Slope Stability 2011: International Symposium on Rock Slope Stability in Open Pit Mining and Civil Engineering, Vancouver, Canada (September 18-21, 2011)

Monitoring Underground Landslide Displacement: A New MUMS Based Device

A. Segalini DICATeA, University of Parma, Parma, Italy

C. Carini GEI Elettronica, Parma, Italy

L. Cristalli Self-Employed Mathematician, Parma, Italy

Abstract This paper describes a new type of inclinometer chain, which is under development by the authors. It is intended to be applied in the underground excavation and slope monitoring fields. In the first part, the paper describes the new instrumentation which should allow for greater understanding of the type, location and origin of slope movements. This should help in understanding the triggering causes and mechanisms of landslide movements, and provide an innovative contribution to slope stability analysis and control. The second portion of the paper is dedicated to a comparison between the classic instruments and the new MUMS device. This device can also be automated and there is economy in coupling the devices with other electronic instruments (such as pore pressure, temperature, stresses, etc.) together with displacement components.

1 Introduction Automatic systems are becoming increasingly important for slope engineering. Environmental monitoring either for defense against catastrophic natural disasters or for controlling the efficiency of remediation intervention, have been widely applied in all the activities connected with territorial engineering. Particularly in the geological, geotechnical and geomechanical fields, these systems constitute a fundamental element in the evaluation of the natural systems characteristics and in the definition of the interactions between these systems and the man-made structures that are related with them.

In order to design and set up an efficient monitoring system, it is necessary to clearly define the main objectives (i.g. displacement control, variation of state of stress, variation of geometry, etc.) which precede the definition of the physical entities to be measured and recorded. The choice of mechanical and/or electronic apparatus most suitable for those measures, in terms of precision, resolution, repeatability and reliability is also important. One of the most serious problems regarding the choice of monitoring instrumentation is related to the environmental conditions to which these apparatuses will be exposed. Field installations in difficult and extremely variable environmental conditions can be exposed to large temperature variations, contact with corrosive elements, humidity and saturation problems. The site location relative to infrastructure such as electricity and telephone distribution networks have to be considered as well.

The scale of the natural phenomena to be monitored is also an important consideration in the monitoring system design, since it forces engineers to position the instrumentation taking into consideration :

Effectiveness of measurements: the instruments should be installed in locations where the variations of the measured physical entities are most apparent and, therefore, most easily resolved and measured;

Generalization of the results: since the measurements are carried out at single (or few) locations within the monitored area, it is important that the acquired measures can be reliably extended to the whole area of study;

Cost effectiveness of the system: single measurement apparatuses have costs that, even if reduced in recent years due to the application of microelectronics, are still significant in the overall budget; moreover, their installation costs are frequently high, limiting their number and diffusion.

In recent years, the increasingly widespread access to cellular phone coverage and wireless data connections has allowed greater use of remote data transmission, reducing and/or eliminating the need for on-site operators to recover data. This has reduced the costs involved in the post installation system management for most of the monitored physical entities. On the other hand, the large amount of data generated by these monitoring systems requires a time-consuming rationalization and analysis, which can be only partially carried out automatically and needs the continuous control of specialized technicians and engineers. Only after a sufficiently extended monitoring time and with the help of statistical approaches can some threshold values be inferred and used to define and manage emergency situations. One of the most critical aspects, both for slope stability and settlement, relates to the automated monitoring of underground displacements.

Until now, the underground monitoring of moving slopes has been carried out using inclinometers (Stark & Choi 2008) that require the presence of at least one operator to measure displacements along a vertical borehole. Such measurements are carried out using a biaxial servo-accelerometer device that is repeatedly lowered and recovered from the borehole. This operation prevents the possibility of automated monitoring. Some authors (Lollino et al. 2002) have proposed the installation of automated mechanical systems which often prove to be extremely expensive and unreliable. Another proposed solution, which is still widely applied, is based on the installation of fixed inclinometer probes (an inclinometer chain) positioned around the predetermined sliding surface (or shear belt). However, this solution has drawbacks, mostly related to the large approximation of the measurements carried out at a restricted depth interval and the high cost of the inclinometer probes (which are frequently lost in situ due to a large amount of displacement of the landslide body).

