Evaluation of electrical resistivity maps for ancient masonry

Transcription

1 Materials and Structures/Matériaux et Constructions, Vol. 29, April 1996, pp SCIENTIFIC REPORTS Evaluation of electrical resistivity maps for ancient masonry D. Van Gemert, H. Janssens, F. Van Rickstal Department of Civil Engineering, Katholieke Universiteit Leuven, De Croylaan 2, B-3001 Heverlee, Belgium A B S T R A C T The use of electrical resistivity maps for the evaluation of ancient masonry is a well-known non-destructive measuring technique. However, these maps do not only contain the information sought, i.e. the localisation of the inhomogeneities, but also the influence of the physical layout and the geometrical boundaries on the measurements. These elements partly hide the desired information. Therefore, computer programs are developed in which this particular boundary effect is incorporated. This leads to maps of relative differences in resistivity that are a picture of the real anomalies in the structure. The evaluation and interpretation of the electrical resistivity maps are thereby made much simpler. R É S U M É L utilisation de cartes de résistivité pour l évaluation de la maçonnerie ancienne est une technique non-destructive déjà bien connue. Cependant ces cartes contiennent non seulement l information désirée, c est-à-dire la localisation des inhomogénéités, mais aussi l influence des bords géométriques. Ces éléments masquent partiellement l information désirée. On a développé des programmes qui prennent en compte cet effet de bord. Cela donne des cartes de différences relatives qui sont une image des anomalies réelles de la structure interne. Par voie de conséquence, l interprétation et l évaluation des cartes de résistivité électrique se trouvent simplifiées. 1. INTRODUCTION An electrical resistivity map is a useful instrument to analyse ancient masonry for restoration purposes [1]. The information on the internal state of the structure visualised in an electrical resistivity map is partly masked due to the influence of the limited dimensions of the analysed masonry element. This observation led to the idea of making maps in which the influence of the boundaries would be eliminated. The resulting maps can then directly be correlated to the real properties or anomalies of the structure. The influence of the geometrical boundaries on a resistivity measurement can be formulated in a parametrical way. The underlying theory is based on the image theory. In this theory, every interface between two materials with different material properties is considered as a semi-transparent mirror that transmits a part of the current and reflects the rest. The formulae are translated into computer programs and the validity of the procedures is tested using case studies. 2. INFLUENCE OF GEOMETRICAL BOUNDARIES A boundary in this context is not only an external boundary, but also the interface between two materials with a different electrical resistivity. The image theory states that each boundary acts as a semi-transparent mirror for the electrical current [2,3]. One part of the current lines penetrates this mirror, while the other part is reflected. At any point in the structure, the electrical current can be considered as being the sum of the current provided by Editorial note Prof. Dionys Van Gemert is a RILEM Senior Member. He is involved in the work of RILEM Technical Committee 151-APC on Adhesion technology in concrete engineering Physical and Chemical aspects. For several years, Prof. Van Gemert has served on the Scientific Committee of Materials and Structures /96 RILEM 158

2 Van Gemert, Janssens, Van Rickstal Fig.1 Schematic view of the column. (M: measuring point, S: electrode) the real current source and the current coming from the mirror image of the real source. To illustrate the influence of the boundaries, a theoretical example was calculated with the computer programs. It concerns a column (Fig.1) consisting of materials with resistivities ρ 1 and ρ 1, where ρ 1 /ρ 1 = The resistivity ρ 2 of the foundation is assumed to be equal to ρ 1. The apparent resistivity, derived from potential difference measurements at the surface, is defined as the relation between the potential difference and the current by the following formula : ρ a =G V I where G = geometrical factor V = potential difference I = electrical current. When an asymmetrical Schlumberger configuration (Fig. 2), with the measuring point M above the current elec- Fig. 2 Asymmetrical Schlumberger configuration. trode S, is moved from the top to the bottom of this column, the apparent resistivity changes as displayed in Fig. 3. The curve reveals that the apparent resistivity is not equal to the real resistivity of the material. Near the boundaries (positions 0, 0.5 and 1), there is a large difference between the two. The shape of the curve can be explained using the evolution of current and equipotential lines in the structure [2]. 3. INFLUENCE ZONE OF BOUNDARIES Fig. 3 Apparent resistivity related to the height. The computer programs can also be used to quantify the zone where there is an influence of the boundaries. By computer simulation, it was found that a mathematical relation exists between the minimal thickness of a wall necessary to have no influence of the upper border on the one hand and the height of the wall on the other. This relation approaches a negative exponential function, 159

3 Materials and Structures/Matériaux et Constructions, Vol. 29, April 1996 Fig. 4 Relation minimal thickness - height (length/height = 10). Fig. 5 Position of measuring point where the influence of the upper edge is negligible. Fig. 6 Two-layered wall. represented by a straight line in a semi-logarithmic diagram. For the particular configuration of a homogeneous isotropic wall with an aspect ratio length-to-height of 10, this is shown in Fig. 4. If one considers a wall with a length of 40 m or more and a height of 4 m, then the minimum thickness to have zones without the upper border influence is 0.21 x 4 m = 0.84 m. The higher the wall, the thinner the wall may be before the measurements are highly influenced by the geometrical boundaries. For a wall with a certain height, the influence zone of the upper edge decreases with increasing wall thickness as illustrated in Fig. 5. Consider a wall 7 m high and 0.60 m thick. The influence zone extends over (0.26 x 7 m =) 1.82 m from the upper edge. This example is shown in Fig

