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ELSEVIER The Science of the Total Environment 167 (1995) 1-14

Physical weathering of stones

Dario Camuffo

National Research Council CNR·/CTlMA, Padova, Italy

Abstract

This paper reviews the main physical agents responsible for stone weathering. Particular emphasis is placed on the effects of wind and water. Aeolian erosion occurs in windy regions with sandy terrain, but in urban areas it is extremely rare and is often confused with other forms of deterioration. The problem of condensation on surfaces and in pores is extensively discussed, in relation to pore shape and size. Physical effects dominate in the smallest pores, and solution effects in the largest ones. The Kelvin law and thermodynamic considerations are used to explain condensation-evaporation cycles and adsorption isotherms. Capillary rise, increase in pressure in air pockets, freezing-thawing cycles and micro meteorological conditions favorable for the soaking of monuments are discussed. A final section is devoted to the dissolution of stones and the formation of black crusts as a consequence of the way the stone is washed out or simply wetted by meteoric water. The intensity of rainfall is important in activating or removing the dry pollutant deposits that form on monuments, especially during the dry periods characteristic of the Mediterranean climate. Condensation plays a minor role compared with rainwater. However, the porosity, geometri· cal shape and exposition of the stone are also important factors which can characterize different local balances and, consequently, the form of weathering.

Keywords: Weathering; Erosion; Condensation-evaporation cycles; Relative humidity; Mediterranean climate

1. Wind erosion

Alveolarization of stones may be due to several causes, and is often incorrectly interpreted as 'wind erosion'. Apparently, the action of the wind is very often involved: e.g. the formation of severe pitting and interconnected, deep holes with loss of granular material is very common in biocal­carenites (Fig. 1) where the rainwater dissolves and weakens the bonds between granules. or the wetting/drying cycles favored by the action of wind and solar radiation cause solution, mobiliza-

tion and recrystallization of internal salts with the consequent breaking down of the internal struc­ture. At this point, any mechanical factor may be responsible for the ultimate fall of the disaggre­gated granules. In particular, moisture is one of the factors involved in the adhesive forces (inter­particle surface forces and electrochemical forces) acting on the independent granules (Fletcher, 1976). For these reasons the loss of material may be visible on windy days when the wind reduces the adsorbed moisture and the cohesion forces and the turbulence favors the fall of the disaggre-

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2 D. Camuffo / Science of the Total Environment 167 (1995) 1-)4

Fig. 1. Severe weathering of a biocalcarenite with loss of granules (Town Hall, Seville, Spain (Camuffo, 1994».

gated granules in an unstable equilibrium. Al­though the wind action is apparently involved in this fonn of weathering, this is not wind erosion.

Wind erosion (also called 'corrasion') occurs when abrasive particles impact with great energy on a stone for long periods, causing extensive micro mechanical damage which eventually re­sults in macroscopic effects. The energy of the particle is linearly proportional to its density, proportional to the second power of the wind speed and the third power of its diameter. Fine particles follow the wind stream and fly around obstacles without impacting on them, whereas the coarsest particles, the inertial force of which is greater than the viscosity of the air, can impact with great strength on surfaces. However, when the size of the particles is increased, the weight increases also and the coarser grains cannot be raised by the wind, so that there is an intermedi­ate size interval where the grains are sufficiently large to be dangerous, and can be swept by the wind very short distances.

To this end, the particles can be divided into the following four groups. The finest dust parti­cles, with a diameter d < 100 ILm, are airborne and their main effect is soiling, not abrasion. In

the medium size range, Le. 100 < d < 600 ILm, the granules are temporarily lifted and fall in successive leaps and bounds, so that these proceed by 'saltating' according to the wind direction. The height of the leaps depends on the roughness of the soil, but on average this phenomenon only affects the 1st m at the base of the monuments. Particles with d > 100 ILm cannot be lifted by the wind and move by creeping and rolling. Particles that are coarser than 6 mm cannot be moved by the wind. Further details can be found in Bagnold (1941), Pye (1987), Barndorff-Nielsen and Willets (1991).

In conclusion, only grains in the leaping range, 100 < d < 600 ILm, are effective in terms of erosion but only near the base of the monuments. This weathering is important only in sandy, windy regions and has been extensively discussed in the case of the Great Sphinx (Camuffo, 1993) which is situated near the border of the Giza desert, Egypt. In this case, signs of severe corrasion actu­ally appear at elevated levels of the monument, i.e. between the mid-body and the neck. This paradox is explained in that the Sphinx was eroded when it was submerged (except the head) in the

D. Camuffo / Science of the Total Environment }67 (1995) }-}4 3

desert sand and corrasion occurred following the changing levels of the dunes (Fig. 2).

