APPLICATIONS OF ULTRASONIC TECHNIQUES TO IN-SITU INVESTIGATION OF CRITICAL STRUCTURES IN ROCK AND CONCRETE

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1 APPLICATIONS OF ULTRASONIC TECHNIQUES TO IN-SITU INVESTIGATION OF CRITICAL STRUCTURES IN ROCK AND CONCRETE Calum Baker Applied Seismology Consultants Ltd., 10 Belmont, Shrewsbury, United Kingdom R. Paul Young Department of Earth Sciences, University of Liverpool, Liverpool, United Kingdom ABSTRACT: Ultrasonic methods can be used in both passive and active modes of operation to monitor volumes of rock and concrete. These methods are able to provide both qualitative and quantitative measurements of damage and changes in material properties. The techniques have important applications for routine in situ monitoring and characterisation of critical structures in rock and concrete. The potential of this technology is highlighted in this paper with reference to the monitoring of a concrete bulkhead, part of the Tunnel Sealing Experiment (TSX) at the Underground Research Laboratory in Canada. An array of ultrasonic transducers installed within a concrete bulkhead and in the surrounding rock is used to monitor the bulkhead using both passive and active methods during 3 phases. The concrete was poured in September This paper highlights the ways in which the data have been used to assess the behaviour of the key over a three-year period. This includes measurements during the curing process, identifying the occurrence of cracks, investigating the extent to which these cracks were stabilised through remedial grouting and a study of the long-term behaviour of the bulkhead. Ultrasonic monitoring provides a powerful method of evaluating the behaviour of a volume of material. Increasingly, numerical models are used in conjunction with these field observations to provide a robust interpretation of the results. An example of how a thermal-mechanical model can improve our interpretation of the ultrasonic measurements is described. 1. INTRODUCTION Within the field of rock mechanics, ultrasonic methods are applied to the study of rocks in both laboratory and in-situ experiments [1]. A number of recent field experiments, carried out to assess the behaviour and stability of rock excavations as part of investigations into the geological storage and disposal of nuclear waste, have highlighted the potential of this technology for routine characterisation and in-situ measurements of critical structures. The methods have also been employed for the direct monitoring of concrete structures with conspicuous success. This technology is particularly appropriate for critical structures, i.e. any volume of rock or concrete whose integrity/behavior is essential for the safe operation of a particular facility. An important factor accounting for the versatility of ultrasonic methods is that the technology can be used for both active and passive monitoring of a volume. When used in a passive mode, the sensors listen for acoustic emission (AE) activity within the volume. When used in an active mode, an acoustic wave is transmitted through the volume from one transducer to another at predetermined time intervals and variations in the velocity and amplitude of both P and S waves are measured. From these variations, it is possible to quantitatively evaluate the changing material properties along the ray-path in question. When used for routine monitoring, these techniques are very sensitive, as very small changes in the properties of the material can be identified (see Section 4). One factor that is increasing the importance of this technology is improvements in our ability to interpret the results in terms of the engineering behavior of the material over operational time periods. These improvements are the result of two key developments. The first arises from improvements in hardware and software that enhance the quality of the data, the information we can obtain from these and the speed with which that information can be processed. It is now possible, for example, to obtain key results, such as AE locations and magnitudes, in real time. The second key development arises from the use of numerical modelling techniques in conjunction with the in situ monitoring. It can be difficult to provide a unique interpretation of the results obtained from ultrasonic surveys because of the complexity of the system being studied. By incorporating numerical modelling it is possible to test hypotheses derived