4 Van Gemert, Janssens, Van Rickstal Fig. 7 Electrical resistivity map for the left half of the wall. Fig. 8 Electrical resistivity map for half of a homogeneous wall. Fig. 9 Map of relative differences. 161

5 Materials and Structures/Matériaux et Constructions, Vol. 29, April 1996 Fig. 10 In situ measuring system to determine apparent resistivity of the wall. Fig. 11 Measured electrical resistivity map. Fig. 12 Calculated map of relative differences. 162

6 Van Gemert, Janssens, Van Rickstal 4. MAPS OF RELATIVE DIFFERENCES The concept of a map of relative differences is to simulate numerically the observed structure, taking into account the influence of the internal and external boundaries. The electrical resistivity map of this numerical wall is subtracted from the map measured in situ. This leads to a map where the influence of the boundaries is eliminated, which simplifies the interpretation. This approach is illustrated in a theoretical example. Consider a homogeneous wall of ten meters long, three meters high and one meter thick, with a resistivity of 2000 Ωm. The resistivity of the soil is 100 Ωm. The artificial anomaly in this wall consists of a thin layer (0.5 m) at the upper edge with a resistivity of 200 Ωm. In the map of relative differences, this anomaly will be visualized. The electrical resistivity map for the wall is given in Fig. 7. For reasons of symmetry, only one half of the wall is drawn. The nearly vertical contour lines at the left side are completely due to the left edge. As a consequence, they are nothing but an edge effect. This can be easily understood because there is no lateral variation of the resistivities. The overall picture of the electrical resistivity map shows a value of 2000 Ωm. A conclusion might be that it concerns a homogeneous wall with an anomaly at coordinate 0.5 m. To visualize this anomaly, the edge effects have to be removed. This can be achieved by subtracting the electrical resistivity map of the homogeneous wall with a resistivity of 2000 Ωm. That electrical resistivity map is given in Fig. 7. If the two maps are subtracted, the so-called map of relative differences is left (Fig. 9). The map of relative differences clearly shows a concentration of isodifference lines at the dividing line of the two layers in the wall. Electrical resistivity varies very suddenly at this place and, just as in the case of contours on a geographical map, this results in a higher concentration of isolines. In this case, which represents a theoretical and simplified example, a high relative difference is caused by the two-layer composition of the wall. In other weak zone cases, other anomalies cause this high difference in electrical resistivity. So, the weak zone can be located on the relative difference map by looking at the concentration of the isolines. In case of a perfectly-homogeneous wall and perfect measurements, the relative difference values should be zero everywhere because all geometrical influences have been removed. In more complex situations, the procedure for making an easily interpretable map remains the same. In cases of complex structures, such as pillars or arches, the geometrical influences are calculated and eliminated using finite element models. 5. CASE STUDY The method described above is used to visualize the internal structure of a thin wall (0.4 m) surrounding the park of the Castle of Arenberg in Heverlee. An area of 2.2 m by 1.6 m was measured with a measuring distance L of 0.3 m. The measuring device is shown in Fig. 10. The resulting electrical resistivity map is shown in Fig. 11. After modelling the structure, the map of relative differences can be obtained (Fig. 12). Comparing Fig. 11 and Fig. 12, it is clear that there is no special attention needed for the area at 1.1 m from the upper edge nor for the lower 0.4 m of the wall, as one might have concluded looking at the electrical resistivity map. The map of relative differences indicates the location of anomalies in the wall. In an area around measuring point 0.4, 1.3 there is a large difference with the theoretical value, even in the right corner above and at point 0.4, 2.1. Once the relative difference exceeds 100%, an anomaly is present at that location. An isolated relative difference of about 50% is probably due to inaccurate measuring. The cores taken in these anomalies did indeed reveal the poor internal situation of the masonry, while cores taken outside these zones were intact and sound. 6. CONCLUSION It is desirable to evaluate the internal state of a structure with the help of a map of relative differences of electrical resistivities. Maps of relative differences are calculated by comparing measured values of electrical resistivities and calculated values, obtained by the image theory or by finite element calculations. In these maps, the influence of the geometry and of the interfaces between layers has been eliminated. This makes interpretation easier because the real anomalies in the structure are no longer being masked. This information is necessary for developing a good repair or consolidation strategy in an efficient way. REFERENCES [1] Haelterman, K., Lambrechts, L., Janssens, H. and Van Gemert, D., Geo-electrical survey of masonry, Materials and structures 26 (1993) [2] Janssens, H., Geo-electrical control of consolidation injections on masonry structures (in Dutch), PhD thesis, Department of Civil Engineering, Katholieke Universiteit Leuven (1993). [3] Müller, H., Geo-electrical treatment of a vertically layered soil (in German), Otto-Graf-Institut, Schriftenreihe Heft 24, Technische Hochschule, Stuttgart,