STATISTICAL INTERPRETATION OF RESULTS OF POTENTIAL MAPPING ON REINFORCED CONCRETE STRUCTURES

Transcription

1 STATISTICAL INTERPRETATION OF RESULTS OF POTENTIAL MAPPING ON REINFORCED CONCRETE STRUCTURES Joost J. Gulikers (1) and Bernhard Elsener (2) (1) Rijkswaterstaat Bouwdienst, Utrecht, Netherlands (2) ETH Zurich, Switzerland Abstract Potential mapping is the most widely applied and accepted non-destructive measuring technique to assess the condition of reinforcement in concrete with respect to osion. However, there is much debate on the appropriate potential criterion as to allow for a distinction between actively oding and sive steel. In the RILEM Recommendation for half-cell potential measurements [1] a statistical analysis of the results of potential mapping is advocated in order to arrive at reliable potential criteria taking into account the characteristic features and exposure conditions of the concrete structure under investigation. Unfortunately, the underlying calculation procedure has not been elaborated and consequently there is no practical and unambiguous guidance how to perform such a statistical analysis. In this paper the theory for the statistical analysis is presented based on the assumption that the potential distribution for both actively oding and sive steel can be adequately described by a normal density distribution. This theory is then applied to a number of situations to exemplify the procedure by clear graphs. The potential criteria thus derived will demonstrate a significantly smaller range as compared to the criteria presented in ASTM C 876 [2]. Moreover, with this statistical analysis any desired probability level can be chosen. Keywords Concrete, reinforcement, osion, potential mapping, statistical analysis 1. INTRODUCTION During the last decades half-cell potential mapping has developed into a common technique to allow for a cost-effective and overall non-destructive assessment of concrete structures with respect to reinforcement osion. Although it is recognized that this 221

2 technique will not provide any quantitative information on the kinetics of the osion process as well as the residual cross sectional area of the embedded reinforcement bars, the measurement results obtained can be used to draw reliable conclusions concerning the extent and locations of osion activity within a structure. In most situations half-cell potential measurements are interpreted by using supplementary data such as cover depths, rebar spacing, chloride profiles, depths of carbonation, electrical concrete resistivity, environmental exposure conditions, and structural detailing. Although the measurement procedure is simple and straightforward, the interpretation of the results is often not that easy as is suggested by the criteria presented by ASTM C 876 [2]. In practice these ASTM criteria are often employed, however, practical experience has shown that these will yield only rough guidance in the interpretation of the measurement results of potential mapping. Half-cell potential measurements taken from the concrete surface are influenced not only by the electrochemical state of the steel bars but also to a significant extent by the cover thickness as well as the electrical resistivity of the concrete. According to the RILEM Recommendation [1] the potential criteria used in the ASTM C 876 should therefore be treated with caution and should not be employed as absolute criteria valid for all structures to determine the electrochemical condition of reinforcement steel. Consequently a statistical treatment could prove to be more advantageous to deduce more reliable potential criteria pertaining to a specific concrete structure or element for the exposure conditions prevailing shortly prior and during the execution of potential mapping. Although such a statistical approach is mentioned in the RILEM Recommendation on Halfcell potential measurements, this document provides insufficient information on how to actually perform a sound statistical analysis. In this paper an attempt will be made to develop a procedure for such a statistical analysis and how to derive more reliable potential criteria. In [3] a more detailed and elaborated description is provided. 2. POTENTIAL MAPPING The basic equipment to be used for potential mapping comprises a standard half-cell, normally referred to as a reference electrode, and a high impedance digital voltmeter. Most often a pre-wetted sponge folded around and attached to the tip of the reference electrode is used to provide a low electrical resistance liquid bridge between the surface of the concrete and the porous plug of the reference electrode. In order to complete the electrical circuitry a direct electrical connection to the steel has to be made by means of a compression-type ground clamp, or by brazing or welding a protruding rod. By convention the positive terminal of the voltmeter is used to make the connection with the reinforcing steel and the negative terminal is reserved for the reference electrode. Prior to performing potential mapping, it is essential that the reinforcement steel mesh to be investigated will be checked for electrical continuity. With this arrangement the potential difference with the steel surface at some distance below the tip of the reference electrode is measured. By moving the reference electrode along the concrete surface a quantitative impression of the potential field is obtained. A sketch of the common measurement arrangement is shown in Figure

