Establishment of Deformation and Subsidence Monitoring Baseline in the Coastal Environment: A Case Study of University of Lagos

Deformation and subsidence measurements are very vital for stability of structures and buildings. Deformation and subsidence monitoring are easily carried out with the aid of established baselines. This study focuses on the establishment of baseline for monitoring deformation and subsidence within university of Lagos. Geodetic method of control establishment was adopted, where five (5) control stations were established on stable grounds across the university of Lagos main campus with Differential GPS observation carried out on them and data obtained were processed and analysed statistically. The result of the findings shows that the baseline established is very reliable, given that the vertical controls have their relative redundancy number rij ranging between 0.1<rij<1.0 and the standard deviations ranges from 0.002 to 0.005. Also, the relative precision of the established baselines fell within the range of 7.36e-06ppm-2.54e-05ppm. From the findings of this research, deformation and subsidence studies can be reliably monitored within the University of Lagos and its environ using the baseline established through this research in order to safeguard lives and properties – including high rise structures within the university’s main campus.


Introduction
Ground subsidence can be caused by several geological factors, climatic processes and anthropogenic sources, or by mixture of the above factors. Subsidence is frequently linked to intense faulting and opening of fissures in urban areas, generating a significant geologic hazard that needs to be accurately assessed and monitored (Ferretti et al., 2004;Mazzotti et al., 2009;Brunori et al., 2015).
Recent researches have demonstrated the applicability of Global Positioning System (GPS) techniques to precisely determine the 3-D coordinates of moving points in the field of natural hazards such as earthquakes, landslides, and volcanic activity. Indeed, the detailed analysis of the motion of a landslide, in particular for a near real-time warning system, requires the combination of accurate positioning in three dimensions (infracentimetric) and fine temporal resolution (hourly or less) (Malet et al., 2002). Besides, in order to detect and measure the vertical displacement or subsidence of offshore platforms, GPS is considered as the best tool to determine relative position between control stations because GPS allows us to achieve a desirable precision (i.e. +0.1ppm) that is necessary for subsidence monitoring (Leick et al., 2015) Techniques of positioning on various time and space scales have made a lot of progress in the last decade, in particular in the field of geomorphological mapping, or in the realization of Digital Elevation Model (DEM) by numerical photogrammetry (Girault, 1992;Miyazawa et al., 2000;Weber and Herrmann, 2000). As a result of the constantly growing technological progress in all fields of engineering, the increasing demand for higher accuracy, efficiency, and sophistication of the deformation measurements, geodetic engineers have continuously searched for better monitoring techniques and have to refine their methods of deformation analysis. The infiltration of space techniques such as GPS has opened a new dimension in data acquisition which involves offshore structures such as gas and oil platforms which are situated hundreds of kilometers offshore (Setan and Othman, 2006). A suitable technique of data acquisition has to be identified such that a high accuracy observation can be obtained and its results can be used for deformation analysis. Amiri-Simkooein et al. (2017) proposed a method that identified the unstable points of a network based on the generalized likelihood ratio (GLR) test. The method simultaneously uses the observations of two epochs called the simultaneous adjustment of two epochs (SATE) method. SATE is applicable to one-, two-, or three-dimensional deformation networks with any type of observations, including distances, angles, global positioning system (GPS) baselines, and height difference. Samsonov et al. (2017) developed a Multidimensional Small Baseline Subset (MSBAS) methodology which is a semiautomatic processing system for computing temporally dense two-dimensional, horizontal east-west and vertical time series of ground deformation from ascending and descending SAR imagery acquired by various satellites. The MSBAS was used for mapping ground deformation at the Piton de la A research like this is highly justified in the coastal area like that of University of Lagos because there is need to provide accurate, wide area ground deformation data to complement accurate ground survey data of generally more limited spatial coverage, identify areas of high differential settlement for potential damage to surface infrastructure, provide historic ground movement for baseline and monitoring, identify subsidence depressions that may pose flood risk potential and identify areas of high seismic risk (ground shaking, liquefaction, fault rupture). Coastal environments tend to have weak soil structure resulting from the nature of the vegetation such as mangrove swamps logged with water, hence, the need to monitor structural facilities built in the area using subsidence monitoring baseline (Kirwan and Megonigal, 2013) This paper focuses on the establishment of a baseline for the purpose of monitoring cases of subsidence and deformation that could likely happen within coastal environment of University of Lagos since population and human activities are increasing geometrically in the area.

