Near-field non-radial motion generation from underground chemical explosions in jointed granite

Near-field non-radial motion generation from underground chemical explosions in jointed granite Abstract This paper describes analysis of non-radial ground motion generated by chemical explosions in a jointed rock formation during the Source Physics Experiment (SPE). Such motion makes it difficult to discriminate between various subsurface events such as explosions, implosions (i.e. mine collapse) and earthquakes. We apply 3-D numerical simulations to understand experimental data collected during the SPEs. The joints are modelled explicitly as compliant thin inclusions embedded into the rock mass. Mechanical properties of the rock and the joints as well as the joint spacing and orientation are inferred from experimental test data, and geophysical and geological characterization of the SPE site which is dominantly Climax Stock granitic outcrop. The role of various factors characterizing the joints such as joint spacing, frictional properties, orientation and persistence in generation of non-radial motion is addressed. The joints in granite at the SPE site are oriented in nearly orthogonal directions with two vertical sets dipping at 70–80 degrees with the same strike angle, one vertical set almost orthogonal to the first two and one shallow angle joint set dipping 15 degrees. In this study we establish the relationship between the joint orientation and azimuthal variations in the polarity of the observed shear motion. The majority of the shear motion is generated due to the effects of non-elastic sliding on the joints near the source, where the wave can create significant shear stress to overcome the cohesive forces at the joints. Near the surface the joints are less confined and are subject to sliding when the pressure waves are reflected. In the far field, where the cohesive forces on the joints cannot be overcome, additional shear motion can be generated due to elastic anisotropy of the rock mass given by preferred spatial orientations of compliant joints. Geomechanics, transient deformation, numerical modeling, wave propagation 1 INTRODUCTION In this study we present the analysis of ground motion caused by underground explosions in granite observed during the Source Physics Experiment (SPE) conducted and the Nevada National Security Site (NNSS), formerly known as the Nevada Test Site (NTS). One of the main goals of this experiment was to understand the nature of non-radial ground motions observed during underground explosions. From a modelling perspective, the main difficulty of this problem is due to the nonlinear material responses in the vicinity of the explosive source where the ground motion is very sensitive to the dynamic strength of rock mass. The strength of the rock mass is significantly smaller than the strength of small intact rock samples measured at the lab due to the presence of meso and macro scale traces of cracks and joints. In rock mechanics and engineering various measures of strength degradation are used to scale the strength from the intact sample to heavily jointed rock masses (see e.g. Hoek & Brown 1997). Yet, such strength scaling still assumes that the rock mass strength remains isotropic. In hard rock formations, joints are distributed in family of sets which are not randomly oriented. It has been shown (e.g. Oda et al. 1986; Tsvankin 2012, and references therein) that such jointed rock masses behave as an anisotropic elastic-plastic medium with a pressure dependent yield surface. The shape of this surface can be found numerically for a representative volume given properties of the intact rock and properties and orientations of the joints for a given deformation history (see e.g. Vorobiev 2008; Zhang et al. 2012). In the far field, where material response can be considered elastic, anisotropy in elastic properties related to the joint orientation plays a role in polarization of the waves and the generation of shear motion. Wave propagation in elastic media with anisotropy has been studied in the past. Seismological applications of wave propagation in anisotropic media are reviewed in Crampin (1981). Tsvankin & Grechka (2011); Tsvankin (2012) studied wave propagation in geologic media with orthorhombic anisotropy corresponding to jointed rock masses. In this work we are focused on the non-radial motion generated in the near-field. Shear wave generation observed in underground explosions has been an area of interest during the last decades (Kisslinger et al. 1961; Wright & Carpenter 1962; Randall 1962; White & Sengbush 1963; Salvado & Minster 1980; Lash 1985; Babich & Kiselev 1989; Liu & Ahrens 1998; Mandal & Toksöz 1990; Murphy et al. 2009; Hirakawa et al. 2016). In Vorobiev et al. (2015) sliding on the joints was identified as the main mechanism responsible for generation of tangential ground motion in the near-field from a spherically symmetric source. Numerical simulations showed that tangential motion observed in the near-field during Source Physics Experiment SPE3 can be explained by plastic slip on the joint surfaces. In this work, we extend our analysis to the latest tests SPE4P and SPE5 which have also shown significant shear motion around the source. In fact, the new experimental data provide enough information to further validate our hypothesis that near-field tangential motion is caused by the joints present in rock formations. We show that given the joint set orientation and spacing one can predict both the magnitude of the shear motion and the azimuthal variations in polarity of the tangential motion. Even though the SPE site is well studied, there is still significant uncertainty in joint distribution between the boreholes where they were characterized as well as in the measurements of the mechanical properties of the joints. Therefore, stochastic methods are needed to predict ground motion with confidence at multiple locations. Recently we have demonstrated that using stochastic approaches it is possible to predict the expected ground motion for SPE (e.g. Ezzedine et al. 2015). Furthermore, we also study the relationship between the joint distribution, joint mechanical properties and apparent mechanical anisotropy of the rock mass. We investigate the role of both sliding on the joints and elastic anisotropy introduced by preferred orientation of the compliant joints. In our computational study we apply isotropic plasticity for rock blocks and additional constitutive laws for the joints to understand mechanical anisotropy at the large scale. With joint aperture on the order of 1 mm, joint spacing approximately 1 m, the wave length on the order of 100 m and the problem size is approximately 1 km, the study of such anisotropy presents a daunting computational challenge. Here we rely on advanced numerical techniques to model diverse spatial and temporal scales as well as on high performance parallel computing (HPC) capabilities available at Lawrence Livermore National Laboratory (LLNL). Detailed computational models of realistic rock formations can be achieved using in-site geological characterization data. We applied the 3-D massively parallel hydrocode GEODYN-L (Vorobiev 2012) to perform the numerical simulations of nonlinear wave generation and propagation in heavily jointed rock masses. To understand experimental observations reviewed in Section 2, we conduct multiple simulations of ground motion caused by underground chemical explosions. Results of the study of various effects of rock joints on the ground motion are presented in Section 3. 2 EXPERIMENTAL OBSERVATIONS 2.1 SPE underground chemical explosions in granite Six chemical explosions of different yields have been conducted during the first phase of SPE. All SPE explosions were conducted at the same site in the same well but at different depths over the last 5 yr at NNSS. The site was characterized before and after the shots. Details of the experiments and geological characterization of the site can be found in Townsend & Obi (2014). Granite samples were excavated from multiple wells and tested in laboratories. The tests have shown fairly uniform mechanical properties which did not change significantly with depth. Unconfined compressive strength (UCS) was in the range 100–200 MPa and ultrasonic sound speed was 5–6 km s−1. Additionally, rock joints excavated with the sample were tested to determine their mechanical properties. Joints were characterized in each borehole at the site to determine the joints spacing and orientations. The Climax stock is moderately to highly fractured. Using data from cores and logs, geologists have identified four sets of natural fractures based on fracture orientation. Three of these (Sets 1, 2 and 3) have high dip angles, and one (Set 4) has very low dip angles (0–30 degrees east). Sets 1 and 2 both strike west–northwest (285–310 degrees azimuth) but have opposite dip directions. Set 3 strikes north–northeast (010–055 degrees azimuth) and dips to the east–southeast. Set 4, the low-angle set, is by far the most ubiquitous of the four fracture sets (Townsend et al. 2012). For the present study both set 1 and 2 were combined to a single joint set leading to 3 sets of joints in total. Ground motion was measured both at various depths and ranges and at the surface in various azimuthal directions using accelerometers which measured three components: radial (R), vertical (L) and tangential (T) in a frequency range of 10–1000 Hz. Measures were taken to ensure that the gauges were properly aligned and coupled to the ground. After the first SPE shot, SPE1, has been executed it has been revealed that few gauges have been, unfortunately, rotated during the installation (see Townsend & Obi 2014; Steedman et al. 2016). In the current analyses we are not using data from gauges which may have been rotated. Locations of accelerometers are depicted in Fig. 1. Vertical ground motion was also measured at the surface in 5 azimuthal directions L1–L5 (shown in Fig. 1b) with 100 m interval. Figure 1. View largeDownload slide Near-field gauge locations for SPE shots: circles —SPE1, SPE2, SPE3 shots, squares—SPE4P shot, triangles—SPE5 shot, solid squares—surface gauges. Figure 1. View largeDownload slide Near-field gauge locations for SPE shots: circles —SPE1, SPE2, SPE3 shots, squares—SPE4P shot, triangles—SPE5 shot, solid squares—surface gauges. The first shot, SPE1, was conducted at depth 55 m and had a yield of 0.1 ton TNT equivalent. The second shot, SPE2 had 10 times bigger yield and was centred at 45.5 m depth. The third shot, SPE3, was conducted at the same location as the second one and had similar yield. It is worth noting that the slight difference between SPE2 and SPE3 yields is approximately 10 per cent. The goal of SPE2 and SPE3 is to investigate the role of damage on the observable ground motion in subsequent shots. SPE4P was conducted at depth 87 m and had a yield equal to that of SPE1. The biggest yield shot, SPE5, was conducted at depth 76 m and had a yield of 5 ton. It is worth noting that the scaled depth of burial for shots SPE3 and SPE5 was almost the same and equal to 447 m/kT1/3. This made it possible to directly compare the surface motions of these two shots, SPE3 and SPE5. Not surprisingly, similar to ones observed in historic nuclear tests, significant shear motion was detected in all SPE shots. Therefore, SPE chemical explosions provide a unique opportunity to test various hypotheses behind the nature of these motions and their geneses. It was suggested after the first three shots that the joints in the granite formations were the main cause of the observed shear motion (see Vorobiev et al. 2015; Steedman et al. 2016). Not surprisingly, two of the last SPE shots, SPE4P and SPE5, have underscored and confirmed this hypothesis. Understanding the nature of shear motion may allow us to build source models for the seismic codes to predict far-field ground motion in the event of underground explosions in jointed rocks. In the following subsections, we present the latest observations and analysis of the ground motions in the near-field up to 1000 m/kT1/3. 