Corrasion is extremely rare or unknown in ur­ban areas. In general urban environments haven't many grains of a dangerous size and buildings reduce the wind speed near the ground, except for some narrow places where wind channeling occurs; in addition, monuments are situated on a base which is usually above the dangerous height. The weathering that affects the base of urban monuments is mainly due to frequent mechanical collisions, capillary rise of rainwater, anthro­pogenic dissolved pollutants and animal urine and/or other biological attacks; in cold regions freezing thawing cycles are also important near ground level.

2. Condensation

The water vapor becomes saturated at relative humidity RH = 100% when the air (and there­fore the moisture dispersed in it) reaches the dew point. Cases of formation of droplets in the free atmosphere, or condensation on a smooth or porous surface, or inside internal pores must be distinguished (Camuffo 1984a; 1988; 1991/1992).

The problem of surface moisture and condensa­tion is very complex, and depends on the chemico-physical characteristics of both the at­mosphere and the work of art. In the case of a non-reactive, non-porous surface, condensation occurs when the temperature of the stone surface T, reaches, or drops below the dew point (OP) of the air, i.e. T, ~ OP, irrespective of both the degree of saturation of vapor (RH) and the tem­perature of the air at some distance from the surface. Evaporation occurs when T, > Tw, where Tw is the wet bulb temperature of the air. The T, value distinguishes between the two processes and determines, for example, whether a surface is wet because it is cold (condensation) or it is evaporating as a consequence of capillary rise. Contamination with soluble salts which raise the OP may cause departures from this simple scheme.

In the droplets, all the water is in a liquid state; in porous bodies some water is absorbed and bound (solid state), some is liquid and free. In pores with a radius r p « 1 /Lm the physical effect dominates; in pores with an rp ~ 1 /Lm

and contaminated by soluble salts, the physico­chemical effects which determine the equilibrium

Fig. 2. The Great Sphinx partially submerged in the desert sand (photo Donald Mac Leish).

4 D. Camuffo I Science of the Total Environment 167 (]995) 1-14

pressure for solutions may also cause condensa­tion at lower RH, occurring typically in a marine environment due to contamination with sea salts. Further chemical details are neglected here as this paper focuses on the physics of stone weath­ering.

Water supplied by condensation causes dissolu­tion of the material matrix. Condensation­evaporation cycles cause migration of dissolved salts and recrystallization elsewhere, e.g. efflo­rescences and subflorescences, thus weakening the material and causing loss of the aesthetic value. Wet materials, e.g. rocks or mortars, may have their mechanical resistance diminished. In other cases, the presence of a film of water may decrease the free surface energy of the material, thus weakening it (Winkler, 1985).

In certain cases, e.g. clay minerals, water may alter the structure of the material, causing expan­sion, stress and fractures. In fact, the crystal structure is composed of a series of wafers and positive ions are frequently trapped between the wafers. Water is able to penetrate the crystal as it is attracted by the hydroxy groups causing the clay to swell. When the RH decreases, the adsor­bed water evaporates, but the structure between the wafers may have changed due to the forma­tion of new crystals. The contraction leads to hysteresis, and in the long run, adsorption­evaporation cycles cause irreversible damage (Torraca, 1981).

Dampness and humidity favor biological life and biological weathering; this negative pheno­menon becomes greater and greater when the duration, or the frequency, of the time of wetness (TOW) increases. During the time in which the stone is wet, chemical reactions occur between the pollutants deposited and the stone (Laurenzi Tabasso and Marabelli, 1992); the damage is thought to be related to TOW, although no gen­eral formula has yet been found to link the da­mage to TOW.

Condensation is also responsible for increasing the deposition rate of airborne pollutants. This fact is due to two different factors: 0) the parti­cles and the hydrophilic gases that impact on a wet surface stick to it without bouncing, so that the capture efficiency of the surface is increased;