2 from the observational data and to include the effects of coupled processes such as mechanical, chemical and thermal effects which may be important in some scenarios. The uses of ultrasonic monitoring technology for in situ studies are highlighted in this paper using the example of a concrete seal from the Tunnel Sealing experiment (TSX) at the Underground Research Laboratory (URL) in Canada. These techniques have also been used for studies of rock at the URL and in other underground facilities [2]. 2. ULTRASONIC MONITORING Ultrasonic surveys are defined here as those that record acoustic data in the 35 to 250 khz range (or greater). The optimal frequency for a particular scenario depends on the volume of interest and the resolution that is required. Higher frequencies provide better resolution, but attenuation means that in some cases these can only be used for small volumes. In practice, for in situ measurements in rock, volumes up to 10 3 m 3 can be monitored. As outlined in the preceding section, the technology allows two modes of operation passive monitoring and active monitoring. The hardware allows a system to automatically switch between these modes of operation according to a pre-determined schedule of measurements. Thus, a system can be programmed to passively listen for AE activity for the majority of the time, and undertake a routine active velocity survey once per day at a pre-defined time. 3. THE TSX CONCRETE BULKHEAD 3.1. The Tunnel Sealing Experiment(TSX) The TSX is a major international experiment being carried out at the URL in Canada with the aim of investigating the technology that could be used for tunnel sealing in underground nuclear waste repositories [3]. Different plug and seal technologies are being investigated, together with the technologies that can be used to monitor their performance. The experiment consists of a 40 meter long tunnel (see Fig. 1), with an elliptical profile (4.375 m across, 3.5 m high) excavated parallel to the maximum principal stress direction (σ 1 ). The elliptical profile and orientation of excavation were features designed to minimize the effects of the high compressive stresses that are observed in other sub-horizontal tunnels at the URL. The tunnel is sealed at either end with a bulkhead, one constructed from clay blocks and one from low heat, high performance concrete. This Sand Filler Steel Support Keyed Highly Compacted Clay-Block Bulkhead Keyed Concrete Bulkhead Sand Filler Highly Compacted Backfill Figure 1: Schematic drawing of the Tunnel Sealing Experiment (courtesy of AECL, [3]). Pressure Supply and Withdrawal Headers (from room 415) paper focuses on the results from monitoring the concrete bulkhead The concrete bulkhead monitoring system Prior to casting the concrete key, an array of ultrasonic transducers (and an extensive suite of other geo-mechanical instrumentation) was installed within the volume by attaching them to a frame constructed from fiberglass rods. Additional transducers were installed within the rock adjacent to the bulkhead, thus providing ray-paths that passed through the interface between the rock and the concrete. The ultrasonic array was used for both active and passive evaluation of the concrete during three phases of monitoring, from the initial pouring of the concrete to the end of the first main pressurization phase. These are outlined in Table 1. Table 1: The 3 periods during which the concrete bulkhead was monitored. Phase Dates Details 1 16 September to 15 October February to 22 April March to 1 October 2001 Period following initial pouring and during curing of concrete Period following grouting of macro fracture & initial pressurization. Period during pressurization of TSX tunnel The array consists of 24 transducers, 16 of which are used as receivers and 8 as transmitters. The geometry of the array (Fig. 2) was designed to take advantage of the predicted symmetrical response of the bulkhead. 4 of the sensors are installed in short boreholes in the adjacent rock mass at a distance of about 1.75-m from the front face of the bulkhead. These were installed to allow investigations of the rock-concrete interface to be made. During each

3 Plan A 5.0 m m 0.1 m R m 30 P8 P1 R3 R1 R4 R16 R7 R10 R5 R15 Section A 2x R8 R6 P2 R14 P5 R11 R12 P6 2x 2x Sensors Side Facing up Facing down R9 P3 R13 P4 P7 R2 Figure 2: The locations of the AE transducer array in and around the concrete bulkhead. The left-hand side of the diagram shows the location of the sensors in the rock. Note the location of the sensors in an arc around the tunnel perimeter, at a distance of 1.75 meters from the face of the bulkhead. The right-hand diagram shows the location of the transducers fixed within the bulkhead. P# represents a pulser (transmitter), R# represents a receiver. monitoring phase the system was programmed to monitor continuously for AE activity. In phase 1 and 2 active velocity surveys were automatically undertaken every hour. In phase 3 these surveys were undertaken once very 24 hours at 01:00 (local time). 