2.2 Experimental peak radial and tangential velocity attenuation Fig. 2 presents peak radial and tangential velocity attenuation versus scaled range for various SPE shots. On average, the peak tangential velocity is about 15 per cent of the peak radial velocity but in some locations it reaches as high as 30–40 per cent. The colours for the markers in Fig. 2(a) correspond to the sinus of the angle between a horizontal line and the direction to the gauge. Thus, the gauges above the shot level are shown in red while below the shot level are shown in blue. The solid line designates the legacy nuclear data fit (Perret & Bass 1975). Figure 2. View largeDownload slide (a)Near-field radial and tangential peak velocity attenuation for various SPE shots. Solid line is the fit based on published nuclear tests; dashed lines are power-law fits for radial and tangential velocities; dotted lines are their ratio. Point colour designates vertical direction towards the gauge. (b) Radial velocity attenuation for SPE shots where the marker colour corresponds to tangential-to-radial velocity ratio. Figure 2. View largeDownload slide (a)Near-field radial and tangential peak velocity attenuation for various SPE shots. Solid line is the fit based on published nuclear tests; dashed lines are power-law fits for radial and tangential velocities; dotted lines are their ratio. Point colour designates vertical direction towards the gauge. (b) Radial velocity attenuation for SPE shots where the marker colour corresponds to tangential-to-radial velocity ratio. We have found that power-law fits for both peak velocities as functions of scaled range. For radial velocities, average peak velocity can be expressed as 31925 R−1.813 m s−1, while for tangential velocities, the peak velocity can be expressed as 1676 R−1.594 m s−1, where the scaled range, R, is in m/kT1/3. The ratio of these fits (tangential to radial) grows with scaled range (plotted with the dotted line in Fig. 2a). It is interesting to note that the gauges with a high ratio of observed tangential velocity to the radial velocity often record below average radial velocity, as shown in Fig. 2(b). This can be explained by redirection of part of the radial motion into tangential motion. This growth of tangential motion is especially noticeable at the surface, where the tangential velocity very often has similar or even larger magnitude than radial velocity. Fig. 3 shows peak tangential (large solid markers) and radial (large empty markers) velocities measured at the far-field geophone lines, L1 through L5, at the surface in various azimuthal directions (directions for these gauges are designated in Fig. 1). The curves plotted on top of the markers are power-law fits for peak radial (solid line) and tangential velocities found for deep gauges. The small markers in Fig. 3 (which are also plotted in Fig. 2) are peak velocity data for the gauges at 15 m depth. It is seen that at the same scaled range (about 1000 m/kT1/3) tangential velocities at the surface are significantly higher than at depth. Other factors such as topography and presence of a dry weathered granite layer at the surface may have contributed to the enhancement of this motion. Figure 3. View largeDownload slide Radial and tangential surface motion recorded at L gauges. Solid line—power-law fit for peak radial velocities for the deep gauges; dotted line—power-law fit for peak tangential velocities for the deep gauges; small markers—peak radial and tangential velocities for some deep gauges measured during SPE4P shot. Figure 3. View largeDownload slide Radial and tangential surface motion recorded at L gauges. Solid line—power-law fit for peak radial velocities for the deep gauges; dotted line—power-law fit for peak tangential velocities for the deep gauges; small markers—peak radial and tangential velocities for some deep gauges measured during SPE4P shot. 2.3 Observed onset of tangential motion In many gauge locations the onset of tangential motion was coincident with the arrival of the radial motion for large amplitude shots (SPE3, SPE5). Yet, at the same locations, tangential motion was delayed for the lower magnitude SPE4P shot. This can be explained by insufficient shear stress on the joints during SPE4P when radial motion arrives, inhibiting plastic slip in the vicinity of the gauge. Fig. 4 shows recorded motion at station #15-1 in both SPE4P and SPE5 shots. As we have shown in Vorobiev et al. (2015), the delay of tangential motion relative to radial motion is controlled by the joint cohesion. Also, the maximum tangential velocity was often observed later during the unloading phase of the pulse. The polarity of tangential motion changes multiple times. As observed in the past (see e.g. Kisslinger et al. 1961), the high frequency tangential motion is often followed by a low frequency motion which sometimes reaches higher magnitudes. We have found this to be the case especially for the low yield shots or farther from the source. This can be explained by higher shear strength for joints confined by the compressive radial motion. As the pressure drops during the unloading phase, joints are more likely to start sliding because of reduced shear strength. Fig. 4 shows that for SPE4P the larger tangential motion always comes after the compressive pulse passes, when the joint compression is reduced, while for SPE5 the maximum tangential motion is observed simultaneously with the compressive phase. Tangential motions recorded during SPE4P and SPE5 at the same gauges seem to have the same polarity. This indicates that the polarity of this motion is mainly controlled by the azimuthal direction of the gauge rather than the shot depth. Figure 4. View largeDownload slide Radial (solid) and tangential (dashed) motion recorded at stations #15-1, #19-1 and #19-2 during SPE4 (on the right) and SPE5 (on the left) shots. Figure 4. View largeDownload slide Radial (solid) and tangential (dashed) motion recorded at stations #15-1, #19-1 and #19-2 during SPE4 (on the right) and SPE5 (on the left) shots. 2.4 Azimuthal variations of tangential motion We have found that tangential motion measured at various ranges but in the same azimuthal directions very often look similar. For example, for SPE5, the first tangential motion at all gauges located in wells #9 and #11 are always counter-clockwise (see Figs 5a and c) even though they are located at various ranges and depths. Negative polarity of the first tangential motion was also observed at these stations during SPE3, as shown in Figs 5(b) and (d). Figure 5. View largeDownload slide Tangential motion recorded in the same azimuthal direction at stations located in wells #9 and #11 for SPE5 (a,c) and SPE3 (b,d) shots. Figure 5. View largeDownload slide Tangential motion recorded in the same azimuthal direction at stations located in wells #9 and #11 for SPE5 (a,c) and SPE3 (b,d) shots. Fig. 6 shows tangential motion recorded at different ranges in two opposite directions: north (#16-1 at 20 m range and #19-1 at 45 m range) and southwest (#15-1 at 20 m range and #18-1 at 34 m range). Both SPE4P and SPE5 shots seems to show this trend. Polarity of tangential motion may look reversed for the gauges located in opposite directions (see e.g. #18-1 vs. #19-1 in Fig. 6). Polarity reversal was also observed in the past during analysis of shear motion (see Kisslinger et al. 1961). Figure 6. View largeDownload slide Tangential motion recorded in the same azimuthal directions at stations #19-1,#16-1 (north) and #18-1,#15-1 (south) during SPE5 (a,c) and SPE4P (b,d) shots. Figure 6. View largeDownload slide Tangential motion recorded in the same azimuthal directions at stations #19-1,#16-1 (north) and #18-1,#15-1 (south) during SPE5 (a,c) and SPE4P (b,d) shots. 2.5 Vertical and tangential motion at shot level In Vorobiev et al. (2015) we have shown that vertically oriented joints are mainly responsible for generating a significant tangential motion in jointed granite. In this work we have also observed vertical motion at shot level which should not be present if the material is behaving isotropically. We have found that both in the historic shots (e.g. Piledriver, Hardhat) and recent SPE experiments such motion was observed. If sliding on the joints were responsible for such motion it would be observed to the same extend as the tangential motion. Joints with low dip angle would have caused the vertical motion since their normal direction (which favours the wave propagation) is more aligned with the vertical direction. Fig. 7 shows observed vertical motion for SPE3 experiment at gauges #7-2, #8-2 (southwest direction from the ground zero) and #11-2 and #9-5 (northeast), for SPE4P experiment at gauges #18-2 and #19-2, for SPE5 experiment at gauges #19-4 and #18-4. Vertical velocity histories are shown for some of these gauges. The arrows designate observed dip directions for shallow angle joints at each borehole (joint set #4). The longer the arrow, the higher the prevalence of joint dipping. It is seen from the picture that most of joints dip in the northeastern direction. This may explain why the initial vertical motion detected at gauges in the northeastern direction was upwards while for the gauges located in the southwestern direction the first motion was downwards. The mechanism of the generation of such motion is explained on the side view where both the joints and the gauges are shown. It is remarkable that for all shots performed at different depths the direction of vertical motion agrees with the dipping direction of the shallow angle joints. Figure 7. View largeDownload slide Gauge location and observed polarity of vertical motion at shot level plotted on top of the areal photo. Measured dip directions for shallow angle dipping joints are shown with arrows next to well locations. Gauge locations with upward movement are shown in green colour and with downward movement are shown in red. Velocity histories for some gauges are also shown. Figure 7. View largeDownload slide Gauge location and observed polarity of vertical motion at shot level plotted on top of the areal photo. Measured dip directions for shallow angle dipping joints are shown with arrows next to well locations. Gauge locations with upward movement are shown in green colour and with downward movement are shown in red. Velocity histories for some gauges are also shown. 3 NUMERICAL MODELLING OF GROUND MOTION 3.1 Modelling assumptions We have performed 3-D modelling of ground motion for the SPE shots. Material model calibration for granite was described in Vorobiev et al. (2015). UCS was 128 MPa, density was 2.643 g cc−1 and the porosity was assumed to be 1 per cent. We modelled the source as an instant energy deposition in an ideal gas of the same density and internal energy as the high explosive used in the shots. The shape of the source canister was cylindrical as described in Townsend & Obi (2014). The radius of the cylindrical canisters used in the experiments is $${1}\!\!\!^{^{\sim}} 5$$ inches but the canister length varied from shot to shot. Indeed, numerical study has shown little effect on the energy release rate within the source , whether cylindrical or spherical source shape, on the shock wave generation. Therefore, in this study we assumed that energy within the source was instantly released in an equivalent spherical source. This helped to reduce computational cost because the radius of the cylinder is few times smaller than the radius of the sphere with the same volume and thus coarser mesh could be employed to resolve the source. The joints were assumed to be planar inclusions with finite extent and were represented by a centre and an orientation normal vector in each element intersected by joints. In our earlier work only a single joint was allowed per each finite volume (for details see Vorobiev 2010). Currently we have extended the model to support multiple joints crossing a single numerical element (Hurley et al. 2017). Gravity initialization was used to pre-stress both the rock and the joints to a stress state defined by overburden pressure (vertical stress). We also assumed that both horizontal stresses were assumed to be equal to the vertical stress. 3.2 Peak radial and tangential velocity attenuation We have performed 3-D simulations of the latest SPE experiments using the modelling assumptions described above. Stochastic realizations of joint distributions based on in-situ characterization were used in these calculations. Details on the joint generation for these calculations were published in Vorobiev et al. (2015) and in Ezzedine et al. (2015); and we refer the reader to the last subsection of the present section for more details. For each stochastic realization, simulations have shown both azimuthal variations in radial velocities and significant tangential motion generated at various ranges. Fig. 8 shows attenuation for peak radial and tangential velocities calculated in one of these realization to emphasize the mechanisms for energy conversion and shear motion polarization. Solid lines represent the best power-law fits to the results. The ratio of peak tangential and radial velocities is plotted with dotted lines next to the experimental ones. It is interesting to note that in both cases this ratio has a tendency to grow with range. However we observe a discrepancy between the calculated and the simulated attenuation curves. Calculations also reveal the main mechanisms behind this trend. Joint sliding is mainly responsible for energy redirection from radial to non-radial motion within the elastic radius region. Beyond the elastic radius, elastic anisotropy is the main cause of radial energy scattering. The extent of the elastic radius depends mainly on the slipping conditions at the joints, which in turn depend on the overburden pressure which depends on depth, water saturation and joint cohesion. Figure 8. View largeDownload slide Calculated radial and tangential peak velocity attenuation for SPE4P and SPE5 shots. Solid lines are power-law fits for radial and tangential velocities, dotted lines is their ratio. Point colour represents the ratio of peak velocities. Figure 8. View largeDownload slide Calculated radial and tangential peak velocity attenuation for SPE4P and SPE5 shots. Solid lines are power-law fits for radial and tangential velocities, dotted lines is their ratio. Point colour represents the ratio of peak velocities. 3.3 Study of azimuthal variations of tangential motion in a medium with two orthogonal vertical joint sets Vertical joints at SPE site can be grouped into four sets (Townsend et al. 2012). Two of these sets dip in opposite directions with 70–80 degree angle. For simplicity, they can be replaced by a single vertical joint set. The third joint set is almost orthogonal to the first two and has a high dip angle as well. In order to understand how the shear motion is generated in jointed granite during the spherical explosion let us consider a perfectly symmetric system with two vertical orthogonal joint sets spanning from east to west and from south to north. The size of the domain was 100 × 100 × 100 m, the joint spacing was 2 m. The joint aperture was taken to be 2 mm, initial joint normal stiffness was set to 0.1 GPa, joint friction coefficient was 0.35 and the joint cohesion was varied from 0 to 15 MPa. The source was modelled as an ideal gas with initial density of 1.711 g cc−1 and initial specific energy of 5.55 kJ g−1 occupying a sphere with radius of 0.9 m. The energy released corresponded to SPE5 shot yield of $${5}\!