(2) when condensation occurs near the wet sur­face several microphysical processes occur, the ultimate result of which is the transport of gases and particles towards the surface, as follows. In the presence of condensation (or evaporation) two opposite concentration gradients of water vapor and dry air are generated which cause two opposing flows of water molecules and dry air. These two flows exert opposing drags on the aerosol particles, but the drag of the air molecules dominates, having the mass (MN = 28 and Mo = 32) greater than the vapor molecules (M v = 18), so that net diffusive transport is generated in the opposite direction to the pure water diffusion ('diffusiophoresis'). On the other hand, the migra­tion of dry air molecules by diffusion tends to cause a pressure imbalance near the surface which is immediately counteracted by the hydrodynamic flow of the medium, called the 'Stefan flow'. This aerodynamic flow, which compensates for the diffusive flow of dry air, is a micronic wind capa­ble of transporting all the particles which arrive near the surface, irrespective of the particle size: it is so powerful that it overcomes the opposing net phoretic force due to pure diffusion. In the case of condensation, the Stefan flow transports all the particles towards the surface; in the oppo­site direction in the case of evaporation. Gener­ally, condensation continues for many hours, es­pecially during night time, and solar radiation causes the rapid evaporation of all the condensed water. Therefore, deposition is favored for a long period time, and is followed by a short period when deposition is prevented by the opposing Stefan flow during evaporation. 'Thermophoresis', i.e. the transport of particles towards a surface that is colder than the air, or vice versa for a warmer surface, can, like the Stefan flow, at times aggravate the effects of other deposition processes or even oppose them to such an extent that the overall rate of deposition is, at times, greatly reduced.

3. Droplets and pores

Inside the wet pores, or in the presence of suspended droplets, saturation is not reached at

D. Camuffo / Science of the Total Environment 167 (]995) 1-]4 5

RH = 100%, which is in thermodynamic equilib­rium with a plane water surface. The RH in equilibrium with a spherical water meniscus is computed by means of the Kelvin equation,

In (RH/lOO) = (2a-Vm/rRT)cos8

where the radius of curvature r of the water meniscus is the main parameter; a- is the water surface tension; Vrn the molar volume of the liquid adsorbate, i.e. 18 cm3

; (J the contact angle with the solid surface (if any; cos8 is positive for wettable surfaces; negative for hydrorepellent ones); R the gas constant and T the absolute temperature. The formula can be rewritten for any shape of meniscus, by substituting instead of 2/r the ratio of the incremental values dS/dV of the meniscus surface dS and the related volume dV; e.g. dS/dV = 2/r for a sphere; dS/dV l/r for a right circular cylinder or a circular torus (where r is the radius of the cylinder or the generating circle, respectively); dS/dV = 3(2r2

+ h2 )/(r2h J(r 2 + h2» for a cone of height h. In this paper only the simplest case of spherical geometry is considered.

In the case of pure water, the Kelvin formula states that the logarithm of the RH in equilib­rium with the meniscus is inversely proportional to the radius of curvature of the water surface. Higher RH levels cause condensation, and lower RH evaporation. The vapor tension of a solution is lower than that of pure water. In the presence uf hygroscopic salts, condensation is anticipated and the equilibrium RH for a spherical meniscus can computed by means of the following two formulas:

In (RH/100) = «2~ Mw/psrRT)

-( Pw/ p)ln(l + ins/nw))cos6

In (RH/lOO) = «2~Mw/psrRT)

where the labels sand w refer, respectively, to the solute or water, M is the molar mass, V. the actual volume of the solute, i a parameter closely associated to the Vant'Hoff coefficient for solu-

tion and depends on the molality, n the molar fraction and ms the actual mass of the solute.

In the case of atmospheric processes such as the formation of droplets in a cloud or fog (Ma­son, 1971; Pruppacher and K1ett, 1980), the sys­tem is composed of spheres of water floating in air, and the radius of the droplets is positive, i.e. r > 0 for a convex water surface. In this case supersaturation is required for eqUilibrium with the curved water surface, i.e. RH > 100% and, consequently, T < DP. The smaller the droplet, the greater the supersaturation necessary for equilibrium. For this reason, droplets may only form by adsorption of water on some condensa­tion nuclei which, when water vapor condenses upon them, form solutions on which the equilib­rium vapor pressure is relatively low. In other words, the depression formed by the chemical solution compensates for the overpressure gener­ated by the convex meniscus of the droplet, so that condensation occurs and the droplet grows.

On porous materials, however, when water starts to wet the inner cavity of the pores, the situation appears complementary to that of the droplet, as the air pockets in pores can be con­sidered to be approximately spheres of air with water outside them and the radius of curvature is negative, i.e. r < 0 for a concave meniscus. The RH required for eqUilibrium with a negatively curved surface is lower than the RH = 100% required for saturation in the atmosphere (Fig. 3). In the pores, saturation is anticipated at RH < 100% and at a critical temperature of Tc > DP, making condensation easier. Condensed water may be found in micropores under usual condi­tions, but also in relatively dry environments.

