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Moisture regime of historical sandstone masonry — A numerical study
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Original article
Moisture regime of historical sandstone masonry — A numerical study Tomas Vogel ∗ , Jaromir Dusek , Michal Dohnal , Michal Snehota Czech Technical University in Prague, Faculty of Civil Engineering, Thakurova 7, 16629 Prague, Czech Republic
a r t i c l e
i n f o
Article history: Received 28 May 2019 Accepted 23 September 2019 Available online xxx Keywords: Sandstone masonry Rising damp Moisture-reduction measures Retention curve Unsaturated hydraulic conductivity Richards equation
a b s t r a c t Rising damp causes deterioration of masonry walls in many historical buildings. Although the phenomenon of capillary rise in porous structures is relatively well understood, reliable numerical modeling of the moisture regime, applicable to the assessment of current state as well as to the predictions of changes induced by various corrective moisture-reduction measures, remains a challenge. This paper presents the results of a numerical modeling study dealing with the moisture regime of a masonry wall of the baroque Church of All Saints in Heˇrmánkovice. The numerical approach used is based on general concepts of mass conservation and Darcian flow of capillary water in porous media. The model was parameterized and validated using experimental data obtained by on-site survey, laboratory analysis and monitoring. The modeling results confirmed our hypothesis that, in a long-term perspective, the secondstage evaporation—controlled by the hydraulic properties of the masonry—prevails over the first-stage evaporation—controlled by the atmospheric conditions—for most simulation scenarios conducted. Of the two corrective moisture-reduction measures considered, i.e. a closed drain versus open drain installation, the latter was found to be significantly more effective, leading to a greater reduction of moisture in the masonry. © 2019 Elsevier Masson SAS. All rights reserved.
1. Introduction Rising damp is one of the main problems affecting historical masonry structures all over the world as it endangers the integrity of construction materials and the performance of building envelopes [1]. Excess moisture is responsible for unsuitable indoor conditions, poor thermal insulation efficiency of building walls and decrease in the mechanical performance of masonry. Wet building materials may be exposed to frost decay and migration and crystallization of soluble salts. Damp walls cause high humidity of indoor air and may lead to growth of mold on cool surfaces. The extent of masonry affected by capillary rise is determined by a combined effect of infiltration into the wall foundations, evaporation from the above-ground wall surfaces and wall hydraulic properties. A dynamic equilibrium is established between the water uptake by capillary rise and the water loss by evaporation. A classical method for controlling rising damp in walls of historical buildings is the construction of subsurface drains along the masonry, limiting the supply of water from the ground. Drain ditches may be filled with soil or left open to enhance evaporation from the wall. Alternative methods for rising damp prevention,
∗ Corresponding author. E-mail address: [email protected] (T. Vogel).
such as the insertion of damp-proof membranes, injection of chemical liquids, or application of electro-osmosis, are rarely suitable for historical buildings. There is an extensive literature related to the description of rising damp phenomena in building materials [2–4]. However, many approaches reported are difficult to apply to historical structures, often built of nonstandard materials. Properties of these materials are unknown and their determination is complicated as the experimental, surveying and monitoring tools are limited by the requirement of preservation of historical authenticity. A well-established approach, enabling a simple quantitative analysis of rising damp in masonry walls, is the Sharp Front (SF) approach [5,6]. The SF approach combines the overall (nonlocal) mass balance equation with the Green–Ampt approximation of moisture front advancement in a homogeneous one-dimensional porous medium [7]. A more rigorous approach based on the Richards equation [5,8], combining the distributed (local) mass balance equation with the Darcy-Buckingham law, is used less frequently, perhaps because of inherent difficulties related to the numerical solution of the equation and experimental uncertainties associated with the determination of the required hydraulic characteristics of masonry materials. An important component of the rising damp analysis is the estimation of the wall surface evaporation. In most recent studies [9] the evaporation rate is evaluated based on the external atmospheric
https://doi.org/10.1016/j.culher.2019.09.005 1296-2074/© 2019 Elsevier Masson SAS. All rights reserved.