Another newer solution is the application of Time Domain Reflectometry (TDR) to measure the position and amount of displacement along a vertical borehole (Pierce 1998, O’Connor & Murphy 1997). This system does not, however, resolve the problem of the automation of measurements unless a fixed readout unit is left in place for each vertical borehole which results in excessive increase in costs. Another drawback of the technique is related to the fact that it does not allow the recognition of the direction of movement.

In order to overcome these problems, a new Modular Underground Monitoring System (MUMS) has been studied and developed. The system is modular, having the possibility to accommodate various sensors (such as pore pressure cells, extensimeter, load cells etc) which can be installed in the same borehole and are connected by a single communications cable to a readout unit located at the borehole head. The purpose of the MUMS is the measurement of the underground displacements along the whole length of a borehole by an array of devices within the borehole. The principle of the measurements is analogous to that of inclinometer probe but, instead of having a single probe to be inserted and moved along the borehole, this system has several units, referred to as nodes, each one containing a Micro Electro-Mechanical System (MEMS) that will remain in place underground. The spacing of the nodes is variable with the spacing a function of required precision, the presumed duration of monitoring and the estimated velocity of the landslide. The readout unit of the MUMS can be equipped with a data transmission system, either radio or GSM. Each MUMS apparatus has an on board memory (SD card) that backs up the measured data according to its memory capacity. The unit is powered up by a battery which can be connected with a photovoltaic panel for recharge.

This paper describes the functionality of the MUMS apparatus, examines its reliability and precision and deals with errors that should be considered and resolved during data processing.

2 Operating principles The measurement of underground deformation is normally carried out inside specifically drilled boreholes, using and inclinometer to measure horizontal displacements or extensometers to measure vertical displacements.. By comparing the measurement at a given time with those made after the installation of the inclinometer casing

(zero reading) the total displacement that has occurred in the time interval between the zero reading and the current measurement is obtained. This allows for the identification of the surface/shear band where there is a transition between the deep and stable portion of the ground and the upper unstable part of the monitored slope. Furthermore, the calculated data enables the definition of the average speed and direction of the moving mass. Measurement errors can be grouped in two main sets: bias errors and instrumental errors. Some of them can be compensated by appropriate measurement techniques, while others remain and are propagated in the calculations. The highest resolution of the instrumentation is 0.02 mm for 500 mm, while the repeatability of the measurements is 0.01% FS (Durham Geo Slope Indicator 2009).

The MUMS instrumentation was born from the idea of replacing the above measurement procedure by locating nodes at known distances from each other along a connecting pipe placed within a vertical borehole. Each node is able to measure its local orientation from the vertical (gravitational acceleration) by means of a micromechanical 3D digital linear acceleration sensor (MEMS). This will allow us to determine the direction cosines of the pipe axis in each node and, by means of linear geometry and trigonometry, calculate its 3D shape and deformation along the whole borehole. The system can be described as shown in Figure 1

The basic hypotheses of this procedure are: the lower node must be located in a stable portion of the soil/rock and must be accurately cemented to it; and the distance between two subsequent nodes along the pipe must not vary. This configuration - with 3D inclinometers only - requires particular attention during the installation procedure since, in order to achieve the required accuracy and a correct estimate of the displacement direction all of the nodes must be originally aligned along a single diametral plane of the pipe. This mechanical condition can lead to errors, due to a possible spiralling of the pipe and to a possible incorrect assembly of the nodes, which could degrade the evaluation of the displacement heading and therefore compromise their final measurement integration from the bottom up along the borehole. To avoid this inconvenience, it is possible to add to each node a 3D digital magnetic sensor which enables us to determine the heading (azimuth) of each node related to magnetic north. This added MEMS element eliminates the uncertainties and any errors due to spiralling or to system assembly imprecisions.

The accuracy of the measurements depends on the appropriate calibration of each node (carried out at the production laboratory) and on the site specific constants tied to the local orientation of the Earth’s magnetic field. The Earth’s magnetic field (Campbell 1997) is well known and accurately modeled by several geomagnetic models (EMM2010, HDGM, etc.) which are compiled from satellite, marine, aeromagnetic and ground magnetic surveys around the globe. These models are constantly updated and already in use by directional drillers as a natural reference frame to orient drilling. The calibration procedure reduces all the instrumental errors caused by the sensors and their assembly in each node, but it is not capable of correcting errors (although it does recognizes their presence) caused by local magnetic anomalies that may be present. However, this correction can be done once the vertical axis direction is known from accelerometer measurement, since the node is supposed to be still at the time of each reading and the only acceleration measured is that of gravity. With the increased complexity of each single node, the amount of data to be transferred along the MUMS system increases as well and, for this reason, an innovative connecting system has been studied which allows for the use of a single cable (4 poles) for the serial querying of each node and data recording. The total number of data collected, when all the sensors described are installed, is a minimum of 7 for each node, considering also a temperature sensor that is deemed useful especially on sites where severe variations are expected. Furthermore, the possibility is foreseen of adding, along the MUMS instrument, several other sensors for the measurement of more physical features (pore pressure, load cells, etc.) that might be needed.

