present Address: C. Cle´ment 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. Du¨nner Institut National de l’Environnement Industriel et des Risques (INERIS), Parc de Saurupt, CS 14234, 54042 Nancy, France
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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 concentration, 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; Cle´ment 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
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Fig. 1 Estimated initial stresses in the case of a valley side, according to Goodman (1980, pp. 104–105)
•
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´ Franc¸ais de Me´canique 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 Tine´e 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; Du¨nner et al. 2007) and the Ge´osciences Azur and Ge´osciences
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Fig. 2 Location of the Rochers de Valabres experimental site in the Southern French Alps
Besanc¸on 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 N110–140E. 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
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Fig. 3 Description of the experimental area of the Rochers de Valabres study slope
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 (Du¨nner 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 (Amade´i 1983). The stress tensor is calculated, using inversion methods, from the strain response and elastic
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Fig. 4 Location of the six stress measurements within the horizontal borehole over a cross-section
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.
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Fig. 5 Response curves observed during overcoring Tests 1–6. The dark curves with squares correspond to transverse gauges, the gray curves with triangles to inclined gauges, and the gray curves with circles to axial gauges
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 discontinuities 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 110–140NE, with a dip of 65N. On the drilling scale however, foliation layers are undulating and often discontinuous, with quartz-
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Fig. 6 Location of overcoring tests and the petrological sections
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.
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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
18.2
33.6
27.5
5.6
Test 1 Eeq: Young’s modulus (GPa) veq: Poisson’s ratio
0.06
0.19
0.12
0.07
Test 5 Eeq: Young’s modulus (GPa) veq: Poisson’s ratio
23.1 0.05
42.1 0.06
29.7 0.05
7.8 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)
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20
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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 SYTGEOStress 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 1 þ 2v12 1 ¼ þ G12 E2 E1
•
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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Stress Measurement by Overcoring at Shallow Depths in a Rock Slope Table 3 Random mechanical parameter intervals
Mechanical parameter
597
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) v
23.1
42.1
0.05
0.06
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 b1 R þ b2 v12 þ b3 v23 þ b4 A þ b5 D
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: Pn ðy^i yÞ2 2 ð3Þ R ¼ Pi¼1 n Þ2 i¼1 ðyi y where y; yi, and y^i 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.
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Table 4 Results from the linear regression analysis: calculation of regression coefficients Constant
R = E2/E1
v12
v23
A
R2
D
m_r1
-0.11
0.62
20.46
0.30
-0.13
0.02
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
0.98
Bold values are corresponding to the most important values
Fig. 8 Response surface for a magnitude of r1 versus both v12 and R
• •
The variation in plunge r1 depends on both v23 and the geometric parameters (A and 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 290N, 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.
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Fig. 9 Polar stereographic projection of the principal stress directions and stress magnitudes from overcoring Test 1 performed at a depth of 2.45 m (lower hemisphere)
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:
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600 Table 5 Stress measurement results: average values and standard deviations
Test 1
Test 2
Test 3
Test 4
Test 5
Test 6
•
• •
Principal stress
Magnitude (MPa)/standard deviation
Trend (N)
Plunge ()
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
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
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
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
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
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
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., 40–50N, 50–70SE) 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
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Fig. 10 Stress profile (overcoring Tests 1 through 6). Upper part principal stress directions plotted on a polar 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%) of each data set, which serve to create the middle box. The curves cross the median values. Construction extremities are limited by the interquartile range
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. 5.1.3 Stress Tensor for Test 5 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. 5.1.4 Stress Tensor for Test 6 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
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Fig. 11 Summary depiction of stress measurements and the geological and geometric setting
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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
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Fig. 12 Digital elevation model (DEM)—close-up of the experimental area for altitudes ranging from 700 to 900 m. A, B, C, and D are the cross-section references. Cross-section B is positioned at the borehole location
model, we extracted four cross-sections passing through the exact location (crosssection 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 displacements 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.: 1 D=2 Erm ¼ Ei 0:02 þ ð4Þ 2 þ eðð60þ15DGSI Þ=11Þ 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.
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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 GSI characterization
Erm: Young’s modulus of the rock mass (GPa)
10
v: Poisson’s ratio
0.24
p: relative density (kg m-3)
2,700
Laboratory measurements on samples
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.
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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 lines represent 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% and upper quartile Q3 = 75% of the data). The curves cross the median value points
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
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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 de Valabres rock slope site, the shallow stress field has been determined experimentally 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.
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