4. DATA PROCESSING The data processing is divided into three phases. The first involves an initial investigation of the velocities along the ray-paths between each pulser and receiver. A reference survey is chosen and the P and S (where possible) arrivals are picked by manual inspection of the waveforms. The velocities are then calculated for this reference survey from knowledge of the sensor positions and the assumption that the raypath is a straight line joining the transmitter to the receiver. The reference velocities are thus defined. The corresponding velocities for each raypath at other times are then automatically computed using a picking algorithm (to identify the phase arrival times) and a crosscorrelation method (to compare the arrival times of the two surveys). This allows very precise measurements of the variation of velocity from the reference survey to be made ( m/s over a raypath length of meters). Once the P and S velocity histories for each raypath are computed, these are used to compute an average velocity for the volume. The second phase of processing involves using this average velocity to locate the AE events that have been detected by the system. An automated picking routine is used to pick the P phase arrivals that are then used to give a location and an uncertainty. The resulting data set can be filtered to discard events that have uncertainties greater than a certain limit or are recorded on less than a pre-defined number of sensors. At least 5 picks are required to provide a constrained solution and, for this experiment, a minimum of 8 sensors was used. The events are then plotted and any event with a spurious location is manually checked to ensure that the automatic picking correctly identified the P arrival. The third phase of processing involves inspecting all the velocity survey data and corresponding amplitude variations over the full monitoring period The waveforms associated with any sharp jumps in velocity or amplitude are manually checked to ensure the automatic processing has identified the correct phase. The cross-correlation requires the shape of the reference and comparison waveforms to have a similar form and this manual check confirms that this is the case and that any "jumps" are a true reflection of the trend in velocity and/or amplitude. 5. PHASE 1 MONITORING The first phase of monitoring was undertaken for 1 month immediately following the pouring of the

4 concrete bulkhead. The objectives were to investigate the changes in material properties of the bulkhead during curing, assess whether any cracking was occurring within the bulkhead due to shrinkage and to investigate the integrity of the rock-concrete interface in response to the thermal, chemical and mechanical processes. The concrete was poured on 15 September 1998 and the first AE event was detected by the ultrasonic system around 16 hours later on 16 September. Over the next 40 hours 143 AE events were located within the bulkhead, mostly along the 45 o interface between the rock and the concrete in the upper part of the key. Until 24 September this pattern continues with events mostly occurring along this interface between the concrete and the rock. These occur both in the roof and floor sections of the keyed region and gradually increase in magnitude over this period. A distinct change in the pattern of events occurs from 04:00 on 24 September. At this time the events start to nucleate and a distinct lineation develops over the subsequent 48 hours. The events occur along a slightly curved sub-vertical feature extending from the NE side of the 90 o rock-concrete interface down towards the front of the key and intersecting the lower 45 o rock-concrete interface (Figure 3A). This feature develops over the next 6 days, first propagating along a curved path in the lower half of the key (Figure 3B) and then extending upwards from the original nucleation point to form a third surface striking axially to the tunnel and dipping at 45 o towards the crown of the key (Figure 3C). Although the rate of activity reduces after this time, the AE events detected continue to nucleate on these three features. The pattern of events was interpreted in terms of the formation of a series of distinct fractures, possibly resulting from the shrinkage of the concrete during the initial curing process. The active velocity surveys carried out during this period confirm the opening of a fracture in the concrete. Figure 4 shows the variation in P wave velocity and amplitude over the monitoring period for a ray-path that intersects the first lineation of AE events. The increase in velocity and amplitude during the first 48 hours during curing is clearly seen. This change can be quantified in terms of the changing material properties of the concrete. For example, between pulser 3 and receiver 15, the P- and S-wave velocity is computed from the surveys. The values indicate a corresponding change in Dynamic Young s modulus (E) given by [4]: A. Midnight 24 September midnight 26 September events B. Midnight 26 September midnight 1 October events C. Midnight 1 October midnight 3 October events Figure 3: Development of AE activity in the concrete bulkhead between midnight on 24 September and midnight on 3 October. The development of 3 distinct zones defined by AE activity is clearly seen (A-C).