Figure 1. Schematic representation of the original and displaced configuration. Xb, Yb and Zb are the global reference system axes (as further defined) while Xbt, Ybt and Zbt are the same axes translated in the node centre.

3 Data processing

3.1 Brief description of the standard inclinometer measurement

The standard inclinometer instrumentation generally used for the measurement of underground displacements requires the installation of an inclinometer casing inside a borehole appropriately drilled; the casing has two pairs of diametric grooves normal to each other, in which the inclinometer probe is inserted and lowered along the borehole. The casing normally has a diameter varying between 48 and 85 mm and is normally cemented inside boreholes of a diameter varying between 110 and 130 mm. The main requirement for measurement interpretation is the rigid connection of the lower part of the casing to a stable substratum (either soil or rock). The system operation requires a first reading usually called “zero reading”, which is the reference measurement for all the subsequent surveys; the readings are carried out by an operator who lowers the probe to the end of the casing along the first couple of grooves, waits for the temperature stabilization of the sensors and then starts to retrieve the instrument at 50 cm intervals. At each interval the instrument is stopped and the measurement of the two axial accelerometers is recorded (after temperature stabilization) either manually or by means of a surface data logger. Once the first reading is completed, the probe is rotated through 90 degrees and lowered again in the same set of grooves. The same procedure is done for the other set of grooves, recovering all the data needed for measurement analysis and displacement calculation. The entire procedure requires the operator on site for an average time of 1.5 to 3 min/m of casing (30/60 minutes for a 20 m long casing); to this operation time must be added the time to reach (and get back from) the location of the inclinometer hole. This is a time-consuming and costly task that doesn’t allow for a frequent repetition of the surveys.

3.2 Description of the new MUMS measurement installation

The new apparatus requires an installation procedure that is analogous to that of a standard inclinometer casing, except for the fact that the MUMS pipe has a diameter of only 5 cm, it is pre-assembled at the production laboratory for the requested length. The assemblage can easily be and installed in smaller boreholes and/or inside old inclinometer casings that are partially broken (and unusable) due to previous landslide movements. The average lifespan of a standard inclinometer ends up with a recorded horizontal displacement of 8 to 15 cm, depending upon the dimension of the shearing surface/band. During the laboratory pre-assembly, all the nodes are installed and fixed inside pipe portions of appropriate length (usually 1 m), cabled between each other and tested for a correct response; their calibration files are recorded and stored on the data logger memory (SD card).

Once the installation site is reached, the single pipe portions are aligned and permanently connected using a practical technique that provides compound glue and rivets. Note that the pipe does not need to be watertight, since each node is waterproofed independently; in fact, the connecting pipe has micro holes to allow the expected water to get into the pipe without any buoyancy effect during installation. Once the MUMS pipe is introduced all the way into the borehole (stabilized with a temporary casing), cementing of the lower portion of it (1.5 – 3 m) is carried out by injecting a suitable fast-hardening grout from the bottom. The remaining portion of the borehole is then filled with clean gravel with a diameter of 3 to 8 mm, recovering the borehole stabilization casing in such a way to maintain 2 – 3 m difference between the level of the gravel inside the borehole and the bottom of the casing. The new conception MUMS instrumentation is based on principles that are analogous to those of the standard inclinometer, with a few substantial differences:

It is formed by a series of nodes, which measure and record the absolute orientation of the MUMS pipe axis relative to the vertical (if the nodes are instrumented with a 3D digital axial accelerometer only), or the absolute orientation of the MUMS pipe axis relative to the vertical and the Earth’s magnetic north (if the nodes have a 3D digital magnetic sensor as well); in this case the orientation of the nodes is determined using the flight convention attitude (Tait-Bryan angles), appropriately modified to treat our problem (Figure 2);