3 reference electrode mV DVM - + concrete reinforcement Figure 1: Test arrangement for potential mapping of reinforced concrete structures 3. THEORETICAL BACKGROUNDS In order to allow for a statistical treatment some basic assumptions have to be made. The primary assumption is that the potential values for both sive and oding steel show a normal probability distribution. In addition it is required, that the mean potential value for actively oding steel is significantly more negative than that for sive steel. Figure 2 shows an example for the distribution of the probability density, p, for a specific situation in which 80% of the potentials pertain to reinforcement steel being in an electrochemically sive condition whereas the remaining 20% espond to actively oding steel. In the following the relative number of potential readings pertaining to sive and oding steel will be referred to by R and R, respectively, with: R = 1.0 with 0.0 <R < 1.0 and 0.0 < R < 1.0 (1) R The potentials demonstrated by sive steel are referred to by E, and in this specific situation the electrochemical condition of sive steel is characterised by a mean value µ(e ) = -150mV and a standard deviation, σ(e ) = 50mV. Likewise, actively oding steel is characterised by µ(e ) = -350mV and a standard deviation, σ(e ) = 100mV. In this paper the potential values will be given relative to a saturated copper/copper sulphate (Cu/CuSO 4 ) reference electrode. The potentials of both sive and actively oding steel will contribute to the overall probability density distribution. Thus sive steel will contribute by a relative amount of R, whereas oding steel will contribute by a relative amount of R. This will result in a surface area covered by the overall density distribution equal to 1.0. However, for this situation there is an overlapping potential region extending from 250 to 310 mv. It is obvious that the overlapping region will increase when the difference between the mean potential values µ(e ) and µ(e ) will become less or when the standard deviations σ(e ) and σ(e ) will increase. The presence of such an overlapping potential region will complicate the interpretation of the results of potential mapping, as values in this region may 223

4 either pertain to sive or actively oding steel. As an example the influence of a shift in σ(e ) is presented in Figure 3. In the latter Figure the situation with σ(e ) = 25mV will 0,007 probability density, p [-] 0,006 0,005 0,004 0,003 0,002 0,001 R = 0.20 µ(e ) = -350 mv σ(e ) = 100 mv sive oding total µ(e ) overlap µ(e) 0, potential, E [mv; vs Cu/CuSO 4 ] Figure 2: Probability density distribution showing the individual contribution of sive and oding steel on the overall distribution 0,007 0,006 R = 0.20 µ(e ) = -350mV probability density, p [-] 0,005 0,004 0,003 0,002 0,001 σ(e ) = variable 200mV 150mV 100mV 75mV 50mV 25mV µ(e) µ(e) 0, potential, E [mv; vs Cu/CuSO 4] Figure 3: Probability density distribution showing the influence of the standard deviation of actively oding steel σ(e ) 224

5 result in 2 distinctly different potential regions separated by a limited in-between region around -290mV showing a relatively small probability density. This implies that only a very limited number of readings will be available that show values in this range. Consequently, for σ(e ) = 25mV the interpretation of the measurement results will be relatively simple. However, in most situations encountered in practice a wider overlapping potential region will be present which will obscure an unambiguous interpretation. 1,0 cumulative probability, P [-] 0,8 0,6 0,5 0,4 0,2 0,1 R = 0.20 µ(e ) = -350 mv σ(e ) = 100 mv overall sive oding R R 0, potential, E [mv; vs Cu/CuSO 4 ] Figure 4: Cumulative probability distribution showing the individual contribution of sive and oding steel on the overall distribution The distribution of the cumulative probability, P, esponding to the situation characterised by µ(e ) = -150mV, σ(e ) = 50mV, µ(e ) = -350mV, σ(e ) = 100mV, and R = 0.20 is depicted in Figure 4. For this situation 50% of the measurement results will show values E < 165mV, 20% with E < -241mV, 10% with E < -350mV, and 5% E < mV. In this graph the contribution of oding and sive steel to the overall cumulative distribution is also demonstrated. As a further example Figure 5 shows the cumulative probability distribution for 0.50 R 0.95, esponding to 0.05 R Unfortunately, in practice this detailed statistical information is not available beforehand but it has to be derived from the measurement results of potential mapping. Consequently, a straightforward and simple calculation procedure should be developed. 225