The individual pore characteristics affect the weathering of stones. Total porosity, total pore surface, spatial association of pores that may form pockets and necks, pore size, pore form and pore radii distribution are important variables. Stones are characterized by a wide variety of pores and necks, with different shapes and sizes, which range from angstroms to millimeters and can be classi­fied into several classes, depending on their properties based on laboratory analysis (Fitzner, 1993). The porosity may change with time, espe-

6 D. Camuffo / Science of/he To/al Environment 167 (J995) 1-]4

100

90

eo

l 70

:J: 60 11:

50

40

30

0.001 0.01 0.1

r (~m)

Fig. 3. Relative humidity RH (%) in equilibrium with a con­cave meniscus of water with radius r (~m), according to the Kelvin law. C, cylindrical meniscus; S, spherical meniscus.

cially in the subsurface layer where migration of salts, leaching, dissolution, erosion and other physical, chemical and biological attacks occur (Biscontin et al., 1993).

'Open pores', with very large outlets compared with the pore volume, are typically found on the surface of bodies. The typical shape is that of a hemisphere, or a portion of a hemisphere (Fig. 4a). Open pores behave symmetrically with refer­ence to droplets suspended in the atmosphere: the smaller the pore, the lower the RH required for equilibrium with the water meniscus. For each open pore, condensation begins at a low critical RH, determined by the radius of curvature when the RH increases, by keeping the radius of curva­ture of the meniscus (r m) in equilibrium with the variations in RH. An increase in RH corresponds to an increase in both condensed water and in r m

and vice versa. The hemisphere is completely filled at RH = 100%. All the steps in this process occur in equilibrium with RH and the process is reversible.

'Internal pores', with small outlets, are typically found inside bodies (and connected to the atmo­sphere by a small hole facing the surface or entering other pores or capillaries, Fig. 4b) and they behave in a different manner. When conden­sation begins at the low critical RH, the con-

Fig. 4. (a) Condensation in an external pore; (b) condensation in an internal pore.

densed water deposits in the small volume of the pore, reducing the free surface of the meniscus and the radius r m' After a short time, when some condensation has occurred, the smaller the new radius r m the lower the equilibrium RH, so that the actual RH inside the cavity, which was in equilibrium with the former r m' now corresponds to supersaturation for the new smaller rm' and the process is accelerated. Therefore, the RH calculated by using the radius of the pore (r p) in the Kelvin formula, i.e. RH(rp ), is no longer a neutral equilibrium value, but a critical value of unstable equilibrium which triggers off the com­plete filling of the pore. As a consequence, the process is now irreversible.

According to the Kelvin law, condensation oc­curs first in necks, which are the cavities with the smallest radius of curvature. When the necks are filled with water, air-pockets remain entrapped in the pores and further condensation is impossible

D. Camuffo / Science of the Total Environment 167 0995J 1-14 7

in steady state conditions. Internal condensation may only continue when variations or fluctuations in temperature or atmospheric pressure cause the displacement of the water inside the pore necks. Nocturnal cooling of the body may reduce the pressure inside the pores and cause the water condensed in the neck to be sucked into the pore. According to Cantor's law, the required excess pressure is inversely proportional to the neck radius. When the excess pressure is sufficient, plugs of condensed water can be pushed out and trapped inside the pores, or can be forced to migrate into the material. Condensation may con­tinue by means of these steps, so that the amount of adsorbed water is also a function of the pump­ing efficiency of these variations.

Similarly, evaporation from an open pore starts from its outlet, removing water from the pore and increasing the radius of the free meniscus. The equilibrium RH given by the Kelvin formula be­comes accordingly greater and greater, so that the actual RH becomes lower and lower in compar­ison with the value required for equilibrium. Evaporation continues untill all the liquid water (Le. all the water inside the pore, except the first and second molecular layer in contact with the surface which is attached with a stronger ice-type bond) has evaporated. Evaporation is triggered off when the RH exceeds a critical value which is calculated from the radius of curvature of the pore outlet (ro )' As this critical RH(ro ) is lower than all the values in eqUilibrium with the inter­mediate steps when the meniscus increases its radius during evaporation, this process is also accelerated and is irreversible.

The condensation-evaporation cycles being thermodynamically irreversible present noticeable hysteresis as condensation occurs when triggered off by RH(rp ) and evaporation by RH(ro)' In practice, RH(rp) and RH(ro ) are not just two precise levels of RH, but two ranges, determined by the actual distribution of r p and r 0 in the porous material.