The nodes remain inside the ground for the whole duration of the monitoring and will be lost at the end of it (unless they need to be recovered for environmental reasons using a coring technique); they are all connected by means of a single waterproof and durable cable with 4 poles which connects with a data logger that is installed at the top of the borehole;

The distance between nodes can be chosen according to the precision required for the final output of displacement and, if deemed appropriate, can be varied along the MUMS axis (i.e., to monitor the expected shearing surface/band in greater detail);

In addition to the determination of the 3D shape and configuration of the MUMS (and therefore of the underground soils/rock surrounding it), the system is also able to provide other measurements, such as pore pressure, temperature and other physical entities of interest;

The instrument readings and their recordings are carried out automatically by means of an electronic control unit/data logger which is installed at the surface, preferably at the top of the borehole, and is powered by a battery or, if the local conditions permit, by mains electric power; the MUMS control unit is managed either locally, using a pre-programmed configuration transferred to the unit by insertion of an SD card, or remotely by GSM or radio signals. The duration of a single complete readout of the MUMS depends on its length and the amount of sensors installed in it; the average readout time of each node varies between 0.2 and 0.6 seconds. Therefore, the readout time of a 20 m long MUMS with one node per meter varies between 4 and 12 seconds. The time interval between single readouts can be chosen by the operator based on the particular needs (expected velocity of the landslide, available memory, data recovery frequency, reason for the monitoring, etc.) and in a range starting from the single complete readout time of the MUMS and ending at 9999 seconds.

3.3 Measurement interpretation of the standard inclinometer device

At the end of the measurements and after the required corrections, the two rotation angles of the probe relative to the vertical are obtained for each location at which the probe has been stopped during the recovery. Knowing the distance between two subsequent measurement points (measurement step), it is possible to calculate the displacement of the sensor relative to the original zero reading (A0, B0) at depth d using the following formulas:

∝  ∝ ∝∝  ∝ ∝

A  P sin ∝

B  P sin ∝ [1]

Where P is the measurement step, A and B are the rotation angles relative to the vertical of the two planes X and Y containing the inclinometer casing grooves. The components Ad and Bd are referred at depth d from the surface. The total displacement of the inclinometer casing, at D depth, is obtained from Eqn. [2], while the azimuth (heading) angle of the displacement vector on the horizontal plane at the same depth is given by Eqn. [3].

    [2]

  tan   [3]

The value determined in Eqn. [2] is defined as incremental deviation at depth d. In order to obtain the total displacement at the same depth, one needs to postulate the immobility of the casing at the borehole bottom, and cumulate the single displacements calculated starting from the bottom. The total displacement of an inclinometric column of n length at depth d is therefore given by Eqn. [4].

  ∑   [4]

The graphic representations that are normally generated for supporting data interpretation are: a graph where the incremental deviation is plotted against the depth, another graph where the total displacement is plotted against the depth and, finally, a polar representation of the d azimuth (headings).

3.4 Interpretation of the new MUMS device

The data recorded by the MUMS control unit, at both the 3D digital linear accelerometer sensors and the 3D digital magnetometer sensors, associate each readout with the date and time of the reading and provide the three normalized components of the gravity vector along three axes of a coordinate system associated with the sensor’s body (Figure 3). In order to interpret the measurement and calculate the displacement, one needs to postulate that the lower portion of the MUMS (bottom node) is installed and fixed in a stable portion of the ground (i.e. stable portion of the slope) and the linear distance between two adjacent nodes remains the same. The data treatment is different depending upon the presence or absence of the 3D digital magnetic sensors.

3.4.1 MUMS without 3D digital magnetic sensors

For this case the procedure requires, for each reading, firstly the determination of the direction cosines of the MUMS pipe axis relative to a canonical orthonormal system, with the origin located in the centre of the lower node, axis X directed toward the Earth’s magnetic north and axis Z vertical. The orientation of magnetic north is measured at the top of the borehole during installation and is the same for each node since they are hypothesized as aligned. Secondly, the absolute position of each node with respect to the same coordinate system must be determined. Using this technique, each system reading is independent from the previous one, and using a graphical function it is possible to plot the entire shape of the MUMS column in the 3D space. Then, in order to calculate the incremental deviation of each node from its previous position, it is easy to subtract from the coordinates of each node, calculated at a given time, those calculated at the beginning (or any other time) of monitoring.