5 P-wave Velocity (m/s) Sep 16 - Sep 18 - Sep 20 - Sep 22 - Sep 24 - Sep 26 - Sep 28 - Sep 30 - Sep Date 02 - Oct R Oct P-wave Velocity RMS Amplitude 06 - Oct 08 - Oct 10 - Oct P Oct 14 - Oct 16 - Oct RMS Waveform Amplitude (V) P-wave Velocity (m/s) Sep 15-Sep 17-Sep 19-Sep 21-Sep P-wave Velocity RMS Amplitude Figure 5: P wave velocity and RMS amplitude variation Figure 4: P wave velocity and RMS amplitude measured between pulser 8 (within the rock) and receiver 8 (within hourly during phase 1 monitoring between pulser 4 and the concrete). This suggests an opening of the rockconcrete interface around 00:00 on 19 September. receiver 9. The steep increase in these parameters over 72 hours during the initial curing is seen, as is the sharp drop on 24 September associated with the large cluster of AE events. The monitoring was carried out between 26 February and 23 April 1999, during which time the 2 2 3V pressure within the TSX chamber was being held at p 4V s E = ρv 2 s 2 2 V ~ 0.79 MPa. The passive AE monitoring indicated p V (1) s that the grout injection had been very successful in of GPa on the 16 September (first measurement) to GPa on the 19 September (after the velocity values plateau out, as shown, for stabilizing the cracks with a 99.8% reduction in AE activity (only 14 events were detected within the concrete bulkhead volume during the 2-month example, in Figure 4), assuming a density, ρ, of monitoring period). This is evident from a 2460 kg/m 3. comparison of Figure 6 with Figure 3. The results from the velocity surveys for raypaths The velocity surveys indicate that raypaths passing crossing the rock-concrete interface show a range of through the regions of AE activity in phase 1 have responses for different parts of the interface. For stabilized, with the amplitudes of the waveforms example, the raypath between pulser 8 and receiver now sufficiently large to compute interval velocities 8 passes through the side-wall on the NE side of the once more. The velocities thus computed were key shows an initial steep rise in P-wave velocity consistent with those that had been observed prior and amplitude in response to the curing of the to the opening of the fracture, and the on going concrete over the first 3-4 days. However after curing, leading to a slight strengthening of the midnight on 19 September there is a sharp drop in concrete. amplitude and no P-wave velocity can be calculated from the cross-correlation. This is shown in Figure 5. The implication of this result is that a gap has opened along the rock-concrete interface at this time. This effect correlates with a significant level of AE activity along the 45 o interface. NE SW 23-Sep 25-Sep 27-Sep 29-Sep Date 01-Oct 03-Oct PLAN VIEW 05-Oct R8 07-Oct P8 09-Oct 11-Oct 13-Oct 15-Oct RMS Waveform Amplitude (V) 6. PHASE 2 MONITORING The second phase of monitoring began on 25 February The chamber was filled with water at the end of September 1998 and pressurization of the chamber commenced in November. A phase of grout injection took place after the first monitoring period in an attempt to seal the series of fractures that was detected and imaged by the monitoring system during phase 1. One of the key objectives of the phase 2 monitoring was to determine how successful this grouting had been at stabilizing these cracks. 1 m Figure 6: AE events detected during the two-month monitoring period in phase 2. In all, 14 events were detected. The contrast with phase 1 (Figure 3) is clear.

6 P-wave Velocity (m/s) Feb 25-Feb 01-Mar 7_12Vp 7_12Ap 05-Mar 09-Mar 13-Mar 17-Mar 21-Mar 25-Mar Date 29-Mar The active velocity surveys highlight a number of important responses during the phase 2 period. One raypath passing through the floor of the bulkhead between the rock and the concrete shows a 96% drop in amplitude over a three day period. This drop was sufficiently large that it was no longer possible to detect the P wave arrival with the certainty required to compute a P wave velocity (Figure 7). This was interpreted as evidence for the formation of a slight gap along the interface between the rock and concrete in the floor of the key. 7. PHASE 3 MONITORING The third phase of monitoring was undertaken between 27 March and 30 September 2001, i.e. nearly 2 years after the end of the second monitoring period. The main purpose of the phase 3 monitoring was to investigate the response of the bulkhead during a phase of pressurization as the TSX chamber pressure was increased from 2 to 4 MPa. The ultrasonic system was used to collect passive (AE) and active (velocity survey) data as in phases 1 and 2. The only difference between phase 3 and the earlier monitoring periods was that the velocity surveys were undertaken only once in each 24-hour period (at 01:00 each day). During the period of monitoring 42 AE events were detected within the volume of the concrete. The majority of these occurred along the rock-concrete interface in the floor section of the bulkhead. These events would indicate that small amounts of movement were occurring along this interface in response to the pressurization. The key conclusion from this level of AE activity and the locations of the events themselves is that there is no evidence of