6 1,0 cumulative probability, P [-] 0,8 0,6 0,4 0,2 R 50% 75% 80% 85% 90% 95% µ(e ) = -350 mv σ(e ) = 100 mv , potential, E [mv; vs Cu/CuSO 4 ] Figure 5: Cumulative probability distribution for values of R ranging from 0.50 to 0.95 (0.05 R 0.50) 4. CALCULATION PROCEDURE The measurement results obtained from potential mapping can be presented as histograms or graphs of frequency distributions; however, from a practical point of view cumulative plots will be more convenient. A cumulative distribution can easily be accomplished in a spreadsheet program, e.g. Excel. In order to achieve this, the number of readings demonstrating values less than a predefined range of target potential levels has to be calculated and this information is presented in a graph. Figure 6 demonstrates this procedure for the (ideal) situation characterised by µ(e ) = -150mV, σ(e ) = 50mV, µ(e ) = - 350mV, σ(e ) = 100mV, and R = 0.15 in which a total number of readings n tot = is available. The stepped line results from the calculation using target potential levels in steps of 50mV, whereas the dashed line represents the situation when infinitely small potential steps would have been used. By dividing the number of readings by the total number of readings available (here 10000) the scale of the vertical axis is converted into unity and its values have become equal to the cumulative probability, P. The next step in the calculation is to decompose such a cumulative probability graph into 2 distinct contributions, i.e. the contribution by sive steel and the contribution by oding steel. This statistical decomposition can easily be accomplished in an Excel-spreadsheet by applying a regression analysis. In fact 5 parameters have to be quantified, i.e. R, µ(e ), σ(e ), µ(e ) and σ(e ). The equation to be used in Excel is: P(E) + R = R NORMDIST E; NORMDIST ( µ ( E ); σ( E );TRUE) ( E; µ ( E ); σ( E );TRUE) (2) 226

7 number of readings exhibiting E < Etarget [-] R = 0.15 µ(e ) = -350 mv σ(e ) = 75 mv n tot = continuous stepped target potential, E target [mv; vs Cu/CuSO 4 ] Figure 6: Cumulative probability distribution for values obtained from field measurements (graph shows ideal situation) with R relative number of potential readings pertaining to sive steel R relative number of potential readings pertaining to oding steel, R = 1 with ( ) R E potential as measured with a reference electrode on the concrete surface, [mv] µ(e ) mean value of the potentials pertaining to sive steel µ(e ) standard deviation of the potentials pertaining to sive steel µ(e ) mean value of the potentials pertaining to oding steel µ(e ) standard deviation of the potentials pertaining to oding steel This calculation exercise will yield the desired values for R, µ(e ), σ(e ), µ(e ) and σ(e ). Once this information is known the potential criteria esponding to the required probability that the reinforcing steel is sive or actively oding can be calculated. This procedure is neither described in the ASTM Designation C 876 nor in the RILEM recommendation. However, a detailed description of such a procedure is urgently required as to how to allow for a sound and straightforward statistical treatment of the measurement data. At every potential a certain probability, P (E), exists that the steel in that area is actively oding. The value of P can be calculated through the ratio: p ( ) ( E) p( E) (3) P E = = p E p E + p E with p p tot ( ) ( ) ( ) probability density of potentials for actively oding steel probability density of potentials for sive steel 227