The MUMS system offers greater flexibility than the standard inclinometer, since the installation procedure allows for the deformation of the MUMS column and for it to precisely follow the underground deformation; in fact, the data analysis will give the displacement not only along the horizontal plane, but also along the vertical axis Z. The choice of the modulus of the vector (either on the horizontal or vertical plane) allows the calculation of the total displacement relative to a horizontal or vertical plane passing through the center of the node. In the first case, the displacements are directly comparable with those recorded by a standard inclinometer, while in the second case one obtains the total vertical displacement of each node. The charts that can be associated with the data analysis and interpretation could comprise, but not be limited to, the following:

3D graph of the shape and position of the MUMS system at time t;

2D graph of the total displacement of each node on the horizontal plane as a function of the depth (analogous to the chart of total displacement for the standard inclinometer);

2D graph of the total settlement of each node on the vertical plane as a function of depth;

2D polar representation of the direction of displacement of each node as a function of the azimuth (heading).

Obviously, due to the 3D nature of the acquired data, many other analyses are foreseen in order to highlight certain displacement components and features instead of others. In order to evaluate and double check the measurements obtained from the MUMS system, a linear measuring device at the top of the MUMS system is installed; this device will directly and independently measure the lowering of the upper node of the MUMS with respect to the surface and will be useful to check the operational functionality of the system for its entire duration.

3.4.2 MUMS device with 3D digital magnetic sensor

In this configuration, the aircraft convention, aptly modified, appears to be the most suitable for the indication of the nodes/tube axis orientation at each measured location along the MUMS. The aircraft convention defines a device body coordinate using three attitude angles: pitch, roll and heading as shown in Figure 2. Three attitude angles are referenced to the local horizontal plane which is perpendicular to Earth’s gravity. Heading is defined as the angle between the Xb axis and magnetic north on the horizontal plane, measured in a clockwise direction when viewed from the top of the device (or aircraft). Pitch is defined as the angle between the Xb axis and the horizontal plane. When rotating the device around the Yb axis with the Xb axis moving upwards, pitch is positive and increasing. Roll is defined as the angle between the Yb axis and the horizontal plane. When rotating the device around the Xb axis with the Yb axis moving downwards, roll is positive and increasing. For our application, however, the electronic board of each node is generally oriented as in Figure 3 and therefore this convention needs to be modified accordingly. When the node is in the vertical position (Figure 3) pitch and roll angles are 0°. Then the heading angle can be determined as shown in Figure 4, where the local magnetic field has a fixed component Hh on the horizontal plane pointing to the Earth’s magnetic north. This component can be measured by the magnetic sensor sensing axes XM and YM, which are named Xh and Yh. Then the heading angle is calculated as in Eqn. [5]. In Figure 5 when the device body Xb axis is parallel to Hh, which is pointing to the magnetic north, then Xh=max and Yh=0 so that heading = 0°. Rotating the device clockwise on the horizontal plane, the heading increases. When Xh=0 and Yh=min, then heading = 90°. Keep rotating until Xh = min and Yh = 0, then heading = 180°. And so on. After a full 360° rotation, the user sees a centred circle if plotting Xh and Yh values coming from the magnetic sensor measurements.

arctan [5]

Figure 2. Aircraft convention and relation with device body (from STMicroelectronics, 2010 - Modified).

Figure 3. Modified aircraft convention and relationship with MUMS orientation.

If the node is tilted, then the pitch and roll angles are not equal to 0°, as shown in Figure 5, where the pitch and roll can be measured by the 3-axis accelerometer. Therefore, the magnetic sensor measurements XM, YM, and ZM need to be compensated to obtain Xh and Yh as shown in Eqn. [6]. Then Eqn. [5] should be applied for the heading calculation.

  cos sin  sin cos   cos sin cos

[6]

In order to calculate pitch and roll angles from the node, as shown in Figure 3, it should be noted that Xb, Yb, and Zb are the node body axes with forward-right-down configuration. XA,M, YA,M, and ZA,M are the accelerometer and magnetic sensor sensing axes, respectively. Note that the YA,M sensor axis lies on and is in agreement with the Yb node body axis, the ZA,M sensor axis lies on and is in agreement the Xb node body axis and the XA, M sensor axis lies on and is opposite in sign to the Zb node body axis.