\!\!^{^{\sim}}$$ tons of TNT equivalent. As spherical waves propagate through the joints they trigger sliding at the joints oriented at small angle to propagation directions. For two joint sets the horizontal plane is divided into eight segments which preserve the polarity with pressure wave expanding radially. Fig. 9 present polarity of tangential motion for two different times and two different joint cohesions. In the case of zero joint cohesion (panel a), the joints can slide at both sets in many locations. Polarity may change rapidly from closely located points. For a higher cohesion (C = 15 MPa, panel b) there are well defined sectors of polarity not only for the first tangential motion arriving with the pressure wave but for the subsequent motion when polarity is reversed. The joints stop sliding at ranges more than 25 m. Most of tangential motion is caused by the joint sliding. Accounting for joint compliance changes results by a few per cent. Fig. 10 compares polarities of the tangential motion caused by either elastic or plastic anisotropy. When the joint cohesion was set to a very large number, the magnitude of tangential motion was smaller due to elastic anisotropy caused by smaller stiffness in two directions normal to the joints. Sections of similar polarity in this case are much smaller and are located behind the pressure wave at some distance. For sliding stiff joints much wider sectors of tangential motion are observed which follow the pressure wave with a smaller constant delay. Figure 9. View largeDownload slide Polarity of tangential motion at 5 ms and 9 ms at shot level for zero joint cohesion (a) and 15 MPa cohesion (b). Clockwise motion (positive) is shown with red and counter-clockwise motion is shown with blue. Joints with plastic slip are shown with black lines. Figure 9. View largeDownload slide Polarity of tangential motion at 5 ms and 9 ms at shot level for zero joint cohesion (a) and 15 MPa cohesion (b). Clockwise motion (positive) is shown with red and counter-clockwise motion is shown with blue. Joints with plastic slip are shown with black lines. Figure 10. View largeDownload slide Polarity of tangential motion at 9 ms at shot level for compliant joints with no sliding (a) and non-compliant joints with zero cohesion (b). Clockwise motion (positive) is shown with red and counter-clockwise motion is shown with blue. Figure 10. View largeDownload slide Polarity of tangential motion at 9 ms at shot level for compliant joints with no sliding (a) and non-compliant joints with zero cohesion (b). Clockwise motion (positive) is shown with red and counter-clockwise motion is shown with blue. 3.4 Simulated onset of tangential motion We have plotted velocity time histories recorded at various directions in two different azimuthal directions at ranges 10, 15 and 20 m (E30N and S15W shown in Fig. 9) for joints with small and large cohesion. Figs 11 and 12 show both radial (dashed lines) and tangential velocity histories for these two cases recorded at ranges 10, 15 and 20 m. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. It is clear that the tangential motion follows the radial motion with maximum values being reached after the peak of the radial velocity with some delay. For low joint cohesion we observe more frequent variations in polarity of tangential velocity. High joint cohesion causes high tangential amplitudes at some locations and more monotonic tangential velocity histories. In some cases, the biggest tangential motion is reached after polarity of this motion is reversed and radial velocity is decreased during unloading (see e.g. Fig. 11d). Very low tangential amplitudes are observed at 45 degrees to the joint sets where the sliding on both joint sets produces tangential motions of opposite polarity. A 3-D view of the polarity of the calculated tangential motion is shown in Fig. 13. Figure 11. View largeDownload slide Radial (dashed lies) and tangential velocity evolution calculated at ranges 10, 15 and 20 m in the direction E30N. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. Figure 11. View largeDownload slide Radial (dashed lies) and tangential velocity evolution calculated at ranges 10, 15 and 20 m in the direction E30N. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. Figure 12. View largeDownload slide Radial (dashed lines) and tangential velocity evolution calculated at ranges 10, 15 and 20 m in the direction S15W. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. Figure 12. View largeDownload slide Radial (dashed lines) and tangential velocity evolution calculated at ranges 10, 15 and 20 m in the direction S15W. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. Figure 13. View largeDownload slide Polarity of tangential motion calculated at 10 ms for an explosion in granite with two vertical persistent orthogonal joint sets. Joint cohesion was 15 MPa, joint spacing was 2 m. Figure 13. View largeDownload slide Polarity of tangential motion calculated at 10 ms for an explosion in granite with two vertical persistent orthogonal joint sets. Joint cohesion was 15 MPa, joint spacing was 2 m. 3.5 Effect of joint persistency We have shown above that decreasing joint cohesion at all joints may produce less tangential motion. Joint persistency may have a similar effect, since non persistent joints may be modelled as persistent ones but with variable joint cohesion. Indeed, we have found little change in tangential motion when persistency decreases from the fully persistent case until it reaches 70  per cent. In such cases the magnitude of the tangential motion begins to decrease consistently as shown in Fig. 14 where tangential velocity is plotted on the same scale (from −5 cm s−1 for counter-clockwise motion to 5 cm s−1 for clockwise motion). As joint persistency is reduced to 20 per cent, the amplitude of the tangential motion drops roughly by a factor of 3. Polarity of the first tangential motion remains the same but it seems to attenuate more rapidly beyond the elastic radius where the joints stop sliding. According to SPE site characterization the average joint persistency is approximately 70 per cent (see Townsend et al. 2012), thus we do not expect the results to be significantly different from the fully persistent case. Figure 14. View largeDownload slide Tangential motion calculated at 10 ms for joint persistency 100 per cent (a), 60 per cent (b), 40 per cent (c) and 20 per cent (d). Sliding joints are plotted with bold lines. Figure 14. View largeDownload slide Tangential motion calculated at 10 ms for joint persistency 100 per cent (a), 60 per cent (b), 40 per cent (c) and 20 per cent (d). Sliding joints are plotted with bold lines. 3.6 Effect of variations in joint directions The joints grouped in a joint set do not have the same orientation. Azimuthal directions for the joints which belong to the same joint set may vary within 5–20 degrees. We have conducted a sensitivity study on how these variations may affect the tangential motion. For this purpose, the normal of each joint in a joint set was varied around the direction characterizing this set by some random angle which was less than a maximum deviation angle. Fig. 15 shows tangential motion calculated at time 10 ms on the horizontal plane crossing the source for 3 different maximum deviation angles, 5, 15 and 45 degrees and two different joint cohesions 15 MPa (Figs 15a–c) and 0.15 MPa (Figs 15d–f). We have found that the effect of angular deviation of the joints on the tangential motion is very sensitive to joint cohesion. Thus, for very low cohesion at the joints even deviation in 5 degrees make a significant effect especially for shallow explosions where the initial confinement is small as it is shown in Fig. 15(d). Figure 15. View largeDownload slide Polarity of tangential motion at 10 ms at shot level for joints with cohesion 15 MPa : (a) maximum deviation 5 degrees, (b) 15 degrees and (c) 45 degrees, and joints with cohesion of 0.15 MPa: (d) maximum deviation 5 degrees, (e) 15 degrees and (f) 45 degrees. Sliding joints are plotted with bold black lines. Figure 15. View largeDownload slide Polarity of tangential motion at 10 ms at shot level for joints with cohesion 15 MPa : (a) maximum deviation 5 degrees, (b) 15 degrees and (c) 45 degrees, and joints with cohesion of 0.15 MPa: (d) maximum deviation 5 degrees, (e) 15 degrees and (f) 45 degrees. Sliding joints are plotted with bold black lines. 3.7 Tangential motion in jointed rock with two vertical joint sets from SPE site Now, after completing the analysis of tangential motion generation by two orthogonal joint sets, let us consider more realistic joint set orientations from SPE site. Fig. 16 shows intersection of two joint sets (set #1 and set #3) with the horizontal plane at shot level. Polarity of calculated tangential motion is shown with colours. One can see, that despite the joints being inclined and not orthogonal, the polarity sections generated by the explosion are very similar to the orthogonal case considered in the previous study. Fig. 16 shows some azimuthal directions for SPE4/SPE5 boreholes where the gauges are plotted on top of the calculated polarity picture. According to this, if the joint set is perfectly persistent without variations in joint orientation within each set, we would expect the polarity of the first significant tangential motion to be defined by the joint set directions. Thus, gauges in the well bores #16 and #19 would show negative (counter-clockwise) tangential motion while gauges in the well bores #15 and #18 would show positive polarity. This simplistic model for jointed rock was able to predict polarities for most of the gauges located in the middle of the polarity sections. But, in some azimuthal directions uncertainties in joint orientation can have a dominant effect on the polarity of the tangential motion. For example, for well bores #9 and #11 this model predicts low tangential motion due to sliding on both joint sets. Yet, experiments showed a negative polarity for both locations. Figure 16. View largeDownload slide (a) Joint locations, problem dimensions and polarity of tangential motion. (b) Polarity of tangential motion calculated at shot level for rock mass with two joint sets (set 1 and set 3) at 10 ms. SPE gauge directions are also shown. Figure 16. View largeDownload slide (a) Joint locations, problem dimensions and polarity of tangential motion. (b) Polarity of tangential motion calculated at shot level for rock mass with two joint sets (set 1 and set 3) at 10 ms. SPE gauge directions are also shown. 3.8 Stochastic estimation of radial, vertical and tangential motions for SPE4P and SPE5 Geological characterization of rock mass is often expensive and therefore collected site data are limited and spatially sparse. Furthermore, the ability to map joints and inclusions in the rock with the available geological and geophysical tools tends to decrease with depth and scale of the discontinuity. Geological characterization often encompasses measurements of fracture density, orientation, and aperture. These attributes are then abstracted into probability density functions (PDFs) for predictive stochastic modelling. For example, stochastic discrete fracture network (SDFN) generated using the geological characterization PDFs enables, via Monte Carlo simulations, the probabilistic assessment of physical phenomena that are not adequately captured using continuum and deterministic models. Despite the fundamental uncertainties inherited within the probabilistic reduction of the sparse data collected, SDFN has become a very popular tool to quantify uncertainties in complex geological media (Ezzedine 2005, 2010, and references therein). Hereafter we focus our analyses on SPE4P and SPE5 only, we refer the reader to Ezzedine et al. (2015) for a detailed study of SPE3. In line with Ezzedine et al. (2015), we conducted several Monte Carlo simulations to quantify the mean responses of variables of interest: that is, the radial, tangential and vertical velocities as well their uncertainty spreads. All SDFN realizations were generated independent of each other but conditional to the observed data at the specific boreholes. SDFNs are then embedded into LLNL forward hydrodynamic code GEODYN-L as described in Ezzedine et al. (2015). All simulations were performed on 2400 CPUs and each simulation took up to $${4}\!\!\!