Literature Review
Over the last decade, interest has grown among structural engineers and other building professionals such as builders, geotechnical engineers, mechanical engineers and surveyors in monitoring the movement of different types of structure both during and after completion of construction. In different parts of the city of Lagos, numerous cases of building collapse have been recorded (Akpan, 2017;Olowopejo, 2018). It is well known that the foundations of large buildings are affected by changes in ground conditions, and also walls of heavy structures change shape with varying pressure (Tasci, 2008). For all these, deformation surveys can be used to measure the amount by which a structure moves both vertically and horizontally over regular time intervals. Although all the principle of many of the techniques used for doing this are recognizable as those used for site surveying and setting out, however, continuous updating of very precise periodic measurements either on structure or a defined location distinguishes a deformation survey from other types of survey (Uren and Price, 1994). Deformation surveys have been carried out to detect or predict subsidence through several techniques of measurement. These methods include Geodetic techniques, Non-Geodetic (Geo-Technical) techniques (Erol et al., 1999), photogrammetric and remote sensing techniques (Rosu et al., 2015).

Methods of Deformation Monitoring
Geodetic techniques make use of measuring devices that measure geo-referenced displacements or movements in one, two or three dimensions. Geodetic techniques comprise a network of points interconnected by angles and distances measurements. They usually provide a sufficient redundancy of observations, for the statistical evaluation of their quality and for detection of errors (Beshr, 2015).
It includes the use of instruments such as total stations, automatic levels, digital levels and global  (Langley et al., 2017). Technological advancement in satellite geodesy has led to the recent development of dense and continuously operating Global Navigation Satellite System (GNSS) networks worldwide and as such resulted in a significant increase in geodetic data sets that sometimes capture transient-deformation signals (Walwer et al., 2016) Several researches have monitored subsidence using the geodetic networks.  exploited geodetic techniques to assess possible deformations of the embankment structure of Atatürk dam in Turkey. The geodetic approach included differential, trigonometric, and global positioning system (GPS) leveling observation campaigns over a period of 6.5 years from May 2006 through November 2012. The geodetic control network included 32 reference points and approximately 200 object points located on the surface of the embankment structure. All object points were equipped with forced centering mechanisms to support either optical targets, reflectors, or GPS receivers, depending on the type of geodetic measurement campaign. From the observations, the downstream side of the embankment crest appears more stable, with small vertical movement amplitudes (< 10 cm). Nowel (2015) used the Robust M-estimation in the geometric deformation analysis of geodetic control networks, especially in the analysis of single-point displacements in these networks. Two methods for displacement analysis based on robust M-estimation were used. The first method was the classical robust method, in which the displacement vector is determined from differences in adjusted coordinates. The second method was Generalized Robust Estimation of Deformation from Observation Differences, in which the displacement vector was determined from differences in unadjusted observations. Classical and proposed robust methods were tested on the basis of the simulated two-epoch observations of the absolute control network of the Montsalvens Dam in Switzerland (which is well known in the literature) and on the basis of Monte Carlo simulations. The test results showed that the proposed robust method (Generalized Robust Estimation of Deformation from Observation Differences), in some cases, might be more adequate than the classical robust method, especially when low values of displacements that slightly exceed measurement errors are expected. Scaioni (2018) integrated the data collected with Robotic total stations and GNSS (Global Navigation Satellite System) techniques for measuring 3D displacements on precise locations on the outer surfaces of dams.
Non-Geodetic techniques make use of measuring devices that measure non-georeferenced displacements or movements and related environmental effects or conditions. It includes the use of instruments such as extensometers, piezo-meters, rain gauges, thermometers, barometers, tilt-meters, accelerometers, and seismometers. Non-Geodetic methods have been explored in different researches. Wilczyńska and Ćmielewski (2016) used the accelerometer to detect the direction of the gravity Earth's force field which allows to calculate the angle of inclination from the vertical or horizontal line between structural elements such as beams. The accuracy of the sensing angle is better than 0.3mrad, which means the ability to determine the deformation better than 0.3 mm/m. They also proposed the use of measuring set comprising laser diode and CCD camera which enables automatic control in real time. The accuracy of the measurement is better than the pixel in the position of the laser beam footprint which was less than 0.3 pixel.  adopted the geodetic and non-geodetic methods for monitoring the geometric changes at the Atatürk Dam surface. Physical and geometrical changes in embankment inside were defined using the non-geodetic methods while the bathymetric surveying techniques were also used in the water covered area and Real Time

Least Squares Adjustments by Observation Equation Method
The functional relationship between adjusted observations and the adjusted parameters is given as (Ono et al., 2014, Ayeni 2010: Where, L a = adjusted vector of observations and X a = adjusted station coordinates. Equation (1) is non-linear function and the general observation equation model is obtained after linearization.
The system of observation equations is presented by matrix notation as (Mishima and Endo 2002): where, A = Design Matrix, X = Vector of Unknowns, Applying least squares principles and solve for X, Equation (3) is obtained Where, X = estimate, P = weight matrix

Least Squares Adjustments by Condition Equation Method
The general case of non-linear model will be treated since the linear model can easily be derived from it. If we define La in eqn. (5) as La = Lb + V then we have (Ayeni 2010).
where Lb, V are Vector of Unadjusted Observations and Vector of Residual respectively.
The Vector of Residual is given as The formula for a-posteriori variance of unit weight is given by where r is number of condition equations The Variance-Covariance matrix of adjusted observations is then given as However, this study intends to establish geodetic baselines that would be useful in the deformation monitoring of structural elements of buildings in the University of Lagos coastal habitat due to the vulnerability of the earth formed from sand-filling operations. Other methods of deformation monitoring such as the non-geodetic and remote sensing techniques can be integrated with the geodetic deformation monitoring operation from the established baselines.