major reactivation of the fractures that formed and 02-Apr 06-Apr Roof P7 R12 Floor 10-Apr 14-Apr 18-Apr 22-Apr 26-Apr 2.00E E E E E E E E E E E+00 Figure 7: The P-wave velocity and amplitude variations for the raypath between pulser 7 and receiver 12 that passes through the rock-concrete interface in the floor of the bulkhead. This would suggest that, during phase 2 of the monitoring, a gap opened up in this region. P-wave Peak Amplitude (V) were subsequently grouted in phase 1. Furthermore, there is no evidence for the extensive development of new fractures within the bulkhead in response to the pressurization. This provides confidence in the long-term stability of the grouted region and in the performance of the concrete bulkhead overall. The active velocity surveys provide a method of resolving very small variations as the bulkhead responds to the pressurization. All 128 pulserreceiver combinations were investigated for variations in P and (where possible) S velocity and amplitude. These can be grouped into different sets of raypaths in order to investigate the axial and radial response of the bulkhead as well as any changes to the interface between the rock and the concrete at different points. Within the concrete, axial raypaths show a small but steady increase in velocity in response to the pressurization (Figure 8). The variation in amplitude of the transmitted signal showed a wider range of behaviors over the different raypaths. These observations can be interpreted in a number of ways. One explanation is that an increase in fluid saturation is occurring in response to the pressurization and this is leading to a loss in energy along certain raypaths. One way to investigate this is to consider the relative variation in P and S wave velocity. As S waves cannot travel through fluids we would expect to observe no change (or a much smaller change) in the S wave velocity when compared to the P. Results from a few selected raypaths are given in Table 2. These indicate that, while the P wave velocity along these raypaths is increasing over the time period, the S wave is showing no change or, at most, only a very small increase (the changes obtained are at the limit of the resolution of the cross-correlation technique). Therefore, there is some evidence that fluid saturation may be contributing to the observed velocity and amplitude changes for ray-paths within the key. Table 2: Changes in P and S velocity on selected raypaths over the phase 3 monitoring period. Raypath Change in V p % change in V p Change in V s % change in V s P1_R6 +8 ms -1.17% +2 ms -1.07% P4_R4 +13 ms -1.28% < +1ms -1 0% P5_R ms -1.49% +3 ms -1.11% Velocity surveys through the rock-concrete interface at various points suggest that there is

7 P velocity (m/s) Start P2_R4 P2_R5 P5_R4 P5_R14 P_start P_end Pressure Chamber pressure End Pressure (Pa) P2/5 Section R4/5 R14 P velocity (m/s) Mar 05-Apr 15-Apr 25-Apr 05-May 15-May 25-May 04-Jun 14-Jun 24-Jun 04-Jul DATE 14-Jul 24-Jul 03-Aug Figure 8: P velocity variations along selected axial raypaths through the concrete bulkhead between 27 March and 30 September The plot shows that these raypaths show similar absolute velocities and similar magnitude increases in response to the pressurization. The variation in chamber pressure, from 2 to 4 MPa, is shown by the thick black line. movement across these in some places, which supports the observation from the passive surveys indicating that the majority of AE events occur along the interface in the floor of the bulkhead. A sharp rise in the amplitude of the waveforms transmitted across the floor of this boundary occurs over a period of about 3 days between 7 and 10 August 2001 as the chamber pressure reached 3.5 MPa. Comparison of the velocities obtained during the phase 2 monitoring (1999) with phase 3 monitoring (2001) allow a quantitative investigation of the long-term behavior of the concrete to be made. Figure 9 shows the variation in P and S wave velocity from the start of phase 2 (February 1999) to the end of phase 3 (September 2001). This is for a raypath between pulser 1 and receiver 6 that passes through the corner of the concrete key on the lower NE edge (i.e. it does not intersect any of the Mar Jun Sep Dec Apr Jul-00 Date 21-Oct Jan-01 P1_R6_P P1_R6_S Figure 9: Long term variations in P and S wave velocity for raypath P1_R6 from the start of phase 2 to the end of phase May Aug S velocity (m/s) 13-Aug 23-Aug 02-Sep 12-Sep 22-Sep 02-Oct Plan R4 R5 R14 grouted zones). The results indicate the P-wave velocity has increased by about m/s per day between the end of phase 2 and the start of phase 3. The corresponding change for S-waves is.035 m/s per day between 2 and 3. Using equation 1, this gives values for dynamic Young s modulus E of 45.3 GPa at the end of phase 2, GPa at the start of phase 3 and GPa at the end of phase 3. These values suggest that the concrete is showing increased rigidity that is most probably associated with a continuing increase in strength over this period. 8. NUMERICAL MODELLING Numerical modelling is increasingly used in conjunction with field observations of the type described in this paper to provide an improved understanding of the physical processes that are occurring. Numerical modelling allows an investigation of the range of parameters that are compatible with the observations; conversely, field observations are essential for the validation of models undertaken prior to an experiment. An integrated approach provides a very powerful method of understanding the in situ behavior of the material. This approach can be demonstrated with reference to a numerical modelling study used to investigate the behavior of the concrete bulkhead during the first month after it was constructed [5]. The aim was to investigate the hypothesis that the cracking that occurred in phase 1 could be explained in terms of thermo-mechanical processes, and that the chemical processes occurring during the concrete P2 P5