^{^{\sim}}$$ hr of CPU time for 50 ms of physical time and required up to 10 GB of storage space. It is worth mentioning that the domain of the numerical simulations for SPE4P and SPE5 has doubled in size compared to SPE3 and that is the main reason the HPC requirements have been augmented. More details regarding the statistical sample size and the convergence of the statistical moments can be found in Ezzedine et al. (2015) and in Vorobiev et al. (2015). We present here the direct application of the SPE3 simulation framework to SPE4P and SPE5. Fig. 17 depicts a subset of random realizations of the SDFN (labelled DNF0-2 and plotted using different colours and thin lines), the observed SPE4P data collected is depicted in a purple thick line while the mean and the 95 per cent confidence interval (CI) of the entire set of the Monte Carlo simulations are depicted in thick red continuous and discontinuous lines, respectively. The history of the radial (R, left column), tangential (T, middle column) and vertical (L, right column) velocities (km s−1) have been plotted for three different borehole gauges #14-1 (bottom row), #15-1 (middle row) and #14-2 (top row), respectively. Similarly, Fig. 18 depicts the same set of curves for SPE5 at borehole gauges #14-2 (bottom row), #15-2 (middle row) and #16-2 (top row), respectively. Figure 17. View largeDownload slide Radial (left column), tangential (middle column) and vertical (right column) velocities (cm s−1) as function of time (milliseconds, ms) at three borehole locations #14-1 (bottom row), #15-1 (middle row) and #14-2 (top row). Thick purple curves are the observed pulses for SPE4P, while the think red curves are the Monte Carlo statistics mean (continuous line labelled A) and the envelop of the 95 per cent confidence lower bound (labelled L) and upper bound (labelled U). Figure 17. View largeDownload slide Radial (left column), tangential (middle column) and vertical (right column) velocities (cm s−1) as function of time (milliseconds, ms) at three borehole locations #14-1 (bottom row), #15-1 (middle row) and #14-2 (top row). Thick purple curves are the observed pulses for SPE4P, while the think red curves are the Monte Carlo statistics mean (continuous line labelled A) and the envelop of the 95 per cent confidence lower bound (labelled L) and upper bound (labelled U). Figure 18. View largeDownload slide Radial (left column), tangential (middle column) and vertical (right column) velocities (cm s−1) as function of time (milliseconds, ms) at three borehole locations #14-2 (bottom row), #15-2 (middle row) and #16-2 (top row). Thick purple curves are the observed pulses for SPE5, while the think red curves are the Monte Carlo statistics mean (continuous line labelled A) and the envelop of the 95 per cent confidence lower bound (labelled L) and upper bound (labelled U). Figure 18. View largeDownload slide Radial (left column), tangential (middle column) and vertical (right column) velocities (cm s−1) as function of time (milliseconds, ms) at three borehole locations #14-2 (bottom row), #15-2 (middle row) and #16-2 (top row). Thick purple curves are the observed pulses for SPE5, while the think red curves are the Monte Carlo statistics mean (continuous line labelled A) and the envelop of the 95 per cent confidence lower bound (labelled L) and upper bound (labelled U). Note that these simulations were conducted without calibration of the model simulations to observations, but using only intact physical and geomechanical properties of the rock measured in the laboratory on core samples collected at the SPE site. It is remarkable that the simulation of wave propagation through the SDFNs embedded in the granite rock matrix shows very good agreements with the experiments. By inspecting both Figs 17 and 18, one can see that the spreads of the modelling results bracket the observed velocities at every depicted location and capture well arrival times and, in average, peak radial and vertical velocities. Despite that tangential velocities are very sensitive to density, orientation and persistency of joints, as it has thoroughly been demonstrated in Ezzedine et al. (2015) and in Vorobiev et al. (2015), it is remarkable that the spread of the uncertainty in the predictions covers considerably well the observed tangential spread due to polarity changes from positive to negative values and vice-versa, which underscores further that the genesis of shear motions is mainly due to the presence of the joints. 4 DISCUSSION The latest SPE tests showed that significant shear motion was generated in the near-field. The test site geology was favourable to investigate tangential motion generated during underground chemical explosions because of insignificant spatial variations in mechanical properties of granite, flat site topography and thorough pre and post shot geological characterization done at the site. All SPE tests show radial motion consistent with the historic tests performed in the same granite formation in the past. Tangential motion was observed both at shot depth and at the surface. The peak tangential velocity can reach 30–40 per cent of the radial one in the near-field. The ratio of tangential to radial velocity magnitudes tends to grow with range. Tangential velocity changes polarity with time at least once. Similar to observations done by Kisslinger et al. (1961), initial high frequency tangential motion often is followed by lower frequency but higher magnitude motion of reversed polarity. Also, similar to observations in Kisslinger et al. (1961), polarity of tangential motion in opposite azimuthal directions may seem to be reversed. In reality, it depends on how the opposite directions are selected relative to joints directions. For example, directions #18 and #19 (Fig. 16) show opposite polarities but directions L1 and L3 would show the same polarity in tangential motion. Experiments showed that recorded tangential motion is similar in the same azimuthal direction even for different dip angles. This was also confirmed in calculations which showed that the vertical joints define azimuthal directions with constant polarity for the tangential motion. Thus, polarity of this motion can be predicted for persistent joints with small variation in joint directions. Tangential motion always follows the radial one with some delay, which varies for each gauge location. We believe that this delay is related to local joint conditions. As it was shown in Vorobiev et al. (2015), it may be controlled by joint cohesion and friction in the vicinity of the gauge. Increasing joint cohesion from a very low level may enhance observed tangential motion when multiple joint sets are present. This is due to competition between various joint sets which may cause sliding in opposite directions when sliding conditions are reached on differently oriented joints for low cohesion. By increasing joint cohesion, this condition is reached only at the joints preferably oriented towards the sliding direction. Increasing it even more will suppress the sliding and thus reduce the tangential motion. We have found, that for randomly oriented joints on the scale of the wave length with small cohesion very little tangential motion would be generated. Vertical motion at shot level seems to correlate with the orientation of the low dip angle joints, which are the most effective at deflecting the horizontal motion up or down depending on the azimuth. Enhancement of the vertical motion in some azimuthal direction may be responsible for asymmetry of the vertical surface displacement observed around ground zero. We conducted computational studies on ground motion from underground explosions in jointed rock masses using realistic rock and joint models. The results of this study help to explain anisotropy in ground motion observed at SPE site and relate it to the geological site characterization. We have found correlations between the joint properties and observed tangential motion in the near-field. According to the present work joint sliding is the dominant factor responsible for tangential motion generation within the elastic radius. Beyond the elastic radius, elastic anisotropy provides an additional mechanism to convert the radial motion into the tangential motion. Here, elastic radius is defined as a range from the source beyond which both rock and joints exhibit elastic mechanical response. For joint cohesion of 15 MPa elastic radius is defined by the joints and is roughly 15m/t1/3. The method used in the near-field where the mesh size is controlled by the joint spacing is not practical at seismic distances. We hope that results of this study will be useful to develop a source model for seismic codes which will include not only radial but also tangential motion for jointed rock masses. The seismic codes with the validated source term can be used to propagate signals to large distances (tens and hundreds of kilometres). Acknowledgements The work was performed under the auspices of the US Department of Energy by University of California, Lawrence National Laboratory under Contract W-7405-Eng-48. The work was supported by National Nuclear Security Administration under contract DE-AC52-07NA27344. REFERENCES Babich V.M., Kiselev A.P., 1989. Non-geometrical waves–are there any? an asymptotic description of some ‘non-geometrical’phenomena in seismic wave propagation, Geophys. J. Int. , 99( 2), 415– 420. Google Scholar CrossRef Search ADS   Crampin S., 1981. A review of wave motion in anisotropic and cracked elastic-media, Wave motion , 3( 4), 343– 391. Google Scholar CrossRef Search ADS   Ezzedine S., 2010. Impact of geological characterization uncertainties on subsurface flow using stochastic discrete fracture network models, in Annual Stanford Workshop on Geothermal Reservoir Engineering , Stanford. Ezzedine S., Vorobiev O., Glenn L., Antoun T., 2015. Application of HPC and non-linear hydrocodes to uncertainty quantification in subsurface explosion source physics, in 49th US Rock Mechanics/Geomechanics Symposium , San Francisco, CA, American Rock Mechanics Association. Ezzedine S.M., 2005. Stochastic modeling of flow and transport in porous and fractured media, in Encyclopedia of Hydrological Sciences , Wiley Online Library. Google Scholar CrossRef Search ADS   Hirakawa E., Pitarka A., Mellors R., 2016. Generation of shear motion from an isotropic explosion source by scattering in heterogeneous media, Bull. seism. Soc. Am. , 106( 5), 2313– 2319 Google Scholar CrossRef Search ADS   Hoek E., Brown E., 1997. Practical estimates of rock mass strength, Int. J. Rock Mech. Min. Sci. , 34( 8), 1165– 1186. Google Scholar CrossRef Search ADS   Hurley R., Vorobiev O., Ezzedine S., 2017. An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints, Comput. Mech. , 60( 2), 235– 252. Google Scholar CrossRef Search ADS   Kisslinger C., Mateker E.J., McEvilly T.V., 1961. SH motion from explosions in soil, J. geophys. Res. , 66( 10), 3487– 3496. Google Scholar CrossRef Search ADS   Lash C., 1985. Shear waves produced by explosive sources, Geophysics , 50( 9), 1399– 1409. Google Scholar CrossRef Search ADS   Liu C.L., Ahrens T.J., 1998. Wave generations from confined explosions in rocks, AIP Conf. Proc. , 429( 1), 859– 862. Mandal B., Toksöz M., 1990. Computation of complete waveforms in general anisotropic media—results from an explosion source in an anisotropic medium, Geophys. J. Int. , 103( 1), 33– 45. Google Scholar CrossRef Search ADS   Murphy J., Barker B., Sultanov D., Kuznetsov O., 2009. S-wave generation by underground explosions: Implications from observed frequency-dependent source scaling, Bull. seism. Soc. Am. , 99( 2A), 809– 829. Google Scholar CrossRef Search ADS   Oda M., Yamabe T., Kamemura K., 1986. A crack tensor and its relation to wave velocity anisotropy in jointed rock masses, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. , 23, 387– 397. Google Scholar CrossRef Search ADS   Perret W.R., Bass R.C., 1975. Free-field ground motion induced by underground explosions, Tech. rep. , Sandia Labs., Albuquerque, NM, USA. Randall M.J., 1962. Generation of horizontally polarized shear waves by underground explosions, J. geophys. Res. , 67, 4956– 4957. Google Scholar CrossRef Search ADS   Salvado C., Minster J.B., 1980. Slipping interfaces: a possible source of s radiation from explosive sources, Bull. seism. Soc. Am. , 70( 3), 659– 670. Steedman D.W., Bradley C.R., Rougier E., Coblentz D.D., 2016. Phenomenology and modeling of explosion-generated shear energy for the source physics experiments, Bull. seism. Soc. Am. , 106( 1), 42– 53. Google Scholar CrossRef Search ADS   Townsend M., Obi C., 2014. Data release report for Source Physics Experiments 2 and 3 (SPE-2 and SPE-3), Nevada National Security Site, National Security Technologies Technical Report DOE/NV/25946-2282. Townsend M., Prothro L., Obi C., 2012. Geology of the Source Physics Experiment site, climax stock, Nevada National Security Site, Tech. rep. , NTS. Tsvankin I., 2012. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media , no. 19, SEG Books. Tsvankin I., Grechka V., 2011. Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization , Society of Exploration Geophysicists. Google Scholar CrossRef Search ADS   Vorobiev O., 2008. Generic strength model for dry jointed rock masses, Int. J. Plast. , 24( 12), 2221– 2247. Google Scholar CrossRef Search ADS   Vorobiev O., 2010. Discrete and continuum methods for numerical simulations of non-linear wave propagation in discontinuous media, Int. J. Numer. Methods Eng. , 83( 4), 482– 507. Vorobiev O., 2012. Simple Common Plane contact algorithm, Int. J. Numer. Methods Eng. , 90( 2), 243– 268. Google Scholar CrossRef Search ADS   Vorobiev O., Ezzedine S., Antoun T., Glenn L., 2015. On the generation of tangential ground motion by underground explosions in jointed rocks, Geophys. J. Int. , 200( 3), 1651– 1661. Google Scholar CrossRef Search ADS   White J., Sengbush R., 1963. Shear waves from explosive sources, Geophysics , 28( 6), 1001– 1019. Google Scholar CrossRef Search ADS   Wright J.K., Carpenter E.W., 1962. The generation of horizontally polarized shear waves by underground explosions, J. geophys. Res. , 67( 5), 1957– 1963. Google Scholar CrossRef Search ADS   Zhang H., Zhu J., Liu Y., Xu B., Wang X., 2012. Strength properties of jointed rock masses based on the homogenization method, Acta Mech. Solida Sin. , 25( 2), 177– 185. Google Scholar CrossRef Search ADS   © The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press

Near-field non-radial motion generation from underground chemical explosions in jointed granite

Loading next page...
 
/lp/ou_press/near-field-non-radial-motion-generation-from-underground-chemical-VQ5gV6KryB
Publisher
The Royal Astronomical Society
Copyright
© The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society.