When the temperature of the stone drops below freezing point, freezing-thawing cycles develop, and the pressure exerted by the ice crystals may have disruptive effects. Of course, the greater the size of the pores the greater the force, so that

damp stones characterized by large pores and high total porosity are more likely to be damaged (Fitzner, 1993). However, Torraca (1981) noted that in the Mediterranean climate the damage by frost is more likely to occur in materials which have a prevalence of small pores, Le. with size between 0.1 and 1 /Lm. This paradox is explained by the fact that in a non-humid climate the small pores have the largest probability of being filled with water at intermediate RH values, due to a combined action of the Kelvin law, solution effect and adsorption hysteresis. In addition, the Kelvin law can be adapted to the vapor-solid and liquid-solid changes of phase. The result is that small curvature radii are associated with deep freezing point depressions.

4. Adsorption isotherms

The condensation-evaporation cycles can be represented by the so called BET (Brunauer, Emmett and Teller) adsorption isotherms (Brunauer, 1945; Gregg and Sing, 1967; Mikhail and Robens, 1983), in which the amount of adsor­bed water, WA, is plotted against RH. In practice, this kind of graph shows the weight increase due to the adsorption of water by an initially dry sample of material when the RH increases from 0 to 100% and then decreases again to 0%. The most common type is composed of three branches.

The first branch, characteristic of the very low RH, occurs when all the stone surface, both ex­ternal and internal (i.e. the visible surface and the surface in contact with the air, but inside the pores), is progressively covered with a layer of water in the solid state (i.e. strong bonding with the internal surface of the pores), with a final thickness of two or three molecular diameters. In this branch the graph of the adsorption is coinci­dent with the desorption one. The condensation­evaporation process is characterized by a one-to­one correspondence and is reversible depending linearly on changes in RH.

In the intermediate RH range, after the total surface has been covered with this solid layer, a further increase in the RH leads to the formation of bulk, liquid water in the internal pores. This

8 D. Camuffo I Science of the Total Environment 167 (J995) 1-]4

second branch becomes steeper and steeper as the pores are filled by water. In every pore with a radius rp, condensation occurs when triggered by RH(rp ) or by the chemical effect. If all the pores have the same size the condensation branch is very steep. In this branch the process is no longer reversible: if the RH decreases in this branch some minor hysteresis loops start.

The third branch is characterized by very high RH, when all the internal pores are filled with water. In theory, this branch should be horizontal, as no further increase of W A is possible, also because when RH = 100% the surlace is in thermodynamic equilibrium with the same num­ber of molecules condensing and evaporating. In practice, this branch is tilted because the spec­trum of the pores is wide and before reaching RH = 100% there are always some large pores which are empty and which become progressively filled. In addition, the presence of contaminants or solu­ble salts causes the condensation to occur earlier, so that the environment is in a situation of super­saturation and condensation occurs, forming liq­uid films or droplets on the external surlace. A similar condition of supersaturation occurs when the surface temperature drops below the DP, so that at the interface between the stone sudace and the air the RH is > 100%. In any case, the amount of liquid water that can adhere to the external sudace is modest, and the final branch is slightly tilted, with a sharper rise near the upper extreme due to the solution effect. If condensa­tion stops before the droplets fall from the damp stone, this branch is again characterized by a one-to-one correspondence and is reversible.

On lowering the RH, the process first develops along the last condensation-desorption branch, untill the external water has evaporated. Continu­ing to lower the equilibrium RH after all the pores have been filled with water, evaporation may proceed, emptying the pores and this may occur only when triggered by RH(ro )' If RH(ro )

< RH(rp) a hysteresis loop is generated, the condensation branch being linked to the size of the internal pores rp; the evaporation branch reflects the dimension of the outlet of the pores r o' If all the pores have the same outlet the evaporation branch is very steep. The derivative

of the amount of water W A which is adsorbed in the stone by varying RH, i.e. dW AI dRH, shows peaks corresponding to the dominant features of the pores. These peaks are narrower or broader according to the distribution of the dimensions of the pores and their outlets. After all the internal bulk water has evaporated, lowering the RH, lay­ers of solid water (first branch) start to evaporate, but with a much greater latent heat (e.g. 2 or 3 times greater) than the evaporation heat in the liquid-vapor transition.

Cycles involving the last branch mobilize the salts on the sudace and subsudace layer; cycles involving the hysteresis loop dissolve and re-crys­tallize the soluble salts at a deeper layer and cause outward migration with the formation of new effiorescences. The mechanical stress that follows thermohygrometric changes in a structure weakened by long term dampness may have dra­matic consequences. In addition to the chemical deterioration, the presence of water inside the pores favors biological epilithical and endolitical life, and biological weathering. Saturated environ­ments should be carefully avoided.

5. Penetration of rainwater

Penetration of rain water into the monuments while it is flowing over the sudace also depends on climatic factors, in addition to the nature of the material (Dullen, 1979). Penetration into cap­illaries and porosities is possible only when the whole surface (Le. both external and internal ones) is covered by a single or double layer of water molecules in the solid state, and this process is not possible when the surface is completely dry, i.e. not covered with these layers of solid water (Camuffo, 1991b).