Figure 4. Local Earth magnetic field components.

Figure 5. Tilted node and components.

Pitch/roll/heading angles are referenced to the local horizontal plane which is perpendicular to the Earth's gravity:

Heading (ψ) or azimuth is defined as the angle with respect to the magnetic north pole. It is always positive from 0º to +359º when rotating around the Zb axis clockwise, topview with the right-hand rule. If the heading with respect to geographic north is required, then the declination angle at the user's current geographic location should be added or subtracted from the magnetic heading;

Pitch (ρ) is defined as the angle between the Xb axis and the horizontal plane. It goes from 0º to +90º when rotating around the Yb axis with the Xb axis moving upwards. When the Xb axis is moving downwards, the pitch angle goes from 0º to -90º;

Roll (γ) is defined as the angle between the Yb axis and the horizontal plane. It goes from 0º to +90º when rotating around the Xb axis with the Yb axis moving downwards. When the Yb axis is moving upwards, the roll angle goes from 0º to -90º.

When the device node is at an arbitrary 3D position X'b, Y'b, and Z'b, there are a few rotation procedures to rotate the device node from the local level frame Xb, Yb, and Zb, as shown in Figure 3, to that 3D position. Different rotation procedures result in a different rotation matrix. The aircraft convention of angle rotation is used in this case. Firstly, rotate the device node around the Zb axis clockwise at an angle (ψ) with the view from the origin to downwards. Then rotate the device around Yb at an angle (ρ) with Xb moving upwards. Then rotate the device around Xb at an angle (γ) with Yb moving downwards. The new node device body axes become X'b, Y'b, and Z'b, as shown in Figure 6.

Each rotation matrix is then:

cos sin 0sin cos 00 0 1

     cos 0 sin0 1 0

sin 0 cos        

1 0 00 cos sin0 sin  

[7]

And the relationship between X'b/Y'b/Z'b and Xb/Yb/Zb is given in Eqn. [8]:

[8]

Figure 6. Rotation procedures (from STMicroelectronics, 2010).

Figure 7. Representation of the magnetic field H (Earth’s and nearby interference) in the local level frame.

In the local horizontal plane, as shown in Figure 3, Xb = Yb = 0, Zb = +1g. At X'b/Y'b/Z'b, the accelerometer raw measurements are Ax, Ay, and Az, which are signed integer in terms of LSBs. Let Ax1, Ay1, and Az1 be the normalized values after applying accelerometer calibration parameters into Ax, Ay, and Az. So Ax1, Ay1, and Az1 become floating point values less than 1 in terms of g (Earth’s gravity), and the root sum of their squared values should be equal to 1 when the accelerometer is still. Eqn. [8], remembering the sign convention and switched axes, pitch and roll angle can be calculated:

001                   

ρ arcsin

  arcsin [9]

It should be noted that Eqn. [9] generates some singularities that must be corrected (i.e. when = ± 90° it should be set to 0°). Although normalized accelerometer measurement Ax1 is not used for the pitch and roll calculation, it is useful to check that the magnitude of the normalized vector A is equal to 1; if not, it means that linear or angular acceleration is detected. For the heading calculation, 3-axis magnetic sensor measurements need to be normalized by applying magnetic sensor calibration parameters and then reflected onto the horizontal plane by tilt compensation, as shown in Figure 7. If the device rotates from Xb/Yb/Zb to X''b/Y''b/Z''b by roll angle rotation followed by pitch angle rotation, then the rotation is represented by Eqn. [11].

′′

′′

′′

[10]

Let Mx1, My1, and Mz1 be the normalized magnetic sensor measurements after applying calibration parameters correction into magnetic sensor raw measurements Mx, My, and Mz at new positions X''b/Y''b/Z''b. Mx, My and Mz are signed integers in terms of LSBs, while Mx1, My1, and Mz1 are floating point values less than 1 in terms of the magnetic field strength, and the square root of the sum squared values should be equal to 1 when there is no external interference from the magnetic field. Then from Eqn. [10], remembering the sign convention and switched axes, tilt compensated magnetic sensor measurements Mx2, My2, and Mz2 can be obtained as:

cos ρ sinsin γ sin ρ cos sin cos

cos γ sin ρ sin cos cos [12]

Therefore:

Ψ   2

2       2 0    2 0

 180°     2

2       2 0

 360°     2

2       2 0    2 0

 90°       2 0 and  2 0

 270°      2 0 and  2 0

[13]

The magnitude of M2 should be equal to 1. If not, it means that an external magnetic interference field is detected or pitch/roll error is present. The same representation of the attitude of each node can be carried out, with more elegant and efficient mathematical implications and avoiding singularities, by using the quaternions.

