— Metrological definable parameters: They are defined by the alteration from the initial zero state to the actual state.
— Numerically recorded parameters: These parameters do not describe the deviation from an initial state. They are available as measured values, which, however, have to be classified according to agreed upon criteria. One example is the quantity of precipitation, where the measured values obtained from environmental stations are scaled to numbers between zero and one according to the rain intensity.
According to the calculation method M(i), it will always be a number between zero and one.
The Valuation Number B(i) indicates how much the respective parameter affects the weathering process. It is limited to values between 0 and 10, which are attributed by the user. For example, a parameter with a great impact on the weathering process is rated 10, another with less impact maybe only 5. In the calculation process, these Value Numbers B(i) are fixed and must not be changed 37because otherwise no comparison would be possible between different investigations.
Several exogenous (climate, exposition) and endogenous (stone properties) parameters influence the integrity of stone figures in the outdoor climate. For calculating their Risk Number R(i) it is necessary to measure these parameters quantitatively. Altogether we use 104 different parameters, which are allocated to 10 Excel data sheets according to their meaning. The 11th data sheet serves for the calculation of the Overall Risk Number R(total), which comprises the individual Risk Numbers R(i) of the other data sheets.
1 Object Description
2 Art historical Evaluation B(AE)
3 Restoration History R(RH)
4 Environment / Exogenous Risk Factors R(E)
5 Natural Stone / Endogenous Risk Factors R(N-M) for Marble
6 Natural Stone / Endogenous Risk Factors R(N-S) for Sandstone
7 Damage Caused by Human Beings / Vandalism R(V)
8 Mechanical Damage / Loss of Material R(M)
9 Surface Alteration R(SF)
10 Ultrasonic Diagnosis R(US)
11 Overall Risk Number R(total)
Function of Data Sheets
Content and purpose of the data sheets and the calculation of the Risk Number will be explained using the sculpture of Hera (original) in the Baroque garden, Großsedlitz near Dresden. Bullet impacts during World War II caused severe damages to the figure.
Because of limitations of space, only one data sheet can be shown. The endogenous natural stone properties decisively determine the course of weathering due to mineral content, structure, and thermal as well as hygric expansion. The data sheet shown refers to the sandstone sculpture Hera/Juno in the Baroque Garden of Großsedlitz near Dresden. It can be seen how the different parameters are evaluated and in which way the Risk Number R(i) of the whole sheet is calculated.
On the last data sheet “Overall Valuation” the Partial Risk Numbers are combined to assess the Overall Risk Number R(total). For this purpose, the Partial Risk Numbers R(i) of all data sheets except Nr. 1 (Object Description) and Nr. 2 (Art Historical Evaluation) are summed up and a mean value is formed:
R(total) = [R(RH) + R(E) + R(N) + R(V) + R(M) + R(SF) + R(US)] / 7 = < 1
Figure 1: Data Sheet for endogenous stone properties. Example Hera in the Baroque Garden of Großsedlitz.
38Due to the mean value formation the Overall Risk Number R(total) is also a number between 0 and 1. Zero stands for no risk and one for a very high risk. This scaling gives an immediate indication of the degree of a risk for the sculpture under consideration. Again, it has to be emphasized that the Overall Risk Number R(i) is formed with objective and quantitative measurement values and is therefore free of any subjective evaluation. It is ideal for decision-making, especially for determining a ranking within a group of sculptures. Furthermore, in combination with the Overall Risk Number R(total) the Risk Numbers R(i) of the data sheets can indicate the areas of a sculpture at particular risk.
Risk number: Evaluation and Comparisons
For testing the concept of the Risk Number R(i), 12 objects have been selected, four statues of marble, four of sandstone and four sandstone tombstones from the Jewish Cemetery in Baiersdorf/Erlangen (see Figure 2).
Figure 2: The objects chosen for testing the Risk Number.
The Overall Risk Number R(total) in data sheet 11 of the Excel work sheet is automatically calculated. Although this data sheet lists both the arithmetic mean of the Risk Number and the quadratic mean, only the arithmetic is considered in the following because the overall statement remains the same even if the quadratic mean provides slightly different values.
The individual Risk Number calculations of the 12 examined objects yielded surprising results in an initial, unbiased assessment, which, however, have proved to be very useful.
The Overall Risk Numbers of the individual sculptures and tombstones are depicted in Figure 3.
The object with the lowest Risk Number is tombstone No. 1901, the one with the highest is Vestalin. In addition, at the upper and lower ends of the scale the realistic maximum and minimum limits for marble and sandstone are presented. These limits indicate possible maximum and minimum overall Risk Numbers for these rock types. The range extents from 0.24 to 0.88 for marble and from 0.18 to 0.79 for sandstone. The reason for these limits lies in the fact that certain data sheets or parameters cannot reach a value like zero or one.
For example, data sheet “Environment – Exogenous Risk Factors” could theoretically assume a value of 1 in the case of very extreme climate, but never a value of zero, because a “non-climate” does not exist. This also applies to data sheets “Natural Stone – Endogenous Risk Factors”. Even in a very favourable climate, thermal and hydric expansion and water absorption exert an influence on the weathering.
Figure 3: Overall Risk Numbers of the selected objects.
39The calculation system for the Overall Risk Number permits model calculations for open air exposure or location in a store. Relevant for this are the data sheets “Environment – Exogenous Risk Factors”, “Vandalism” and certain rock properties such as thermal and hygric expansion. These parameters vary according to the location of the sculpture. Comparisons have shown that the risk reduces by 0.22 to 0.25 for marble objects and 0.18 to 0.22 for sandstone objects when moving them from outdoors to a depot.
Whatever the value of an object’s Risk Number, the question arises as to how large the numerical change regarding the Overall Risk Number must be in order to be able to draw a valid conclusion as to a greater or lesser overall risk. As we could see, the values of some sculptures are very close to each other, for example Aeolus (R(total) = 0.60) and Flora (R(total)