When the sudace of the material is still 'wet', Le. covered with the monolayer of solid water, as generally occurs in the more humid climates, liq­uid water penetrates by simply advancing towards the interior with a concave meniscus that does not experience any change in the curvature (no external work due to surface tension); in addition, the concave meniscus forms a lower vapor pres­sure in front of it, which favors penetration into the capillary (positive work).

D. Camuffo / Science of the Total Environmenl167 (1995) 1-14 9

In the case of a completely 'dry' surface, with­out the solid water monolayer, the meniscus of the water penetrating into the capillary is convex in the forward direction, and the meniscus must elongate gradually as the water penetrates into the capillary. The work required against the sur­face tension and the higher vapor pressure over a convex meniscus is so great that water can not penetrate under such conditions and runs over the monument without dampening it. For dry materials a preliminary 'wetting' of the internal surface is a necessary condition for water to pen­etrate and soak into it.

In a hot, dry climate which is predominant during the summer in southern Europe, the exter­nal and internal surfaces of monuments are com­pletely dried out because of the warming associ­ated with strong solar radiation. This then means that water, from a typical sudden shower in the afternoon, can not initially penetrate into the pores and capillaries of the stone, because these are not lined by a monolayer of water molecules in the solid state that would allow for the liquid water to run over it.

Pressure fluctuations associated with wind gusts may cause pressure differences between the inte­rior and exterior of the monument, which may force the water running over the surface to pene­trate into the cavities and be trapped in the pores. With successive steps, water may arrive at the interior of the porous materials. External pollu­tants may also be trapped inside the material and continue the deterioration process each time mi­croclimatic factors are suitable.

6. Capillaries

The amount of water adsorbed varies linearly with the square root of the time t, i.e. WA "" k.jt, where k depends on the characteristics of the material, although some exceptions have been noted (Gummerson et aI., 1980); if there is diver­gence in the water flow with lateral spreading of the water front, the cumulative water adsorption increases more rapidly than It, (Hall, 1981). Cap­illary suction occurs with the progressive displace­ment of water, so that it cannot be stopped by pockets of air entrapped in the pore and capillary

system, except for ducts without an outlet, in which the capillary pressure is counteracted by the entrapped air. Capillary suction (in particular for ground water or collected rainfall) is therefore much more efficient than condensation in causing dampness.

Overpressures generated by heating are impor­tant, e.g. on porous tiles where the cavities are topped by the glaze of the decorative ceramic surface, especially when the thermal shocks are noticeable. Capillaries closed at one extreme may be filled with water un till the pressure of the air entrapped equals the pressure n - 2 if / r de­termined by the meniscus curvature (the Laplace law) minus the contribution due to gravity p pgh, where p is the pressure, g the acceleration of gravity and h the height of the water column (the Stevin law). Solar radiation falling on the material with embedded air pockets causes an increase in the pressure inside the cavities due to the temperature rise aT according to the law of gases, pV = (na + n) RT, where V is the volume, na and ny the number of moles of dry air and water vapor, respectively. This overpressure causes the water meniscus to retreat and reach a new equilibrium due to the simultaneous pres­ence of a gas and a saturated vapor, as follows: (0 na is constant and the partial pressure of dry air is inversely proportional to V; (iD ny is not con­stant and is independent of V; in fact, aT causes a decrease in RH and consequently new water molecules can evaporate untill the original RH is re-established, being the RH determined by the radius of the capillary, here supposed unchanged (Camuffo, 1991a). The partial increase of pres­sure due to the vapor is shown in Fig. 5.

Of course, the damage may be enhanced in the presence of soluble substances, osmotic effects and salt crystallization. On plasters and frescoes, at high humidity, residual crystals of calcium ox­ide may hydrolyze becoming calcium hydroxide, causing pitting as a consequence of its growth. Crystallizing salts have a disruptive effect as a consequence of the pressure generated by the growing crystals, hydration or thermal expansion. The osmotic effect causes an upward rise of the ions that displaces the wet front upwards. In the region where water evaporates, the transported

10 D. Camllffo / Science of the Total Environment 167 (1995) )-14

8

7

6

0" 5

:e:4 '0 (i 3

2

0

0 5 10 15 20 25 30

t ("C)

Fig. 5. Increase in partial pressure p(t)/p(O) of the water vapor following a temperature rise t (OC) in a capillary due to both the vapor heating and the increase of the number of water molecules which had evaporated to re-establish the original RH in the cavity. Note that p(t) is not affected by a retreat of the water meniscus and an increase in the volume of the cylindrical air pocket, the molecules being a saturated vapor and not a perfect gas.

salts accumulate locally causing more and more damage (Arnold and Zehnder, 1990).