Detailed definition of the quaternions and explanation of such a mathematical treatment goes beyond the purpose of this paper, but it can be found in literature (Gebre-Egziabher et al. 2000, Diebel 2006). Once the attitude of each node of the MUMS is detected, the tridimensional reconstruction of the apparatus configuration can be carried out, remembering the hypothesis according to which at least the lower node (node 1) does not move from its original position. Therefore, the centre of this node can be used as the origin of a global reference system (Figure 1) in which the coordinates of the ith node (xbi, ybi, zbi) are calculated by cumulating the relative displacements of all the ith- 1 nodes below.

The MUMS apparatus will therefore output a new configuration for each measurement made according to the time interval between acquisitions, which is arbitrarily chosen at the start of the monitoring and can be changed at any time during the monitoring period. The difference between two acquisitions made at a time difference of t will provide the cumulated and/or local displacement occurring during t, as well as the displacement velocity averaged over that time interval. Further analysis of the monitoring database will allow for a detailed description of geometry and velocity variation of the landslide (and of any other monitored media) and for their relation to other relevant parameters (e.g. rainfall, pore pressures variation, etc.).

4 Performance analysis Several prototypes of the MUMS system were constructed and tested in the laboratory in order to check their performance in a controlled environment. The first MUMS device was built using 10 nodes equally spaced at 50 mm. These nodes were equipped only with a 3D digital linear acceleration MEMS and connected with a double deformable wire solder in order to be able to keep the imposed geometrical configuration. After the first series of experiments, the prototype MUMS size was increased to a distance between nodes of 500 mm for a total length of 5 m. This series of tests allowed us to evaluate the system’s accuracy and the repeatability of measurements; in order to accomplish this task, several configurations of the prototype MUMS were deployed, performing various acquisitions for each configuration and comparing the results with those obtained by direct measuring of the device.

In order to speed up the data analysis process, direct measuring was carried out using photogrammetry techniques; pictures were taken of each predetermined configuration of the MUMS prototype, using a Canon EOS 5D Mark II. The MUMS prototype configurations were rested against a wall in order to minimize errors induced by the photo restitution; however, image calibration techniques, as well as perspective corrections, were applied to the photographs in order to obtain a high precision photomap. Subsequently, the whole device was measured from these pictures, using color and pattern matching techniques.

At the same time several measurement samples were taken and analyzed with the MUMS obtaining the device configuration independently. Lastly, a comparison between the results of the measurements was carried out and gave satisfactory results. At a later stage, some other laboratory tests were carried out using a large scale tilt test machine (Figure 8), that was built earlier by the one of the authors for different purposes (Migliazza et al. 2003). The tests were carried out by installing the MUMS prototype in the machine and fixing it to the bottom of the lower box, filling up the machine with dry sand and applying a shear displacement to the upper box while

measuring the shearing displacement with an external linear potentiometric transducer. The results of the measurements were then compared with those calculated from the MUMS recordings. Several MUMS devices have been installed in landslides and the first results of their measurements will be presented at the Symposium.

Figure 8. MUMS prototype installation in the large scale tilt test box and output after 5 and 180 mm of

horizontal displacement

5 Conclusion This paper describes the functionality of a new apparatus that has been developed for the 3D measurement and monitoring of landslides and underground displacements. The new apparatus has been laboratory tested, examining its performance and reliability, and has subsequently been installed in a few landslides where its behaviour is compared with that of standard inclinometer probes. The paper presents the operating principles of the new device, and shows the basics for data manipulation and interpretation. It is believed that the new apparatus will generate a new and scientifically relevant approach to underground slope stability monitoring, comprehension and control. At this time, several further developments of the apparatus are foreseen, to improve its effectiveness as an innovative and modular underground monitoring tool.

6 References Campbell, W.H. (1997). Introduction to Geomagnetic Fields. Cambridge University Press, ISBN 571936. Diebel, J. (2006). Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors. Matrix. Citeseer. Retrieved

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