ISSN
0956-540X
eISSN
1365-246X
D.O.I.
10.1093/gji/ggx403
Publisher site
See Article on Publisher Site

Abstract

Abstract This paper describes analysis of non-radial ground motion generated by chemical explosions in a jointed rock formation during the Source Physics Experiment (SPE). Such motion makes it difficult to discriminate between various subsurface events such as explosions, implosions (i.e. mine collapse) and earthquakes. We apply 3-D numerical simulations to understand experimental data collected during the SPEs. The joints are modelled explicitly as compliant thin inclusions embedded into the rock mass. Mechanical properties of the rock and the joints as well as the joint spacing and orientation are inferred from experimental test data, and geophysical and geological characterization of the SPE site which is dominantly Climax Stock granitic outcrop. The role of various factors characterizing the joints such as joint spacing, frictional properties, orientation and persistence in generation of non-radial motion is addressed. The joints in granite at the SPE site are oriented in nearly orthogonal directions with two vertical sets dipping at 70–80 degrees with the same strike angle, one vertical set almost orthogonal to the first two and one shallow angle joint set dipping 15 degrees. In this study we establish the relationship between the joint orientation and azimuthal variations in the polarity of the observed shear motion. The majority of the shear motion is generated due to the effects of non-elastic sliding on the joints near the source, where the wave can create significant shear stress to overcome the cohesive forces at the joints. Near the surface the joints are less confined and are subject to sliding when the pressure waves are reflected. In the far field, where the cohesive forces on the joints cannot be overcome, additional shear motion can be generated due to elastic anisotropy of the rock mass given by preferred spatial orientations of compliant joints. Geomechanics, transient deformation, numerical modeling, wave propagation 1 INTRODUCTION In this study we present the analysis of ground motion caused by underground explosions in granite observed during the Source Physics Experiment (SPE) conducted and the Nevada National Security Site (NNSS), formerly known as the Nevada Test Site (NTS). One of the main goals of this experiment was to understand the nature of non-radial ground motions observed during underground explosions. From a modelling perspective, the main difficulty of this problem is due to the nonlinear material responses in the vicinity of the explosive source where the ground motion is very sensitive to the dynamic strength of rock mass. The strength of the rock mass is significantly smaller than the strength of small intact rock samples measured at the lab due to the presence of meso and macro scale traces of cracks and joints. In rock mechanics and engineering various measures of strength degradation are used to scale the strength from the intact sample to heavily jointed rock masses (see e.g. Hoek & Brown 1997). Yet, such strength scaling still assumes that the rock mass strength remains isotropic. In hard rock formations, joints are distributed in family of sets which are not randomly oriented. It has been shown (e.g. Oda et al. 1986; Tsvankin 2012, and references therein) that such jointed rock masses behave as an anisotropic elastic-plastic medium with a pressure dependent yield surface. The shape of this surface can be found numerically for a representative volume given properties of the intact rock and properties and orientations of the joints for a given deformation history (see e.g. Vorobiev 2008; Zhang et al. 2012). In the far field, where material response can be considered elastic, anisotropy in elastic properties related to the joint orientation plays a role in polarization of the waves and the generation of shear motion. Wave propagation in elastic media with anisotropy has been studied in the past. Seismological applications of wave propagation in anisotropic media are reviewed in Crampin (1981). Tsvankin & Grechka (2011); Tsvankin (2012) studied wave propagation in geologic media with orthorhombic anisotropy corresponding to jointed rock masses. In this work we are focused on the non-radial motion generated in the near-field. Shear wave generation observed in underground explosions has been an area of interest during the last decades (Kisslinger et al. 1961; Wright & Carpenter 1962; Randall 1962; White & Sengbush 1963; Salvado & Minster 1980; Lash 1985; Babich & Kiselev 1989; Liu & Ahrens 1998; Mandal & Toksöz 1990; Murphy et al. 2009; Hirakawa et al. 2016). In Vorobiev et al. (2015) sliding on the joints was identified as the main mechanism responsible for generation of tangential ground motion in the near-field from a spherically symmetric source. Numerical simulations showed that tangential motion observed in the near-field during Source Physics Experiment SPE3 can be explained by plastic slip on the joint surfaces. In this work, we extend our analysis to the latest tests SPE4P and SPE5 which have also shown significant shear motion around the source. In fact, the new experimental data provide enough information to further validate our hypothesis that near-field tangential motion is caused by the joints present in rock formations. We show that given the joint set orientation and spacing one can predict both the magnitude of the shear motion and the azimuthal variations in polarity of the tangential motion. Even though the SPE site is well studied, there is still significant uncertainty in joint distribution between the boreholes where they were characterized as well as in the measurements of the mechanical properties of the joints. Therefore, stochastic methods are needed to predict ground motion with confidence at multiple locations. Recently we have demonstrated that using stochastic approaches it is possible to predict the expected ground motion for SPE (e.g. Ezzedine et al. 2015). Furthermore, we also study the relationship between the joint distribution, joint mechanical properties and apparent mechanical anisotropy of the rock mass. We investigate the role of both sliding on the joints and elastic anisotropy introduced by preferred orientation of the compliant joints. In our computational study we apply isotropic plasticity for rock blocks and additional constitutive laws for the joints to understand mechanical anisotropy at the large scale. With joint aperture on the order of 1 mm, joint spacing approximately 1 m, the wave length on the order of 100 m and the problem size is approximately 1 km, the study of such anisotropy presents a daunting computational challenge. Here we rely on advanced numerical techniques to model diverse spatial and temporal scales as well as on high performance parallel computing (HPC) capabilities available at Lawrence Livermore National Laboratory (LLNL). Detailed computational models of realistic rock formations can be achieved using in-site geological characterization data. We applied the 3-D massively parallel hydrocode GEODYN-L (Vorobiev 2012) to perform the numerical simulations of nonlinear wave generation and propagation in heavily jointed rock masses. To understand experimental observations reviewed in Section 2, we conduct multiple simulations of ground motion caused by underground chemical explosions. Results of the study of various effects of rock joints on the ground motion are presented in Section 3. 2 EXPERIMENTAL OBSERVATIONS 2.1 SPE underground chemical explosions in granite Six chemical explosions of different yields have been conducted during the first phase of SPE. All SPE explosions were conducted at the same site in the same well but at different depths over the last 5 yr at NNSS. The site was characterized before and after the shots. Details of the experiments and geological characterization of the site can be found in Townsend & Obi (2014). Granite samples were excavated from multiple wells and tested in laboratories. The tests have shown fairly uniform mechanical properties which did not change significantly with depth. Unconfined compressive strength (UCS) was in the range 100–200 MPa and ultrasonic sound speed was 5–6 km s−1. Additionally, rock joints excavated with the sample were tested to determine their mechanical properties. Joints were characterized in each borehole at the site to determine the joints spacing and orientations. The Climax stock is moderately to highly fractured. Using data from cores and logs, geologists have identified four sets of natural fractures based on fracture orientation. Three of these (Sets 1, 2 and 3) have high dip angles, and one (Set 4) has very low dip angles (0–30 degrees east). Sets 1 and 2 both strike west–northwest (285–310 degrees azimuth) but have opposite dip directions. Set 3 strikes north–northeast (010–055 degrees azimuth) and dips to the east–southeast. Set 4, the low-angle set, is by far the most ubiquitous of the four fracture sets (Townsend et al. 2012). For the present study both set 1 and 2 were combined to a single joint set leading to 3 sets of joints in total. Ground motion was measured both at various depths and ranges and at the surface in various azimuthal directions using accelerometers which measured three components: radial (R), vertical (L) and tangential (T) in a frequency range of 10–1000 Hz. Measures were taken to ensure that the gauges were properly aligned and coupled to the ground. After the first SPE shot, SPE1, has been executed it has been revealed that few gauges have been, unfortunately, rotated during the installation (see Townsend & Obi 2014; Steedman et al. 2016). In the current analyses we are not using data from gauges which may have been rotated. Locations of accelerometers are depicted in Fig. 1. Vertical ground motion was also measured at the surface in 5 azimuthal directions L1–L5 (shown in Fig. 1b) with 100 m interval. Figure 1. View largeDownload slide Near-field gauge locations for SPE shots: circles —SPE1, SPE2, SPE3 shots, squares—SPE4P shot, triangles—SPE5 shot, solid squares—surface gauges. Figure 1. View largeDownload slide Near-field gauge locations for SPE shots: circles —SPE1, SPE2, SPE3 shots, squares—SPE4P shot, triangles—SPE5 shot, solid squares—surface gauges. The first shot, SPE1, was conducted at depth 55 m and had a yield of 0.1 ton TNT equivalent. The second shot, SPE2 had 10 times bigger yield and was centred at 45.5 m depth. The third shot, SPE3, was conducted at the same location as the second one and had similar yield. It is worth noting that the slight difference between SPE2 and SPE3 yields is approximately 10 per cent. The goal of SPE2 and SPE3 is to investigate the role of damage on the observable ground motion in subsequent shots. SPE4P was conducted at depth 87 m and had a yield equal to that of SPE1. The biggest yield shot, SPE5, was conducted at depth 76 m and had a yield of 5 ton. It is worth noting that the scaled depth of burial for shots SPE3 and SPE5 was almost the same and equal to 447 m/kT1/3. This made it possible to directly compare the surface motions of these two shots, SPE3 and SPE5. Not surprisingly, similar to ones observed in historic nuclear tests, significant shear motion was detected in all SPE shots. Therefore, SPE chemical explosions provide a unique opportunity to test various hypotheses behind the nature of these motions and their geneses. It was suggested after the first three shots that the joints in the granite formations were the main cause of the observed shear motion (see Vorobiev et al. 2015; Steedman et al. 2016). Not surprisingly, two of the last SPE shots, SPE4P and SPE5, have underscored and confirmed this hypothesis. Understanding the nature of shear motion may allow us to build source models for the seismic codes to predict far-field ground motion in the event of underground explosions in jointed rocks. In the following subsections, we present the latest observations and analysis of the ground motions in the near-field up to 1000 m/kT1/3. 