7. Rainfall and crusts

Chemical weathering is not directly related to the concentration of pollutants in the air, but to the combined action of the pollutants deposited on the monument surface, when microclimatic or meteorological factors may trigger some deteri­oration processes. Air pollutants may be de­posited either in the dry phase or in the wet one, and wet deposition is the result of the atmo­spheric scavenging occurring in clouds, when the droplets are forming and growing (rainout), and during the fall of the droplets (washout).

The amount of pollutants which is deposited in the dry phase is the result of the concentration of airborne pollutants, the velocities of the different microphysical transport mechanisms near to and at the interface between the air and the artifact and the capture efficiency of the surface itself. It denotes the net fraction of the atmospheric pollu­tants that are ultimately deposited on the monu­ment and that may react with it. A measure of the pollutant concentration in the atmosphere with-

out an estimate of the deposition velocities solves only a part of the problem.

Rainfall transports acid substances from the atmosphere to the surface of monuments. How­ever, the purely meteorological nature of the pre­cipitation is also of very great importance. In the Mediterranean climate it does not rain frequently in summer, and a great quantity of pollutants is deposited in the dry phase. The same occurs in winter in regions which are under the influence of the ridge of high pressure that connects the Rus­sian high with the Azorres anticyclone. Under these conditions, the dry deposition that occurs in urban sites is much greater than wet deposition. If precipitation occurs in the form of a heavy shower, the dry deposit is washed away quickly. Thus, knowing the intensity of the rainfall (Le. amount/day) may be more useful than the total monthly water precipitated. The frequency of rainfall may be even more useful in giving the first indication about the possible dominance of wet or dry deposition.

Although the acidity of the rain as well as the turbulent character of the run-off attacks the stone, this is not as damaging as drizzle which wets the surface making the dry deposit chemi­cally reactive without removing it. Under these circumstances, the pH of the rain may be of little importance in comparison with the acidity of the dry deposit which generally contains elevated quantities of both acidic pollutants and catalysts, such as oil-fired carbonaceous particles (Camuffo et aI., 1984; Camuffo, 1986).

Acid water acts by both dissolving the stone surface and the cement that binds granules to each other. In the latter case modest dissolution is sufficient to cause the loss of many granules resulting in erosion. This rate of erosion may exceed the rate of dissolution by a factor of ,.., 2 for marble and 3 for limestone (Beadecker and Reddy, 1993).

Many sulfation and dissolution processes occur especially in stones which have a calcareous ma­trix; metals are corroded, external frescoes and murals are lost. However, even in those cases where the particles deposited on frescoes or mu­rals are not subjected to direct wetting by rain drops or run-off, an opaque layer is still formed,

D. Camuffo / Science of the Total Environment 167 (1995) 1-14 11

resulting in soiling. This, in turn means that the picture becomes less clear, so that each time a work of art is cleaned, it is subject to a degree of stress brought about by the very nature of the intervention. The fonnation of crusts is related to the presence of water, but the necessary amount is generally supplied by rainwater, which is larger than that locally adsorbed by means of fog or condensation. These processes involve an amount of water «1 mm/day which is very small when compared with rainfall, which can be several tens of cm/day. However, indirect action is possible: condensation on non-adsorbing, external surfaces may continue for some hours and fonn droplets which eventually form descending rivulets. The water collected at the base of the vertical surface is supplied by a relatively large area and may then be adsorbed by capillary suction, which is much more effective (Bernardi et al., 1985).

The visual features of the crusts of marble or limestone monuments is not only a function of the prevailing micrometeorological conditions near the monument, but also of the geometry of the surface and its exposure to rainwater. Similar geometries induce similar patterns of crusts. The pattern of the 'white' and 'black' crusts found on monuments is caused by the way meteoric water wets or washes the surface: where run-off domi­nates, dissolution and erosion occur and calcare­ous rocks form white areas. These areas are char­acterized by crystals of reprecipitated calcite that form when the rainwater with the dissolved stone evaporates (Fig. 6); where the stone is wetted but not washed out, black gypsum crusts originate (Fig. 7), with embedded carbonaceous particles which play an important role in this process.