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Fig. 1. Church of All Saints in Heˇrmánkovice: a: north facade; b: church interior; c: location of the monitoring system.
conditions, which, however, control the wall surface evaporation only under high surface water contents. When the balance between below-ground infiltration and above-ground evaporation is studied over longer time scales and/or under lower wall surface water contents, the evaporation rate often becomes limited by the internal wall conditions, specifically by the unsaturated hydraulic conductivity of the masonry material. In the present study, we use a two-dimensional model of capillary flow, based on the numerical solution of the Richards equation, to study the distribution of water in sandstone masonry walls of the Church of All Saints in Heˇrmánkovice. The analysis involves two types of simulation scenarios: (i) scenarios considering the steady-state flow of water from the wet wall foundations towards the evaporative surfaces of the walls, thus approximating the present state of the church walls, (ii) transient flow scenarios, focused on the future long-term effects of the proposed moisturereduction measures—installation of open or closed drainage systems.
2. Material and methods 2.1. Church of All Saints in Heˇrmánkovice The Church of All Saints in Heˇrmánkovice (Fig. 1) is located in the northeast Bohemia, Czech Republic. The church was built in the period of 1722–1726, designed by Kilian Ignaz Dientzenhofer, a well-known Bohemian architect of the Baroque era. The church belongs to the so called Broumov Group of Churches—a unique complex of ten baroque churches built in the eighteenth century on the territory of the Broumov monastic estate. The church stands in the middle of a cemetery on inclined ground with an average slope of about 13%. The upslope wall, oriented towards the north, is significantly affected by rising damp (Fig. 1b). The church floor is about 20 cm below the soil surface at the north side of the building. The walls are made from sandstone from the local quarries, e.g. ˇ those located in Cerven y´ Kostelec and Boˇzanov. Some historical
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Fig. 2. Water content monitoring results: a: soil water contents in the soil pits; b: water contents in the sandstone masonry.
records report the presence of a quarry directly in Heˇrmánkovice [10]. Interior mortar is mainly made of limes and presents a thickness of about 3 cm. It appears layered in the typical three elements: a first protection thick layer in contact with the masonry made with coarse sand to fill the gaps and prevent stone degradation, a second layer meant to smooth the surface and permit the painting to attach, and a third finishing layer mainly made of gypsum to plaster the surface [10]. In the exterior, a thicker and rougher plaster, richer of small sand pieces covers the walls. Nowadays, the plaster layer on facades is lost or deteriorated on most parts of building (Fig. 1a). In the interior of the church, walls show a high level of surface deterioration due to rising damp and biological activity. Walls have been repainted many times—different colors are visible. Render and mortar are heavily damaged at the bottom part, wet and not cohesive. A biological attack is also affecting the first half a meter with mosses and algae, especially in the niches, where worse ventilation and thus higher relative humidity of air is present. The soil surrounding the church was classified as sandy loam (in average: 53% sand, 37% silt, and 10% clay). The natural layering of the respective soil type was heavily disturbed by burial activity at the cemetery. 2.2. Monitoring system For the purpose of this study, a system for continuous monitoring of water content and water potentials in the masonry of the upslope church wall and in two soil pits, positioned on the adjacent slope, was established (Fig. 1c). Water content reflectometers with 30 cm long rods (CS650, Campbell Scientific, Logan, UT, USA)
were installed in the pillar and the niche wall at heights of 10 and 60 cm above the church floor. The rods of the CS650 water content sensors were installed into pre-drilled holes of 4 mm in diameter. To avoid insertion error, we used purpose-made insertion guides (since the original insertion tool provided by Campbell Scientific was not intended for drilling). Thus, the drilled holes were as close to parallel as possible. Air gaps between the sensor and wall material were avoided by filling the space around the sensor by a mixture of water and fine sandstone material produced by drilling. The Topp equation [11], recommended by the manufacturer as a default method, was used to convert from relative dielectric permittivity, measured by CS650, to volumetric water content. The validity of the Topp equation for the conversion was verified by a three-point laboratory calibration experiment performed on a large sandstone sample taken from the Boˇzanov quarry. Water potential sensor (T8 Tensiometer, METER Group, Inc., Germany) was installed inside the wall foundation 28 cm below the floor level. Each of the two soil pits was instrumented with three tensiometers and two water content reflectometers. The monitoring system was completed with a heated tipping bucket rain gauge (MR2H-01m, Meteoservis v.o.s., CZ). The results of water content monitoring in the wall masonry and in the two soil pits are shown in Fig. 2. The water content data measured in the soil pit situated at 2.6-m distance from the wall (Fig. 2a) reveal high and relatively stable moisture levels throughout the period. The soil profile is nearly saturated most of the time with more dry conditions at the end of the period caused by the drierthan-average summer months of July and August 2018 (23 mm of rainfall over the period of July and August 2018 compared to 74 mm