Study Area
Lagos State is located in the southwestern coast of Nigeria approximately between latitudes

Materials and Methods
Prior to the execution of the field work, an existing in-situ 1st order control within the campus was located which was used as base station for the field observation. Property Beacons with dimensions 35cm x 35cm x75cm were cast at the five chosen reference points. Each beacon was marked and a prefix number was engraved on it. The project planning phase was essential as the network and deformation monitoring design was initiated. Having multiple control stations in the reference network is critical for improving the reliability of deformation surveys, and for investigating the stability of reference monuments over time. The network design ensured that each control station in the reference network was inter-visible to a maximum number of structural monitoring points (placed on the structure) and to at least two other reference monuments.
Coordinates were transferred by GPS observations from reference station, XSR347 being a 1 st order control beacon on campus to the newly established stations (Second Order Controls) in the reference network before the monitoring survey. 3D coordinates were established on all reference stations in the study. The equipment used in the study includes Leica 1200 Differential GNSS ( Figure   2a) and Leica DNA 03 Digital level (Figure 2b) for field observation. Methodology employed in this study is divided into three sections: data acquisition, data processing and network adjustment as described in the Methodology flowchart in Figure 3. The existing coordinates of the Reference Station are presented in Table 1.

GPS Observation
The rectangular coordinates of the five-point forming the monitoring baseline stations were determined relative to the 1 st order control (XST347) with Differential GPS. Observations were taken over a period of two months, the mean of the whole observations on each station were acquired.
Digital level instrument was used to carry out levelling from XST347 through the five baseline stations so as to obtain orthometric height. This first epoch observations of the Differential GPS and digital level were used as reference observations to establish the coordinates (X, Y, Z) of the control points forming the monitoring baseline such that the subsequent epochs observations will be compared with them to ascertain any displacement. The displacement in magnitude and direction of any monitoring structure within the study area could be determined using Equations (9) as the difference in coordinates between the measurement epochs (Ehiorobo and Ehigiator 2011): Where, c) Station data: Specific information related to the data collection was noted and recorded on the appropriate log sheets at each station. d) Recording interval: A five (5) second data logging rate was used in all data collected for monitoring surveys. The logging rate is defined as the time interval (in seconds) between each data value recorded in the receiver's internal memory.

Leveling Operation
The Leica DNA03 digital level was used to transfer height (Orthometric) from a stable reference point (XST 347) to the GPS monument reference points using the principle of differential leveling where the level and the leveling staff are employed to determine vertical distances of points above or below a reference datum. The method of determining elevation using the digital level is through the use of an electronic digital barcode leveling staff to determine the difference in elevation between a known elevation and the height of the instrument, and then the difference in elevation from the height of instrument to an unknown elevation point. The differential leveling operation data were stored in the digital level device due to its ability to retain observation data.

Data Processing and Adjustments
The GNSS data obtained were post-processed in the Leica Geo Office 4.0 software environment.
The Static GNSS observation being a differential observation technique with baselines being "observed" and computed from the reference to the rover was post-processed to provide millimeterto meter-level precision. Typically, the post-processing involves differential processing relative to a fixed base location. Post-processing the data greatly minimizes or eliminates numerous error sources in GNSS positioning, among which are receiver and satellite clock errors, delay of the GNSS signal through the Earth's atmosphere (most significantly, the ionosphere and the troposphere) (Lauer 2018). The processing parameters were set with the cut-off angle set to 12 o from the original 15 o for higher accuracy. The coordinate system of the post-processing operation was set to projection UTM 31N based on the WGS84 ellipsoid. The existing coordinates of the base station were keyed in for the baseline processing of the observation set and the post-processed coordinates were generated as the software was set to repeatedly compute the baselines in the network. Processing was done both in the Automatic and Manual modes. In automatic mode, all jobs were selected and processed at once while in the manual processing mode, the rover stations were selected separately from the reference stations and then processed with the intention of ensuring that both sets of observations (Base and Rover) were void of errors or blunders. The Lagos Geoid model developed by Olaleye et al. (2013) was loaded and used to evaluate the orthometric heights of points as ellipsoidal heights are the obtainable from any GPS observation.
The downloaded levelling data from the Digital level were imported into MatLab environment for adjustment based on the principle of least squares models presented in Equations (6) to (8). Table 2 shows the result of the levelling network which are the distances between the stations as well as the height difference between two stations. Where dH is the height difference between stated points and was obtained from observations made on site and Distance is the linear distance between stated points as obtained from coordinates of points (√∆E 2 + ∆N 2 ). The height of known control, XST347 is given as 4.701 meters.