8 The probability densities p and p can be calculated based on the information derived from the cumulative probability distribution, i.e. R, µ(e ), σ(e ), µ(e ) and σ(e ) according to (Excel): p E = R NORMDIST E; µ E ; σ E ;FALSE (4a) p ( ) ( ( ) ( ) ) ( E) = R NORMDIST( E; µ ( E ); σ( E );FALSE) According to this definition P (E) is the relative number of occasions that at the locations where the potential E is measured actively oding steel will actually be found. In the situation shown in Figure 7 there is 50% probability that sive steel will be present for locations exhibiting a potential E = mV. At locations exhibiting potentials E = mV there will be 80% probability of revealing actively oding steel whereas for locations showing 303.9mV and 314.2mV the probability will amount to 90% and 95%, respectively. (4b) 0,0020 probability density, p [-] 0,0015 0,0010 0,0005 R = 0.20 µ(e ) = -400 mv σ(e ) = 100 mv sive total oding 0, potential, E [mv; vs Cu/CuSO 4 ] Figure 7: Enlarged view of probability density distribution in the overlapping potential region 228

9 1,0 90% 0,8 µ(e ) = -400 mv R 50% 75% 80% 85% 90% σ(e ) = 100 mv 0,6 0,4 ratio p/ptot [-] 95% 0,2 10% 0, potential, E [mv; vs Cu/CuSO 4 ] Figure 8: Probability of finding actively oding steel as a function of potential for 0.50 R 0.95 relative number of readings for sive steel, R [-] 0,5 0,6 0,7 0,8 0, potential, E [mv; vs Cu/CuSO4 ] % 80% 50% 20% 95% 10% µ(e ) = -400 mv σ(e ) = 100 mv 5% mV -350 Figure 9: Potential criteria as a function of the relative number of readings for sive steel 0.50 R 0.95 for a range of probabilities 229

10 As a further example of this calculation Figure 8 shows the overall probability density distribution as well as the distributions for actively oding and sive steel in the potential overlap region 300 E 220 mv for values of R ranging from 0.50 to From this graph the potential criteria for a given probability can easily be deduced, as is shown in Figure 9. For the situation in which 90% of the potential readings pertains to sive steel, R = 0.90, the potential criterion esponding to 95% probability of finding oding steel amounts to E(95%) = -325mV, whereas the 5% probability criterion amounts to E(5%) = - 232mV. At a potential of 284 mv there will be 50% probability that the embedded steel is actively oding. The advantage of this statistical approach is that more reliable estimates of the potential criterion can be derived for any desired probability level. In addition, the difference in potentials for the higher and lower probability can be reduced to a significant extent. For the situation with R = 0.90, the potential difference between E(5%) and E(95%) amounts to 93mV and between E(10%) and E(90%) to 68mV. As a comparison a fixed difference of 200 mv between E(10%) and E(90%) is adopted in ASTM C CONCLUDING REMARKS In this paper the theoretical backgrounds have been elaborated for a statistical treatment of data obtained from potential mapping on reinforced concrete structures. The calculation procedure has been exemplified on a number of ideal situations. Such a statistical approach will result in more reliable potential criteria esponding to the desired probability of indicating actively oding steel. The analysis demonstrates that the potential criterion esponding to a certain probability is also dependent on the relative number of potential readings pertaining to actively oding steel. The less the relative number of readings for actively oding steel the lower the potential value associated with the criterion. For a sound analysis a sufficiently large amount of data should be available for both sive steel and actively oding steel. The total number of potential readings should be 1000 at a minimum. In addition the relative number of potential readings pertaining to actively oding steel should preferably exceed 10% of the total number of readings in order to allow for a reliable statistical interpretation. However, it should also be borne in mind that such a statistical analysis provides no additional information on the actual location of oding steel as it merely supports the overall assessment of a concrete structure or component in terms of relative surface to be suspect of reinforcement osion. REFERENCES [1] Elsener, B., Half-cell potential measurements Potential mapping on reinforced concrete structures, Mat. Struct. 36 (4) (2003) [2] ASTM C , Standard test-method for half-cell potentials of uncoated reinforcing steel in concrete, ASTM (1999). [3] Gulikers, J., Half-cell potential mapping on reinforced concrete structures Development of a procedure for the statistical analysis of measurement results (Rijkswaterstaat, Utrecht, 2007). 230