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for the same period in 2017). The small peaks on the water content graphs correspond to individual rainfall events. The water contents measured in the soil pit situated at 8.8-m distance from the wall reflect more natural water regime characteristic for the hillslope above the church. The soil profile at this location is significantly drier, with larger differences between the water contents measured at different depths. The deeper soil water content is less variable. The figure shows significantly elevated water contents in the soil pit situated near the wall, compared to the conditions observed in the pit situated further upslope—unaffected by the presence of the church wall. This confirms the findings of our preliminary soil survey, which ascribed the rising damp in the wall to water originating from the hillslope subsurface runoff, to which the church wall stands as a barrier, as well as water coming from the malfunctioning rain gutters draining the church roof. Based on the soil survey and laboratory analysis of soil samples, it was concluded that the difference in soil water regimes in the two soil pits is not related to different textural and soil hydraulic properties. The wall sensors show that the interior surface of the north wall is significantly affected by rising damp (Fig. 2b). The recorded water contents suggest only minor seasonal effects, with drier conditions in autumn, and insignificant short-term weather effects. Winter measurements resulted in erroneous data (not shown in the figure). The sensors inserted 10 cm above the church floor show consistently higher water contents than those at 60 cm with an average difference of about 0.01 cm3 cm−3 . The niche sensors suggest drier conditions than the pillar sensors. We note that the application of the water content reflectometer sensor (CS650) is well established in mineral soils but has not been thoroughly tested in construction materials. Therefore, the measured variations of water contents in the sandstone masonry (Fig. 2b) should better be interpreted in relative rather than absolute terms. 2.3. Numerical model of capillary rise We assume that the flow of capillary water in sandstone masonry is described by the Richards equation [8]. This equation combines two fundamental equations–the water balance equation and Darcy’s law. Richards’ equation can be written in the following general form: d ∂h = ∇ · (K (h) ∇ H) dh ∂t
H =h+z
(1)
where h is the water pressure head (m), H is the water potential (m) representing the potential energy associated with capillary forces and gravity, K is the hydraulic conductivity tensor (m s−1 ), is the volumetric water content (m3 m−3 ), z is the vertical coordinate—taken positive upward (m), t is time (s). Under isotropic conditions (assumed in this study), the hydraulic conductivity tensor is reduced to a scalar—further denoted by K. Equation (1) is solved numerically using the finite element code S2D developed at the CTU Prague [12]. The solution is based on the Galerkin finite element method with linear basis functions in the spatial domain, implicit finite difference scheme in the time domain, and adaptive time-stepping and iteration control to deal with the nonlinearity of the governing equation. The model was thoroughly verified and successfully applied to solve a number of water flow and solute transport problems [13–17].
linking the water content with the water pressure head h, and the hydraulic conductivity function K(h) or K(). The functional relationships describing the hydraulic properties of porous materials are usually approximated by simple analytical expressions. In this study, we use the modified form of the van Genuchten–Mualem model [18,19]. In this model, the water retention function is expressed as:
(h) = r + m − r
1 + (−˛h)
n −m
(2)
This formula is used to describe the retention curve in the unsaturated pressure head range (–∞, hs ). For pressure heads larger than the air entry value hs , the corresponding water content becomes equal to the saturated water content. The substitution of the retention function into the Mualem hydraulic conductivity formula [20] yields [19]:
K = Ks
− r s − r
1/2
2
1−F
1 − F s
F =
1−
− r m − r
m1 m
(3)
In the above expressions, Ks is the saturated hydraulic conductivity, r and s denote the residual and saturated water contents, respectively, ␣ and n are empirical fitting parameters. The parameter m is equal to 1–1/n and n is greater than 1. The parameter m is related to the air entry value hs through the relationship [19]:
m = r + s − r
1 + (−␣hs )
n m
(4)