Field observations (Camuffo et al., 1982; 1987; Camuffo, 1984b; 1986; 1990) have shown that, in the zones exposed to run-off, gypsum crystals were found only rarely, whereas a thin layer of spatic calcite crystals due to reprecipitation was common. On the other hand, the maximum quan­tity of gypsum was found where run-off was pre­vented, i.e. in the black crusts. The acid rain hypothesis alone is not sufficient to explain the main phenomenon due to sulfation, i.e. the black crusts, which are one of the main problems af­fecting marble monuments. By the way, the gyp-

Fig. 6. Example of a 'white area' in a zone over which rainwater runs-off. The surface has been worn away and covered by reprecipitated crystals of spa tic calcite. The pitting is due to the biocorrosion of microflora in the past (Trajan Column, Rome, (Camuffo, 1994» .

sum crusts due to simple sulfation by acid rainwa­ter should be whitish, and not black.

The visual features of the deterioration pat­terns could be related to the three main ways the water wetted the surface: (0 run-off is associated with white areas in the zones where the surface had been worn away; (iO damping due to splash­ing droplets, or percolation near zones where run-off was present, is associated with black areas where black crusts dominate; and GiO absence of both run-off and percolation, but possible con­densation is associated with 'gray' areas where the stone was not chemically affected but covered instead by a layer of dust and particles.

12 D. Camuffo / Science of the Total Environment 167 (J995) 1-}4

Fig. 7. Black: crusts that have formed symmetrically in parts of the decoration where rainwater wets but is unable to remove the dry deposit by means of running-off (Altare dell a Patria, Rome).

Although the specific mechanisms involved are still under discussion, fly ash, microsoot and sin­gle carbonaceous particles (formed during the combustion of oil) are active in forming black crusts when they are wetted by the percolation of rainwater. These combustion products contain sulfur compounds and catalysts, and nucleate gyp­sum crystals when wetted, so that they become embedded in a gypsum crust. The gypsum partly results from the transformation of the underlying rock, and partly from particle nucleation. The black crusts have a dendritic appearance as a consequence of the mechanism whereby the par­ticles are deposited and bind together and with the gypsum crystals; the proportion of the gypsum and the airborne deposit determines the mechan­ical strength of the crusts. Where the underlying substrate is not marble or limestone or the cal­careous rock cannot be sulfated, the gypsum is very scarce (i.e. only that originated by the parti­cles) and the crust is very friable. All the black crusts examined, samples of which were taken from many European countries, contained carbo­naceous particles and it has been possible to reproduce this mechanism in the laboratory (Sab­bioni et aI., 1993). Of course, these dendritic

crusts cannot be confused with the black patches of biological origin (e.g. lichens, algae), with growth, combination and repetition of some ele­mentary structures, possibly associated with bio­corrosive pitting. In particular, the microflora also needs special microclimatic conditions to develop; chiefly a frequent supply of water. For this reason black biological patches can be found in places where the formation of crusts composed of soot and gypsum is impossible due to the frequent presence of water.

Although the white areas are also subject to dry deposition, the abundant run-off washes over the monument surface and in general removes most of the attached pollutants. Their action is modest but is, however, continued by the falling rainwater. The result is a modest wearing of the surface which is only slightly dissolved and over which crystals of calcite may reprecipitate.

When the stone is characterized by larger pores and is absorbent, the visual features are quite similar. Vertical surfaces absorb the falling droplets and run-off can not develop, so that the dry deposit is not removed and may be transported into the pores. Wash-out and dissolution may only occur where great amounts of water are

D. Camuffo / Science of the Total Environment 167 (J995) 1-14 13

Fig. 8. Visual features of a porous calcarenite wetted by splashing raindrops (the gray wall), dissolution by run-off where rainwater may collect and run-off with turbulence (the white area below the window) and in a laminar regime after adsorption, releasing the material previously removed (the darker gray area below the dissolution area) (The Mayor's Palace, Brussels).

collected, e.g. under windows. However, the run­ning water is eventually absorbed by the porous stone; the running layer thins and thins, the tur­bulence damps, the flow becomes laminar and then disappears (Fig. 8). In a turbulent regime the surface is cleaned and thinned; in the laminar one the material removed from the upper surface is released onto the underlying rock. When the regime is laminar, the first layer in contact with the surface becomes saturated and is then chemi­cally inactive. When it is turbulent, the chemically active solution continually changes on the stone surface which is subjected to heavy dissolution and erosion due to loss of granules.

Acknowledgements

This paper presents scientific results of studies supported, at different times, by the Commission of the European Communities, DG XII, STEP Programme (Contract no. Cf90-0107-SSMA) and CNR (Comitato Nazionale per la Scienza e Tec­nologia dei Beni Culturali). Thanks are due to Dr. Adriana Bernardi for many useful discus­sions.

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