8 curing were an insignificant effect (in terms of stress change). Recorded temperature data from sensors within the bulkhead were used together with the FLAC3D modelling code [6]. The thermal decay model was computed empirically from the observed temperature records. This was used to compute the thermal stresses that would exist within the bulkhead during the curing phase. Using the Mohr- Coulomb failure criteria, the models indicate that the maximum stress was not great enough to induce failure, suggesting that the observed cracking was not solely the result of thermo-mechanical processes. Indeed the model indicated that the thermal processes were only able to account for around 33% of the stress required to initiate failure. Using a lower value for the tensile strength of the concrete, failure did occur within the model and this was demonstrated to initiate at the same locations as was actually observed from the field data. This indicates that the thermal stresses have an important role to play in the overall stress distribution within the bulkhead and that, once cracking has started, thermal stresses control the subsequent development of these fractures. 9. CONCLUSIONS This paper has used the example of monitoring a concrete bulkhead to highlight the potential of ultrasonic monitoring for studying and understanding the long-term behavior of a critical structure. Although the example used in this paper referred to a man made concrete structure, the technology is equally valid for use in rock. In such cases the sensors are installed around the volume of interest via a series of boreholes. The technology is able to provide useful qualitative and quantitative information about the volume of interest including: Determining where damage is taking place from the location of AE events. Assessing, in a quantitative manner, the extent of the damage from the AE magnitudes and from the changes in velocity and amplitude values detected by the active velocity surveys. Determine the material properties of the volume from a study of velocity and amplitude information. The cross-correlation method, whereby the data is processed to look for small changes in the waveforms, is particularly sensitive to changes in the material behavior. Each raypath can be considered as a separate geotechnical instrument with the added advantage that the instrument does not itself interfere with the material (as would be the case with the installation of an extensometer, for example). Assess the time-dependent behavior of the material in response to engineering activities. The experiment described in this paper highlights the longevity of this equipment, even when used in relatively harsh environments. Providing validation and parameterization for numerical models. These techniques have a range of potential uses in radioactive waste, mining, petroleum and civil engineering scenarios and advances in hardware, software, processing and modelling capabilities will further enhance the range of applications. ACKNOWLEDGEMENTS The authors would like to thank the TSX international project team, AECL, ANDRA, PNC and WIPP for their support and contributions to the project. We thank the staff of the URL for their continued support of this work, especially Neil Chandler and Jason Martino. Dave Collins and Will Pettitt are thanked for their assistance with data collection and processing methodologies. REFERENCES 1. Young, R.P. & C. Baker Microseismic investigation of rock fracture and its application in rock and petroleum engineering. ISRM News Journal Vol. 7(1) 2. Pettitt W.S., C. Baker, R.P. Young, L-O Dahlström and G. Ramqvist The assessment of damage around critical engineering structures using induced seismicity and ultrasonic techniques. Pure appl. Gephys. 159: Chandler, N.A., D.A. Dixon, M.N. Gray, K. Hara, A. Cournut, and J. Tillerson The Tunnel Sealing Experiment: An In Situ Demonstration of technologies for Vault Sealing. In Proceedings of 19 th Annual Conference of the Canadian Nuclear Society, Toronto, Vol Mavko, G. T. Mukerji and J. Dvorkin The Rock Physics Handbook. 1 st ed. Cambridge: Cambridge University Press. 5. Kelly, A. Numerical modelling to investigate the thermomechanical behaviour of a concrete bulkhead. Applied Seismology Laboratory Project Report, University of Liverpool, Department of Earth Sciences, UK. 6. Itasca Consulting Group, Inc FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions), Ver 2.0, Minneapolis, Minnesota, ICG.