2.5. Experimental determination of the sandstone properties To determine the hydraulic properties of the sandstone material, three samples of sandstone were taken to the laboratory (Fig. 3). The saturated water contents of the sandstone samples were measured gravimetrically based on saturated weight after 7 days of free capillary rise from open bath and dry weight after oven drying at 105 ◦ C to a constant weight. Main drainage branches of retention curves (Fig. 4) were determined using the standard sand box and pressure extractor methods [21]. The saturated hydraulic conductivity of the masonry was determined in situ using minidisk infiltrometer on a large sandstone block coming from the church wall. The determined hydraulic parameters of the sandstone samples are listed in Table 1. 2.6. Infiltration/exfiltration below the ground In situations where the masonry material (in our case the material of sandstone blocks) is in a direct contact with the surrounding soil, the water potentials inside and outside the masonry surface are equal, while the water contents differ according to the respective retention curves. This can be expressed as: hwall = hsoil
wall = wall (hwall )
soil = soil (hsoil )
(5)
where hwall and hsoil are the water pressure heads inside the masonry and in the surrounding soil, respectively. This relationship can be used as a boundary condition accompanying Equation (1) in the numerical simulations of capillary rise. Assigning specific values of hsoil , the model can represent either the infiltration of soil water into the masonry or the exfiltration of water from the masonry to the soil after the installation of a subsurface drainage system. 2.7. Evaporation from the wall surface
2.4. Parameterization of sandstone hydraulic properties The application of the Richards equation to model capillary flow in a porous medium requires the knowledge of the hydraulic properties of the medium. These properties are represented by two constitutive relationships: the water retention function (h),
Drying of masonry wall surfaces can be described as occurring in three distinct stages [22–25]: (i) a weather-controlled stage when drying is fully determined by external conditions, i.e. incoming radiation, air humidity, air temperature and air flow velocity, (ii) a capillary-flow-controlled stage when drying is limited by
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Fig. 3. Sandstone samples: Sandstone 1 (90.9 cm3 ), Sandstone 2 (106.4 cm3 ) and Sandstone 3 (146.1 cm3 ).
Fig. 4. Retention curves (a) and hydraulic conductivity functions (b) determined for the sandstone samples and the wall core filling.
Table 1 Hydraulic properties of the sandstone samples and the wall core filling.
Sandstone 1 Sandstone 2 Sandstone 3 Core filling
r (cm3 cm−3 )
s (cm3 cm−3 )
␣ (cm−1 )
n (–)
Ks (cm d−1 )
hs (cm)
0.00 0.00 0.00 0.02
0.27 0.33 0.22 0.35
0.009 0.050 0.001 0.020
1.13 1.19 1.35 3.00
0.1 0.1 0.1 100
−10 −20 −20 0
the internal near-surface capillary water mobility, i.e. the water potential gradient and the unsaturated hydraulic conductivity of the masonry material, and (iii) a vapor-diffusion-controlled stage when drying is limited by near-surface pore vapor mobility, i.e. the vapor pressure gradient and the molecular diffusion coefficient of the masonry material. In the present study, we neglect the third stage and show that the second stage of drying is in our case the most relevant for the long-term rising damp analysis. Both the first- and the second-stage evaporation can be applied on the wall surface in a numerical model based on Equation (1). The first-stage evaporation is implemented using the Neumann (flux type) boundary condition in which the flux is determined based on the actual (instantaneous) or time-averaged weather conditions. The second-stage evaporation can be simulated using the Dirichlet (water potential) boundary condition, i.e. by setting the water potential at the drying wall surface to the hydric equilibrium with water vapor in the surrounding air. The hydric equilibrium water potential can be computed from the Kelvin equation [5], or estimated from the retention curve of the masonry material. 2.8. Model representation of the masonry wall The vertical cross-section of the church wall was represented by a 2.4-m wide and 13.2 m high rectangle rising 12 m above the
ground and 1.2 m below the ground. The computational domain was discretized using a triangular finite element mesh consisting of 71,942 elements. The wall is assumed to consist of a sandstone foundation below the ground and two outer sandstone masonry walls above the ground, each 0.8 m wide, with filling of looser material between the outer walls (perhaps a highly heterogeneous mixture of rough masonry and other porous materials available at the church construction site). The sandstone blocks of the wall allegedly originate from more than one local sources. As the exact origin of the stone was unknown, and systematic destructive sampling of the wall material was not acceptable, the three available parameter sets (denoted as Sandstone 1, 2 and 3 in Table 1) were used as equally probable alternatives characterizing hydraulic properties of the masonry. The differences among the parameter sets demonstrate the uncertainty associated with the determination of the wall hydraulic properties. Since this study is focused on long-term simulations of the masonry moisture regime without the intervention of short-term weather fluctuations, we assumed local water potential equilibrium between stones and mortar. Therefore, the effect of plaster and mortar on the hydraulic functioning of the masonry was neglected.
