Monitoring of the Vertical Settlement In Heavy Structures By Precise Levelling

Monitoring and analysing of the vertical deformations or the settlements of the structures is one of the main research fields in geodetic applications, which is considered a precise periodic measurement, made at different epochs to investigate these deformations on heavy structures. In this research, the deformation measurements were carried out on one of Baghdad University buildings,” Building of Computers Department” of dimensions (70.0 * 81.3 m.). Due to some cracks observed in their walls, it was necessary to monitor the vertical displacement of this building at some particular monitoring points by constructing a vertical network and measured in different epochs. The first epoch (zero epoch) was carried out in April 2006, the second in July 2006, the third in October 2006 and the last one in October 2012. These four epochs include precise levelling measurements were adjusted by Least Squares Adjustment with the aim of investigating the settlement of this building. The two approaches “the Global Congruency test” and “the simple test” are carried out to detect if there any deformation. These two approaches were employed in the analysis and found the difference in elevations between two epochs most be ensured and found that if the monitoring points (P 1 to P 4 ) stayed really stable, when compared with the time interval or not? Then according to the analysis procedure to determine the localization of settlement at specific points in the case may change in elevation must be applied. The results showed in two different statistical techniques a significant settlement in four selected corner points on building (P1, P2, P3 and P4). The statistics are based on the probability 95% test and the congruency test with Fisher distribution table.


INTRODUCTION
Al-jadriya lake was constructed in 2002 for touring purposes, then cracks were observed in Baghdad University buildings nearest the boundary of this lake (especially the building of computers department that was built in 1993), so a settlement or vertical deformations study is needed, in order to analyse the effect of the water level in the lake on the nearby buildings, Fig. 1,   Figure 1. Al-jadriya Lake and Building of Computers Department It is obvious, the movements and deformation effects on building objects and structures due to own weight, water pressure (changes of ground water level), inner temperature and other factors. [Vladimir and Miloš, 2004] There are a lot of deformation monitoring studies for determining and analysing different kinds of engineering structures such as high-rise buildings, dams, bridges, etc., are implemented. During these studies, the used measurement techniques and systems, this could be geodetic or non-geodetic. [Erol et al., 2004] The deformation monitoring may be divided into two parts: planimetry or horizontally (Δx, Δy) and altimetry or vertically (Δz) [Baselga et al., 2011], the combination between them is a three dimensional monitoring. This study will be discussed the vertical deformation analysis using precise levelling measurements at some particular monitoring points on the building.
In general, the deformation analysis is evaluated in four fundamental steps in a geodetic network: 1. The first step, measurement collection,which were carried out in t1 and t2 measurement epochs. 2. Adjusted every epoch separately according to the Least Squares adjustment method.

SETTLEMENT MONITORING
When some cracks appeared in the walls of the building of computers department, of dimensions (70.0 * 81.3 m.), with a height of about (8 m.), as shown in Fig. 2.
A precise vertical deformation monitoring was proposed to be studying the building stability by determination possible settlement at some main particular monitoring points. It was established in one monitoring point over each corner placed on the columns as it is illustrated in Fig. 2,. So there are (four) monitoring points for frequent measuring to be of interest. There are several methodologies are currently followed when a precise determination of settlement is required. The precise levelling is the most accurate method for detecting the smallest change in elevation associated with construction activity, with an accuracy of about (0.001 m.m.) in elevation, since the conclusion about movement must be made with statistical confidence.

PREPARING THE PROCEDURE OF LEVELLING
To start the levelling procedure, a permanent access point of known height above the datum has been needed, which is a main benchmark that constructed far from the lake and the building in order to be free from possible deformation, it defines the height origin that determined by precise levelling , Fig. 3, shows the benchmark which is a monument of reinforced concrete has a metal rod in the middle with spherical head makes only one part at the top that can be used in measurements.  The monitoring points were located in the walls designed from stainless steel rods driven to a point and set in concrete post or bedrock outcrops, with spherical head. As a result, the site plan of points related to a vertical geodetic network illustrated in Fig. 5, which contains a singular benchmark, four (4) monitoring points and other turning points.
The turning points should be taken on the change plate in Fig. 6, which is made from a solid piece of steel and its weight is heavy.