2.2 Experimental peak radial and tangential velocity attenuation Fig. 2 presents peak radial and tangential velocity attenuation versus scaled range for various SPE shots. On average, the peak tangential velocity is about 15 per cent of the peak radial velocity but in some locations it reaches as high as 30–40 per cent. The colours for the markers in Fig. 2(a) correspond to the sinus of the angle between a horizontal line and the direction to the gauge. Thus, the gauges above the shot level are shown in red while below the shot level are shown in blue. The solid line designates the legacy nuclear data fit (Perret & Bass 1975). Figure 2. View largeDownload slide (a)Near-field radial and tangential peak velocity attenuation for various SPE shots. Solid line is the fit based on published nuclear tests; dashed lines are power-law fits for radial and tangential velocities; dotted lines are their ratio. Point colour designates vertical direction towards the gauge. (b) Radial velocity attenuation for SPE shots where the marker colour corresponds to tangential-to-radial velocity ratio. Figure 2. View largeDownload slide (a)Near-field radial and tangential peak velocity attenuation for various SPE shots. Solid line is the fit based on published nuclear tests; dashed lines are power-law fits for radial and tangential velocities; dotted lines are their ratio. Point colour designates vertical direction towards the gauge. (b) Radial velocity attenuation for SPE shots where the marker colour corresponds to tangential-to-radial velocity ratio. We have found that power-law fits for both peak velocities as functions of scaled range. For radial velocities, average peak velocity can be expressed as 31925 R−1.813 m s−1, while for tangential velocities, the peak velocity can be expressed as 1676 R−1.594 m s−1, where the scaled range, R, is in m/kT1/3. The ratio of these fits (tangential to radial) grows with scaled range (plotted with the dotted line in Fig. 2a). It is interesting to note that the gauges with a high ratio of observed tangential velocity to the radial velocity often record below average radial velocity, as shown in Fig. 2(b). This can be explained by redirection of part of the radial motion into tangential motion. This growth of tangential motion is especially noticeable at the surface, where the tangential velocity very often has similar or even larger magnitude than radial velocity. Fig. 3 shows peak tangential (large solid markers) and radial (large empty markers) velocities measured at the far-field geophone lines, L1 through L5, at the surface in various azimuthal directions (directions for these gauges are designated in Fig. 1). The curves plotted on top of the markers are power-law fits for peak radial (solid line) and tangential velocities found for deep gauges. The small markers in Fig. 3 (which are also plotted in Fig. 2) are peak velocity data for the gauges at 15 m depth. It is seen that at the same scaled range (about 1000 m/kT1/3) tangential velocities at the surface are significantly higher than at depth. Other factors such as topography and presence of a dry weathered granite layer at the surface may have contributed to the enhancement of this motion. Figure 3. View largeDownload slide Radial and tangential surface motion recorded at L gauges. Solid line—power-law fit for peak radial velocities for the deep gauges; dotted line—power-law fit for peak tangential velocities for the deep gauges; small markers—peak radial and tangential velocities for some deep gauges measured during SPE4P shot. Figure 3. View largeDownload slide Radial and tangential surface motion recorded at L gauges. Solid line—power-law fit for peak radial velocities for the deep gauges; dotted line—power-law fit for peak tangential velocities for the deep gauges; small markers—peak radial and tangential velocities for some deep gauges measured during SPE4P shot. 2.3 Observed onset of tangential motion In many gauge locations the onset of tangential motion was coincident with the arrival of the radial motion for large amplitude shots (SPE3, SPE5). Yet, at the same locations, tangential motion was delayed for the lower magnitude SPE4P shot. This can be explained by insufficient shear stress on the joints during SPE4P when radial motion arrives, inhibiting plastic slip in the vicinity of the gauge. Fig. 4 shows recorded motion at station #15-1 in both SPE4P and SPE5 shots. As we have shown in Vorobiev et al. (2015), the delay of tangential motion relative to radial motion is controlled by the joint cohesion. Also, the maximum tangential velocity was often observed later during the unloading phase of the pulse. The polarity of tangential motion changes multiple times. As observed in the past (see e.g. Kisslinger et al. 1961), the high frequency tangential motion is often followed by a low frequency motion which sometimes reaches higher magnitudes. We have found this to be the case especially for the low yield shots or farther from the source. This can be explained by higher shear strength for joints confined by the compressive radial motion. As the pressure drops during the unloading phase, joints are more likely to start sliding because of reduced shear strength. Fig. 4 shows that for SPE4P the larger tangential motion always comes after the compressive pulse passes, when the joint compression is reduced, while for SPE5 the maximum tangential motion is observed simultaneously with the compressive phase. Tangential motions recorded during SPE4P and SPE5 at the same gauges seem to have the same polarity. This indicates that the polarity of this motion is mainly controlled by the azimuthal direction of the gauge rather than the shot depth. Figure 4. View largeDownload slide Radial (solid) and tangential (dashed) motion recorded at stations #15-1, #19-1 and #19-2 during SPE4 (on the right) and SPE5 (on the left) shots. Figure 4. View largeDownload slide Radial (solid) and tangential (dashed) motion recorded at stations #15-1, #19-1 and #19-2 during SPE4 (on the right) and SPE5 (on the left) shots. 2.4 Azimuthal variations of tangential motion We have found that tangential motion measured at various ranges but in the same azimuthal directions very often look similar. For example, for SPE5, the first tangential motion at all gauges located in wells #9 and #11 are always counter-clockwise (see Figs 5a and c) even though they are located at various ranges and depths. Negative polarity of the first tangential motion was also observed at these stations during SPE3, as shown in Figs 5(b) and (d). Figure 5. View largeDownload slide Tangential motion recorded in the same azimuthal direction at stations located in wells #9 and #11 for SPE5 (a,c) and SPE3 (b,d) shots. Figure 5. View largeDownload slide Tangential motion recorded in the same azimuthal direction at stations located in wells #9 and #11 for SPE5 (a,c) and SPE3 (b,d) shots. Fig. 6 shows tangential motion recorded at different ranges in two opposite directions: north (#16-1 at 20 m range and #19-1 at 45 m range) and southwest (#15-1 at 20 m range and #18-1 at 34 m range). Both SPE4P and SPE5 shots seems to show this trend. Polarity of tangential motion may look reversed for the gauges located in opposite directions (see e.g. #18-1 vs. #19-1 in Fig. 6). Polarity reversal was also observed in the past during analysis of shear motion (see Kisslinger et al. 1961). Figure 6. View largeDownload slide Tangential motion recorded in the same azimuthal directions at stations #19-1,#16-1 (north) and #18-1,#15-1 (south) during SPE5 (a,c) and SPE4P (b,d) shots. Figure 6. View largeDownload slide Tangential motion recorded in the same azimuthal directions at stations #19-1,#16-1 (north) and #18-1,#15-1 (south) during SPE5 (a,c) and SPE4P (b,d) shots. 2.5 Vertical and tangential motion at shot level In Vorobiev et al. (2015) we have shown that vertically oriented joints are mainly responsible for generating a significant tangential motion in jointed granite. In this work we have also observed vertical motion at shot level which should not be present if the material is behaving isotropically. We have found that both in the historic shots (e.g. Piledriver, Hardhat) and recent SPE experiments such motion was observed. If sliding on the joints were responsible for such motion it would be observed to the same extend as the tangential motion. Joints with low dip angle would have caused the vertical motion since their normal direction (which favours the wave propagation) is more aligned with the vertical direction. Fig. 7 shows observed vertical motion for SPE3 experiment at gauges #7-2, #8-2 (southwest direction from the ground zero) and #11-2 and #9-5 (northeast), for SPE4P experiment at gauges #18-2 and #19-2, for SPE5 experiment at gauges #19-4 and #18-4. Vertical velocity histories are shown for some of these gauges. The arrows designate observed dip directions for shallow angle joints at each borehole (joint set #4). The longer the arrow, the higher the prevalence of joint dipping. It is seen from the picture that most of joints dip in the northeastern direction. This may explain why the initial vertical motion detected at gauges in the northeastern direction was upwards while for the gauges located in the southwestern direction the first motion was downwards. The mechanism of the generation of such motion is explained on the side view where both the joints and the gauges are shown. It is remarkable that for all shots performed at different depths the direction of vertical motion agrees with the dipping direction of the shallow angle joints. Figure 7. View largeDownload slide Gauge location and observed polarity of vertical motion at shot level plotted on top of the areal photo. Measured dip directions for shallow angle dipping joints are shown with arrows next to well locations. Gauge locations with upward movement are shown in green colour and with downward movement are shown in red. Velocity histories for some gauges are also shown. Figure 7. View largeDownload slide Gauge location and observed polarity of vertical motion at shot level plotted on top of the areal photo. Measured dip directions for shallow angle dipping joints are shown with arrows next to well locations. Gauge locations with upward movement are shown in green colour and with downward movement are shown in red. Velocity histories for some gauges are also shown. 3 NUMERICAL MODELLING OF GROUND MOTION 3.1 Modelling assumptions We have performed 3-D modelling of ground motion for the SPE shots. Material model calibration for granite was described in Vorobiev et al. (2015). UCS was 128 MPa, density was 2.643 g cc−1 and the porosity was assumed to be 1 per cent. We modelled the source as an instant energy deposition in an ideal gas of the same density and internal energy as the high explosive used in the shots. The shape of the source canister was cylindrical as described in Townsend & Obi (2014). The radius of the cylindrical canisters used in the experiments is $${1}\!\!\!^{^{\sim}} 5$$ inches but the canister length varied from shot to shot. Indeed, numerical study has shown little effect on the energy release rate within the source , whether cylindrical or spherical source shape, on the shock wave generation. Therefore, in this study we assumed that energy within the source was instantly released in an equivalent spherical source. This helped to reduce computational cost because the radius of the cylinder is few times smaller than the radius of the sphere with the same volume and thus coarser mesh could be employed to resolve the source. The joints were assumed to be planar inclusions with finite extent and were represented by a centre and an orientation normal vector in each element intersected by joints. In our earlier work only a single joint was allowed per each finite volume (for details see Vorobiev 2010). Currently we have extended the model to support multiple joints crossing a single numerical element (Hurley et al. 2017). Gravity initialization was used to pre-stress both the rock and the joints to a stress state defined by overburden pressure (vertical stress). We also assumed that both horizontal stresses were assumed to be equal to the vertical stress. 3.2 Peak radial and tangential velocity attenuation We have performed 3-D simulations of the latest SPE experiments using the modelling assumptions described above. Stochastic realizations of joint distributions based on in-situ characterization were used in these calculations. Details on the joint generation for these calculations were published in Vorobiev et al. (2015) and in Ezzedine et al. (2015); and we refer the reader to the last subsection of the present section for more details. For each stochastic realization, simulations have shown both azimuthal variations in radial velocities and significant tangential motion generated at various ranges. Fig. 8 shows attenuation for peak radial and tangential velocities calculated in one of these realization to emphasize the mechanisms for energy conversion and shear motion polarization. Solid lines represent the best power-law fits to the results. The ratio of peak tangential and radial velocities is plotted with dotted lines next to the experimental ones. It is interesting to note that in both cases this ratio has a tendency to grow with range. However we observe a discrepancy between the calculated and the simulated attenuation curves. Calculations also reveal the main mechanisms behind this trend. Joint sliding is mainly responsible for energy redirection from radial to non-radial motion within the elastic radius region. Beyond the elastic radius, elastic anisotropy is the main cause of radial energy scattering. The extent of the elastic radius depends mainly on the slipping conditions at the joints, which in turn depend on the overburden pressure which depends on depth, water saturation and joint cohesion. Figure 8. View largeDownload slide Calculated radial and tangential peak velocity attenuation for SPE4P and SPE5 shots. Solid lines are power-law fits for radial and tangential velocities, dotted lines is their ratio. Point colour represents the ratio of peak velocities. Figure 8. View largeDownload slide Calculated radial and tangential peak velocity attenuation for SPE4P and SPE5 shots. Solid lines are power-law fits for radial and tangential velocities, dotted lines is their ratio. Point colour represents the ratio of peak velocities. 3.3 Study of azimuthal variations of tangential motion in a medium with two orthogonal vertical joint sets Vertical joints at SPE site can be grouped into four sets (Townsend et al. 2012). Two of these sets dip in opposite directions with 70–80 degree angle. For simplicity, they can be replaced by a single vertical joint set. The third joint set is almost orthogonal to the first two and has a high dip angle as well. In order to understand how the shear motion is generated in jointed granite during the spherical explosion let us consider a perfectly symmetric system with two vertical orthogonal joint sets spanning from east to west and from south to north. The size of the domain was 100 × 100 × 100 m, the joint spacing was 2 m. The joint aperture was taken to be 2 mm, initial joint normal stiffness was set to 0.1 GPa, joint friction coefficient was 0.35 and the joint cohesion was varied from 0 to 15 MPa. The source was modelled as an ideal gas with initial density of 1.711 g cc−1 and initial specific energy of 5.55 kJ g−1 occupying a sphere with radius of 0.9 m. The energy released corresponded to SPE5 shot yield of $${5}\!