Coordinate Transformation
Coordinates were converted from UTM WGS84 datum to UTM Nigerian Local Datum (Minna Datum) using GeoCalc (Geographic Calculator) software. The GeoCalc software is a coordinate transformation software readily available for coordinate transformation and has been used in different researches (Kumar and Murry, 2017;Eteje et al., 2018). The Coordinates were transformed to the UTM Nigerian Local Datum (Minna Datum) to ensure coherence with the locally used coordinate system as the baselines will be used for monitoring engineering structures in the local space.

Results and Analysis
This section presents and discusses the results from the observations and post-processes. Table 3 shows the results of the processed coordinates using Leica Geo Office 4.0 software along with the standard deviations in Easting and Northing.   Note, however that the orthometric heights in Table 2 were obtained using the Lagos Geoid model.
The orthometric heights obtained from actual leveling operations were adjusted with least squares according to Ayeni (2010). Table 3 shows the height differences between stations. Table 4 shows the differences between the Geoid derived orthometric heights and the adjusted heights obtained from actual leveling operation.  Table 4 shows the equal difference in the height referenced to the Geoidal model obtained from the GNSS post-processed result (adjusted) and the orthometric heights (adjusted) obtained from the leveling operation. The difference between the mean sea level and the derived Lagos Geoidal model is seen to be 0.0090metres. Trends in deformation detection can be observed as consistent observations taken using the baseline monuments established in this research. The significance of these initial results is enhanced when considering the reliability of the established baselines judging from their accuracies and precisions acquired with the research.

Reliability of Vertical Controls
Reliability refers to the controllability of observations i.e. the ability to detect blunders in the observations (Kurotamuno, 2016). According to Ayeni (2010), the amount of redundancy (rij) that each observation adds to the solution is given by: Where rij is the observational redundancy number.
qij is the ith diagonal element of the observational weight matrix P pij is the ith diagonal element of the covariance matrix of the residuals

Precision of Established Baselines
In computing the relative accuracy of each of the newly established baselines, the relative precision of a traverse leg formula was adopted from Ghilani and Wolf (2012) and modified to yield the formula below (Table 5). Where: σA is the standard deviation of the baseline between controls in consideration LA is the length of baseline between controls in consideration. Part of the results of establishment of baseline for monitoring deformation in University of Lagos as detailed in Table 5 show that the best precision was acquired between GME02 to GME03 which is 1.46e-05. The results are in correlation with the standard given in the work of Malet et al. (2002) and Gili et al (2000) where surficial displacements and their precision using GPS is found to be between 1-2mm for a typical baseline range of less than 20km. Furthermore, inferring from the accuracy claimed by different deformation monitoring techniques in the work of Savvaidi (2003), GPS L1/L2 static observation must give a typical accuracy of ± (5mm ± 2ppm) for a distance of less than 50km between two stations and ± (1-3mm ± 2ppm) for a distance of less than 1 -2km between two points. Comparing the results in Table 3 from what is the standard from the literature, the results obtained from this research show that the baseline is standard and very reliable to carry out deformation monitoring not in the University of Lagos alone but around its environ.

Conclusions
Deformation and subsidence measurements are very vital for stability of structures and buildings.
Deformation and subsidence monitoring are easily carried out with the aid of well-established baselines. This study focuses on the establishment of baseline for monitoring deformation and subsidence within university of Lagos. Geodetic method of control establishment was used, where five (5) control stations were established on stable grounds across the university's main campus with Differential GPS observation carried out on them and data obtained were processed and analysis statistically. The result of the findings shows that the baseline established is very reliable given that the vertical controls have their relative redundancy number rij ranging between 0.1<rij<1.0, and the standard deviations ranges from 0.002 to 0.005. Also, the reliability of the established baselines fell within the range of 7.36e-06ppm-2.54e-05ppm. From the findings of this research, deformation and subsidence monitoring studies can be carried in University of Lagos corridor in order to safeguard lives and properties in the environment -including high rise structures within the university's main campus.
With the economic and social importance of the coastal environment to the growth and well-being of the inhabitants, which includes implementation of marine and coastal structures and activities, there should be adequate and regular monitoring measurement to forestall any occurrence of deformation on the heavy structures around and within the University of Lagos.