Monitoring of the Vertical Settlement In Heavy Structures By Precise Levelling
Then precise levelling was conducted with a Topcon (DL-102) Digital Level of the highest accuracy Fig. 7, which provides a reading by estimation to (0.0001 m.m.), and observing the codded invar staff shown in Fig. 8, The digital level is an instrument that uses electronic image processing to evaluate the staff reading.For the most precise work, two invar codded staves are used beside the digital level.
All the data of the vertical staff readings and the horizontal distances of the instrument from the staff are automatically stored by the instrument. [Schofield and Breach, 2007] Indeed the two components of precise levelling are precise equipment and precise procedures that need Least Squares Adjustment for a levelling net.
For a system of weighted observation: where W: is a diagonal matrix of weights.
To calculate the residual: The standard deviation of unit weight for a weighted adjustment is: The standard deviation of the individual adjusted quantities is: in the i th row and in the i th column, this matrix is called "covariance matrix" and symbolized by Q xx .
All observations within this levelling network can be simultaneously adjusted using the The covariance can be used to determine the error ellipsoids of an (n-dimensional random variables). In the practical application of adjustment the variance and covariance are often replaced by what should be called "relative variance and covariance" for these the terms "weight coefficient or cofactors" are in common use. The term cofactor is selected and the letter "q" for one element and "Q" for a matrix are used as a symbol for it. [Mikhail, 1976] A cofactor is related to a covariance by: Eq.(7) related to the relation between a cofactor and the variance:

STATISTICAL TESTS
Statistical tests are increasingly applied in engineering and in combination with the least Squares method. They are often used to compare results with previous ones or with given standards. In testing, one seeks adjustment as to whether some estimator function. [Mikhail, E. M., 1976].
In the case study of vertical network, when the differences in elevations occurred for the same point at different periods (will be presented) it is very important to distinguish between the "error" and the "movement" this is done by statistical tests.
The adjusted results, according to the Least Squares method, are based on several assumptions which give anchor to the reliability of the statistical test. Statistical detection in levelling measurement can be achieved by two statistical tests: 1. Simple deformation test.

6-1. Simple deformation Test
From the results of two epochs adjustment (i , f) with (n) points, it is possible to calculate the displacement (deformation) vector and its associated variance covariance matrix (Qxx). When the problem deals with a settlement that means one dimensional deformation required. So the simple deformation test depends on comparing the absolute displacement │dn│ in elevation for each point with the probable error at a (95%) confidence limit (e n ). If computed (d n ) < theoretical (e n ) : Accepted, that means no settlement. Otherwise rejected when computed (d n ) > theoretical (e n ) means there is deformation or settlement.

6-2. Global Congruency Test
The Global Congruency test is the most commonly methodology adopted for the detection of general deformations in a given area i.e. an overall change in shape. [Fagir et al., 2007] After adjusting each epoch separately, then the procedure of deformation analysis is done step by step, with the Global Congruency test.
If the elevations of repeated measurements with its variance covariance matrices of the elevations and its datum are available, the question, congruence between different epochs exist or not? [Denli and Deniz, 2003] The problem of investigation of the stability of network points is solved by a test of the null hypothesis (H o ) "the common points of both epochs (i, ,j) are stable" and thus have: The displacement vector (d) for two different epochs and its associated weight matrix (W dd ) from error propagation can be computed as: hj where: By comparing (f-table) with (f-computed) to decide the case of settlement: Fisher distribution values obtained from prepared tables or interpolated from graph for each level of significance.

6-3. Localization of Elevation Changes
After determining a group of stable points as a result of global test, the following step of the analysis is the localization of elevation changes. For doing this (Ω 2 ) are calculated for the every network point, except the stable points, and they were compared with (F) critical value that is given in the fisher distribution hj , it is said that the elevation of the point changed significantly. Otherwise it is resulted that (d: elevation difference) is not a displacement but it is caused by the random measurement error.

CONCLUSIONS AND ECOMMENDATIONS
By application of the Least Squares method, the adjusted elevations of every epoch are determined. It was possible to compute the possible differences and the corresponding deformation after applying it to the statistical test.
The first third epochs did not show significant displacement, may be for the short period, but then when taking observations over six years the settlement will be appeared as shown in Table (5).
Additional measurement companies are suggested for the next years, in order to obtain a more reliable monitoring modelization.