\!\!^{^{\sim}}$$ tons of TNT equivalent. As spherical waves propagate through the joints they trigger sliding at the joints oriented at small angle to propagation directions. For two joint sets the horizontal plane is divided into eight segments which preserve the polarity with pressure wave expanding radially. Fig. 9 present polarity of tangential motion for two different times and two different joint cohesions. In the case of zero joint cohesion (panel a), the joints can slide at both sets in many locations. Polarity may change rapidly from closely located points. For a higher cohesion (C = 15 MPa, panel b) there are well defined sectors of polarity not only for the first tangential motion arriving with the pressure wave but for the subsequent motion when polarity is reversed. The joints stop sliding at ranges more than 25 m. Most of tangential motion is caused by the joint sliding. Accounting for joint compliance changes results by a few per cent. Fig. 10 compares polarities of the tangential motion caused by either elastic or plastic anisotropy. When the joint cohesion was set to a very large number, the magnitude of tangential motion was smaller due to elastic anisotropy caused by smaller stiffness in two directions normal to the joints. Sections of similar polarity in this case are much smaller and are located behind the pressure wave at some distance. For sliding stiff joints much wider sectors of tangential motion are observed which follow the pressure wave with a smaller constant delay. Figure 9. View largeDownload slide Polarity of tangential motion at 5 ms and 9 ms at shot level for zero joint cohesion (a) and 15 MPa cohesion (b). Clockwise motion (positive) is shown with red and counter-clockwise motion is shown with blue. Joints with plastic slip are shown with black lines. Figure 9. View largeDownload slide Polarity of tangential motion at 5 ms and 9 ms at shot level for zero joint cohesion (a) and 15 MPa cohesion (b). Clockwise motion (positive) is shown with red and counter-clockwise motion is shown with blue. Joints with plastic slip are shown with black lines. Figure 10. View largeDownload slide Polarity of tangential motion at 9 ms at shot level for compliant joints with no sliding (a) and non-compliant joints with zero cohesion (b). Clockwise motion (positive) is shown with red and counter-clockwise motion is shown with blue. Figure 10. View largeDownload slide Polarity of tangential motion at 9 ms at shot level for compliant joints with no sliding (a) and non-compliant joints with zero cohesion (b). Clockwise motion (positive) is shown with red and counter-clockwise motion is shown with blue. 3.4 Simulated onset of tangential motion We have plotted velocity time histories recorded at various directions in two different azimuthal directions at ranges 10, 15 and 20 m (E30N and S15W shown in Fig. 9) for joints with small and large cohesion. Figs 11 and 12 show both radial (dashed lines) and tangential velocity histories for these two cases recorded at ranges 10, 15 and 20 m. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. It is clear that the tangential motion follows the radial motion with maximum values being reached after the peak of the radial velocity with some delay. For low joint cohesion we observe more frequent variations in polarity of tangential velocity. High joint cohesion causes high tangential amplitudes at some locations and more monotonic tangential velocity histories. In some cases, the biggest tangential motion is reached after polarity of this motion is reversed and radial velocity is decreased during unloading (see e.g. Fig. 11d). Very low tangential amplitudes are observed at 45 degrees to the joint sets where the sliding on both joint sets produces tangential motions of opposite polarity. A 3-D view of the polarity of the calculated tangential motion is shown in Fig. 13. Figure 11. View largeDownload slide Radial (dashed lies) and tangential velocity evolution calculated at ranges 10, 15 and 20 m in the direction E30N. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. Figure 11. View largeDownload slide Radial (dashed lies) and tangential velocity evolution calculated at ranges 10, 15 and 20 m in the direction E30N. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. Figure 12. View largeDownload slide Radial (dashed lines) and tangential velocity evolution calculated at ranges 10, 15 and 20 m in the direction S15W. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. Figure 12. View largeDownload slide Radial (dashed lines) and tangential velocity evolution calculated at ranges 10, 15 and 20 m in the direction S15W. Tangential velocity was scaled by a factor of 5 for the purpose of comparison with the radial one. Figure 13. View largeDownload slide Polarity of tangential motion calculated at 10 ms for an explosion in granite with two vertical persistent orthogonal joint sets. Joint cohesion was 15 MPa, joint spacing was 2 m. Figure 13. View largeDownload slide Polarity of tangential motion calculated at 10 ms for an explosion in granite with two vertical persistent orthogonal joint sets. Joint cohesion was 15 MPa, joint spacing was 2 m. 3.5 Effect of joint persistency We have shown above that decreasing joint cohesion at all joints may produce less tangential motion. Joint persistency may have a similar effect, since non persistent joints may be modelled as persistent ones but with variable joint cohesion. Indeed, we have found little change in tangential motion when persistency decreases from the fully persistent case until it reaches 70  per cent. In such cases the magnitude of the tangential motion begins to decrease consistently as shown in Fig. 14 where tangential velocity is plotted on the same scale (from −5 cm s−1 for counter-clockwise motion to 5 cm s−1 for clockwise motion). As joint persistency is reduced to 20 per cent, the amplitude of the tangential motion drops roughly by a factor of 3. Polarity of the first tangential motion remains the same but it seems to attenuate more rapidly beyond the elastic radius where the joints stop sliding. According to SPE site characterization the average joint persistency is approximately 70 per cent (see Townsend et al. 2012), thus we do not expect the results to be significantly different from the fully persistent case. Figure 14. View largeDownload slide Tangential motion calculated at 10 ms for joint persistency 100 per cent (a), 60 per cent (b), 40 per cent (c) and 20 per cent (d). Sliding joints are plotted with bold lines. Figure 14. View largeDownload slide Tangential motion calculated at 10 ms for joint persistency 100 per cent (a), 60 per cent (b), 40 per cent (c) and 20 per cent (d). Sliding joints are plotted with bold lines. 3.6 Effect of variations in joint directions The joints grouped in a joint set do not have the same orientation. Azimuthal directions for the joints which belong to the same joint set may vary within 5–20 degrees. We have conducted a sensitivity study on how these variations may affect the tangential motion. For this purpose, the normal of each joint in a joint set was varied around the direction characterizing this set by some random angle which was less than a maximum deviation angle. Fig. 15 shows tangential motion calculated at time 10 ms on the horizontal plane crossing the source for 3 different maximum deviation angles, 5, 15 and 45 degrees and two different joint cohesions 15 MPa (Figs 15a–c) and 0.15 MPa (Figs 15d–f). We have found that the effect of angular deviation of the joints on the tangential motion is very sensitive to joint cohesion. Thus, for very low cohesion at the joints even deviation in 5 degrees make a significant effect especially for shallow explosions where the initial confinement is small as it is shown in Fig. 15(d). Figure 15. View largeDownload slide Polarity of tangential motion at 10 ms at shot level for joints with cohesion 15 MPa : (a) maximum deviation 5 degrees, (b) 15 degrees and (c) 45 degrees, and joints with cohesion of 0.15 MPa: (d) maximum deviation 5 degrees, (e) 15 degrees and (f) 45 degrees. Sliding joints are plotted with bold black lines. Figure 15. View largeDownload slide Polarity of tangential motion at 10 ms at shot level for joints with cohesion 15 MPa : (a) maximum deviation 5 degrees, (b) 15 degrees and (c) 45 degrees, and joints with cohesion of 0.15 MPa: (d) maximum deviation 5 degrees, (e) 15 degrees and (f) 45 degrees. Sliding joints are plotted with bold black lines. 3.7 Tangential motion in jointed rock with two vertical joint sets from SPE site Now, after completing the analysis of tangential motion generation by two orthogonal joint sets, let us consider more realistic joint set orientations from SPE site. Fig. 16 shows intersection of two joint sets (set #1 and set #3) with the horizontal plane at shot level. Polarity of calculated tangential motion is shown with colours. One can see, that despite the joints being inclined and not orthogonal, the polarity sections generated by the explosion are very similar to the orthogonal case considered in the previous study. Fig. 16 shows some azimuthal directions for SPE4/SPE5 boreholes where the gauges are plotted on top of the calculated polarity picture. According to this, if the joint set is perfectly persistent without variations in joint orientation within each set, we would expect the polarity of the first significant tangential motion to be defined by the joint set directions. Thus, gauges in the well bores #16 and #19 would show negative (counter-clockwise) tangential motion while gauges in the well bores #15 and #18 would show positive polarity. This simplistic model for jointed rock was able to predict polarities for most of the gauges located in the middle of the polarity sections. But, in some azimuthal directions uncertainties in joint orientation can have a dominant effect on the polarity of the tangential motion. For example, for well bores #9 and #11 this model predicts low tangential motion due to sliding on both joint sets. Yet, experiments showed a negative polarity for both locations. Figure 16. View largeDownload slide (a) Joint locations, problem dimensions and polarity of tangential motion. (b) Polarity of tangential motion calculated at shot level for rock mass with two joint sets (set 1 and set 3) at 10 ms. SPE gauge directions are also shown. Figure 16. View largeDownload slide (a) Joint locations, problem dimensions and polarity of tangential motion. (b) Polarity of tangential motion calculated at shot level for rock mass with two joint sets (set 1 and set 3) at 10 ms. SPE gauge directions are also shown. 3.8 Stochastic estimation of radial, vertical and tangential motions for SPE4P and SPE5 Geological characterization of rock mass is often expensive and therefore collected site data are limited and spatially sparse. Furthermore, the ability to map joints and inclusions in the rock with the available geological and geophysical tools tends to decrease with depth and scale of the discontinuity. Geological characterization often encompasses measurements of fracture density, orientation, and aperture. These attributes are then abstracted into probability density functions (PDFs) for predictive stochastic modelling. For example, stochastic discrete fracture network (SDFN) generated using the geological characterization PDFs enables, via Monte Carlo simulations, the probabilistic assessment of physical phenomena that are not adequately captured using continuum and deterministic models. Despite the fundamental uncertainties inherited within the probabilistic reduction of the sparse data collected, SDFN has become a very popular tool to quantify uncertainties in complex geological media (Ezzedine 2005, 2010, and references therein). Hereafter we focus our analyses on SPE4P and SPE5 only, we refer the reader to Ezzedine et al. (2015) for a detailed study of SPE3. In line with Ezzedine et al. (2015), we conducted several Monte Carlo simulations to quantify the mean responses of variables of interest: that is, the radial, tangential and vertical velocities as well their uncertainty spreads. All SDFN realizations were generated independent of each other but conditional to the observed data at the specific boreholes. SDFNs are then embedded into LLNL forward hydrodynamic code GEODYN-L as described in Ezzedine et al. (2015). All simulations were performed on 2400 CPUs and each simulation took up to $${4}\!\!\!^{^{\sim}}$$ hr of CPU time for 50 ms of physical time and required up to 10 GB of storage space. It is worth mentioning that the domain of the numerical simulations for SPE4P and SPE5 has doubled in size compared to SPE3 and that is the main reason the HPC requirements have been augmented. More details regarding the statistical sample size and the convergence of the statistical moments can be found in Ezzedine et al. (2015) and in Vorobiev et al. (2015). We present here the direct application of the SPE3 simulation framework to SPE4P and SPE5. Fig. 17 depicts a subset of random realizations of the SDFN (labelled DNF0-2 and plotted using different colours and thin lines), the observed SPE4P data collected is depicted in a purple thick line while the mean and the 95 per cent confidence interval (CI) of the entire set of the Monte Carlo simulations are depicted in thick red continuous and discontinuous lines, respectively. The history of the radial (R, left column), tangential (T, middle column) and vertical (L, right column) velocities (km s−1) have been plotted for three different borehole gauges #14-1 (bottom row), #15-1 (middle row) and #14-2 (top row), respectively. Similarly, Fig. 18 depicts the same set of curves for SPE5 at borehole gauges #14-2 (bottom row), #15-2 (middle row) and #16-2 (top row), respectively. Figure 17. View largeDownload slide Radial (left column), tangential (middle column) and vertical (right column) velocities (cm s−1) as function of time (milliseconds, ms) at three borehole locations #14-1 (bottom row), #15-1 (middle row) and #14-2 (top row). Thick purple curves are the observed pulses for SPE4P, while the think red curves are the Monte Carlo statistics mean (continuous line labelled A) and the envelop of the 95 per cent confidence lower bound (labelled L) and upper bound (labelled U). Figure 17. View largeDownload slide Radial (left column), tangential (middle column) and vertical (right column) velocities (cm s−1) as function of time (milliseconds, ms) at three borehole locations #14-1 (bottom row), #15-1 (middle row) and #14-2 (top row). Thick purple curves are the observed pulses for SPE4P, while the think red curves are the Monte Carlo statistics mean (continuous line labelled A) and the envelop of the 95 per cent confidence lower bound (labelled L) and upper bound (labelled U). Figure 18. View largeDownload slide Radial (left column), tangential (middle column) and vertical (right column) velocities (cm s−1) as function of time (milliseconds, ms) at three borehole locations #14-2 (bottom row), #15-2 (middle row) and #16-2 (top row). Thick purple curves are the observed pulses for SPE5, while the think red curves are the Monte Carlo statistics mean (continuous line labelled A) and the envelop of the 95 per cent confidence lower bound (labelled L) and upper bound (labelled U). Figure 18. View largeDownload slide Radial (left column), tangential (middle column) and vertical (right column) velocities (cm s−1) as function of time (milliseconds, ms) at three borehole locations #14-2 (bottom row), #15-2 (middle row) and #16-2 (top row). Thick purple curves are the observed pulses for SPE5, while the think red curves are the Monte Carlo statistics mean (continuous line labelled A) and the envelop of the 95 per cent confidence lower bound (labelled L) and upper bound (labelled U). Note that these simulations were conducted without calibration of the model simulations to observations, but using only intact physical and geomechanical properties of the rock measured in the laboratory on core samples collected at the SPE site. It is remarkable that the simulation of wave propagation through the SDFNs embedded in the granite rock matrix shows very good agreements with the experiments. By inspecting both Figs 17 and 18, one can see that the spreads of the modelling results bracket the observed velocities at every depicted location and capture well arrival times and, in average, peak radial and vertical velocities. Despite that tangential velocities are very sensitive to density, orientation and persistency of joints, as it has thoroughly been demonstrated in Ezzedine et al. (2015) and in Vorobiev et al. (2015), it is remarkable that the spread of the uncertainty in the predictions covers considerably well the observed tangential spread due to polarity changes from positive to negative values and vice-versa, which underscores further that the genesis of shear motions is mainly due to the presence of the joints. 4 DISCUSSION The latest SPE tests showed that significant shear motion was generated in the near-field. The test site geology was favourable to investigate tangential motion generated during underground chemical explosions because of insignificant spatial variations in mechanical properties of granite, flat site topography and thorough pre and post shot geological characterization done at the site. All SPE tests show radial motion consistent with the historic tests performed in the same granite formation in the past. Tangential motion was observed both at shot depth and at the surface. The peak tangential velocity can reach 30–40 per cent of the radial one in the near-field. The ratio of tangential to radial velocity magnitudes tends to grow with range. Tangential velocity changes polarity with time at least once. Similar to observations done by Kisslinger et al. (1961), initial high frequency tangential motion often is followed by lower frequency but higher magnitude motion of reversed polarity. Also, similar to observations in Kisslinger et al. (1961), polarity of tangential motion in opposite azimuthal directions may seem to be reversed. In reality, it depends on how the opposite directions are selected relative to joints directions. For example, directions #18 and #19 (Fig. 16) show opposite polarities but directions L1 and L3 would show the same polarity in tangential motion. Experiments showed that recorded tangential motion is similar in the same azimuthal direction even for different dip angles. This was also confirmed in calculations which showed that the vertical joints define azimuthal directions with constant polarity for the tangential motion. Thus, polarity of this motion can be predicted for persistent joints with small variation in joint directions. Tangential motion always follows the radial one with some delay, which varies for each gauge location. We believe that this delay is related to local joint conditions. As it was shown in Vorobiev et al. (2015), it may be controlled by joint cohesion and friction in the vicinity of the gauge. Increasing joint cohesion from a very low level may enhance observed tangential motion when multiple joint sets are present. This is due to competition between various joint sets which may cause sliding in opposite directions when sliding conditions are reached on differently oriented joints for low cohesion. By increasing joint cohesion, this condition is reached only at the joints preferably oriented towards the sliding direction. Increasing it even more will suppress the sliding and thus reduce the tangential motion. We have found, that for randomly oriented joints on the scale of the wave length with small cohesion very little tangential motion would be generated. Vertical motion at shot level seems to correlate with the orientation of the low dip angle joints, which are the most effective at deflecting the horizontal motion up or down depending on the azimuth. Enhancement of the vertical motion in some azimuthal direction may be responsible for asymmetry of the vertical surface displacement observed around ground zero. We conducted computational studies on ground motion from underground explosions in jointed rock masses using realistic rock and joint models. The results of this study help to explain anisotropy in ground motion observed at SPE site and relate it to the geological site characterization. We have found correlations between the joint properties and observed tangential motion in the near-field. According to the present work joint sliding is the dominant factor responsible for tangential motion generation within the elastic radius. Beyond the elastic radius, elastic anisotropy provides an additional mechanism to convert the radial motion into the tangential motion. Here, elastic radius is defined as a range from the source beyond which both rock and joints exhibit elastic mechanical response. For joint cohesion of 15 MPa elastic radius is defined by the joints and is roughly 15m/t1/3. The method used in the near-field where the mesh size is controlled by the joint spacing is not practical at seismic distances. We hope that results of this study will be useful to develop a source model for seismic codes which will include not only radial but also tangential motion for jointed rock masses. The seismic codes with the validated source term can be used to propagate signals to large distances (tens and hundreds of kilometres). Acknowledgements The work was performed under the auspices of the US Department of Energy by University of California, Lawrence National Laboratory under Contract W-7405-Eng-48. The work was supported by National Nuclear Security Administration under contract DE-AC52-07NA27344. REFERENCES Babich V.M., Kiselev A.P., 1989. Non-geometrical waves–are there any? an asymptotic description of some ‘non-geometrical’phenomena in seismic wave propagation, Geophys. J. Int. , 99( 2), 415– 420. Google Scholar CrossRef Search ADS   Crampin S., 1981. A review of wave motion in anisotropic and cracked elastic-media, Wave motion , 3( 4), 343– 391. Google Scholar CrossRef Search ADS   Ezzedine S., 2010. Impact of geological characterization uncertainties on subsurface flow using stochastic discrete fracture network models, in Annual Stanford Workshop on Geothermal Reservoir Engineering , Stanford. Ezzedine S., Vorobiev O., Glenn L., Antoun T., 2015. Application of HPC and non-linear hydrocodes to uncertainty quantification in subsurface explosion source physics, in 49th US Rock Mechanics/Geomechanics Symposium , San Francisco, CA, American Rock Mechanics Association. Ezzedine S.M., 2005. Stochastic modeling of flow and transport in porous and fractured media, in Encyclopedia of Hydrological Sciences , Wiley Online Library. Google Scholar CrossRef Search ADS   Hirakawa E., Pitarka A., Mellors R., 2016. Generation of shear motion from an isotropic explosion source by scattering in heterogeneous media, Bull. seism. Soc. Am. , 106( 5), 2313– 2319 Google Scholar CrossRef Search ADS   Hoek E., Brown E., 1997. Practical estimates of rock mass strength, Int. J. Rock Mech. Min. Sci. , 34( 8), 1165– 1186. Google Scholar CrossRef Search ADS   Hurley R., Vorobiev O., Ezzedine S., 2017. An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints, Comput. Mech. , 60( 2), 235– 252. Google Scholar CrossRef Search ADS   Kisslinger C., Mateker E.J., McEvilly T.V., 1961. SH motion from explosions in soil, J. geophys. Res. , 66( 10), 3487– 3496. Google Scholar CrossRef Search ADS   Lash C., 1985. Shear waves produced by explosive sources, Geophysics , 50( 9), 1399– 1409. Google Scholar CrossRef Search ADS   Liu C.L., Ahrens T.J., 1998. Wave generations from confined explosions in rocks, AIP Conf. Proc. , 429( 1), 859– 862. Mandal B., Toksöz M., 1990. Computation of complete waveforms in general anisotropic media—results from an explosion source in an anisotropic medium, Geophys. J. Int. , 103( 1), 33– 45. Google Scholar CrossRef Search ADS   Murphy J., Barker B., Sultanov D., Kuznetsov O., 2009. S-wave generation by underground explosions: Implications from observed frequency-dependent source scaling, Bull. seism. Soc. Am. , 99( 2A), 809– 829. Google Scholar CrossRef Search ADS   Oda M., Yamabe T., Kamemura K., 1986. A crack tensor and its relation to wave velocity anisotropy in jointed rock masses, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. , 23, 387– 397. Google Scholar CrossRef Search ADS   Perret W.R., Bass R.C., 1975. Free-field ground motion induced by underground explosions, Tech. rep. , Sandia Labs., Albuquerque, NM, USA. Randall M.J., 1962. Generation of horizontally polarized shear waves by underground explosions, J. geophys. Res. , 67, 4956– 4957. Google Scholar CrossRef Search ADS   Salvado C., Minster J.B., 1980. Slipping interfaces: a possible source of s radiation from explosive sources, Bull. seism. Soc. Am. , 70( 3), 659– 670. Steedman D.W., Bradley C.R., Rougier E., Coblentz D.D., 2016. Phenomenology and modeling of explosion-generated shear energy for the source physics experiments, Bull. seism. Soc. Am. , 106( 1), 42– 53. Google Scholar CrossRef Search ADS   Townsend M., Obi C., 2014. Data release report for Source Physics Experiments 2 and 3 (SPE-2 and SPE-3), Nevada National Security Site, National Security Technologies Technical Report DOE/NV/25946-2282. Townsend M., Prothro L., Obi C., 2012. Geology of the Source Physics Experiment site, climax stock, Nevada National Security Site, Tech. rep. , NTS. Tsvankin I., 2012. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media , no. 19, SEG Books. Tsvankin I., Grechka V., 2011. Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization , Society of Exploration Geophysicists. Google Scholar CrossRef Search ADS   Vorobiev O., 2008. Generic strength model for dry jointed rock masses, Int. J. Plast. , 24( 12), 2221– 2247. Google Scholar CrossRef Search ADS   Vorobiev O., 2010. Discrete and continuum methods for numerical simulations of non-linear wave propagation in discontinuous media, Int. J. Numer. Methods Eng. , 83( 4), 482– 507. Vorobiev O., 2012. Simple Common Plane contact algorithm, Int. J. Numer. Methods Eng. , 90( 2), 243– 268. Google Scholar CrossRef Search ADS   Vorobiev O., Ezzedine S., Antoun T., Glenn L., 2015. On the generation of tangential ground motion by underground explosions in jointed rocks, Geophys. J. Int. , 200( 3), 1651– 1661. Google Scholar CrossRef Search ADS   White J., Sengbush R., 1963. Shear waves from explosive sources, Geophysics , 28( 6), 1001– 1019. Google Scholar CrossRef Search ADS   Wright J.K., Carpenter E.W., 1962. The generation of horizontally polarized shear waves by underground explosions, J. geophys. Res. , 67( 5), 1957– 1963. Google Scholar CrossRef Search ADS   Zhang H., Zhu J., Liu Y., Xu B., Wang X., 2012. Strength properties of jointed rock masses based on the homogenization method, Acta Mech. Solida Sin. , 25( 2), 177– 185. Google Scholar CrossRef Search ADS   © The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society.

Journal

Geophysical Journal InternationalOxford University Press

Published: Jan 1, 2018

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off