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The hydraulic properties of the filling material between outer walls are unknown. Therefore, two alternative representations of the filling material were considered in our analysis, assuming that: (i) the hydraulic properties of the filling are identical to those of the surrounding walls, i.e., the wall is hydraulically homogeneous; (ii) the filling resembles a coarse sand material with contrasting hydraulic properties (denoted as Core filling in Table 1). In both cases, the hydraulic parameters of the foundation were assumed identical to those of the above-ground masonry. Altogether, six variants of the wall configuration were considered based on the three alternative sets of hydraulic parameters of the sandstone blocks and two different assumptions about the structural composition of the wall (hydraulically homogeneous and hydraulically heterogeneous with coarse filling between the outer stone walls). 2.9. Steady-state simulations Steady-state simulations were performed to model the present state of the church wall. Along the contact line between the soil and the wall, the Dirichlet boundary condition was applied assuming full saturation at the bottom of the wall foundation, i.e. h = 0, and hydrostatically decreasing soil water pressure towards the soil surface, yielding h = –120 cm at the soil surface. These conditions are consistent with the observed soil water potentials in the nearby soil pit and confirmed by the water potential sensor inserted in the wall foundation. The wall surfaces above the ground were treated as evaporation surfaces, considering a possible coexistence of two different stages of evaporation on different parts of the wall surfaces (first-stage evaporation near the ground surface and second-stage evaporation further above). This approach is complicated by the fact that the vertical extents of these two parts of the wall surface are a priori unknown. Therefore, it was necessary to arrive at the steady-state flow regime through a long-term transient flow simulation starting with the first-stage evaporation along the entire height of the wall above the ground. The second-stage evaporation part of the wall surface then developed over time through a gradual transition of boundary nodes from Neumann to Dirichlet boundary condition. During the first-stage evaporation, the actual evaporation is equal to the potential evaporation rate. This rate was set equal to 0.1 cm d−1 , which is our estimate of the long-term average potential evaporation at the site of interest. During the second-stage evaporation, the actual evaporation is significantly reduced below the potential rate, being controlled by the unsaturated hydraulic conductivity of the drying wall surface. In this stage, the surface water potential drops to extremely low values approaching equilibrium with the air humidity. In our model, the second-stage evaporation of the wall surfaces is represented by the Dirichlet boundary condition assuming h = –15,000 cm. 2.10. Transient simulations Transient simulations were performed: (i) to confirm the hypothesis that the second-stage evaporation is the prevailing type of evaporation from the church wall surfaces after the installation of the projected moisture-reducing measures; (ii) to evaluate the long-term effects of open or closed drain systems installed along the church walls. Initial conditions for the transient simulations were derived from the steady-state distributions of capillary water. In scenarios simulating the effect of the open drainage system, the outer vertical face of the wall foundation (facing upslope) was exposed to evaporation (with a prescribed rate of 0.1 cm d−1 ). This corrective measure reduces the infiltration of water from
Fig. 5. Simulated water content distribution in the church masonry wall, assuming homogeneous hydraulic properties corresponding to Sandstone 1: a: steady-state distribution approximating the present state of the wall; b: projected state after 10 years since the closed drain installation; c: projected state after 10 years since the open drain installation.
surrounding soil into the foundation and allows water to leave the foundation by evaporation. A free drainage condition (equivalent to the unit hydraulic gradient condition) was assumed at the bottom boundary of the wall foundation. No-flow condition was assumed on the inner vertical face of the foundation (facing downslope). The closed drainage system is assumed to bring the soil moisture conditions near the wall foundation to the state currently observed in the soil pit located 8.8 m from the church wall (unaffected by the subsurface water buildup near the church wall). For this scenario, a pressure head of –160 cm was assigned to the bottom boundary of the wall foundation (decreasing towards a soil surface value of –280 cm). 3. Results and discussion The simulated steady-state distributions of capillary water in the church wall (assuming hydraulic properties derived from the Sandstone 1) are shown in Figs. 5a and 6a. The distributions reflect dynamic equilibrium between the infiltration of soil water and the evaporation from the wall surfaces under current conditions. The figures indicate that the foundation of the church is close to saturation and the water content in the wall masonry above the ground is also significantly elevated. The core filling in the heterogeneous wall scenario (Fig. 6a) exhibits lower water content, which is caused by a limited capillary rise in the coarser material of the filling. Similar water content distributions were obtained for the Sandstone 2 and Sandstone 3 scenarios (not shown). In Fig. 7, vertical water content profiles, evaluated at a depth of 20 cm below the surface of the interior fac¸ade, are shown for all steady-state scenarios. It can be seen that the sandstone water content is significantly elevated for large fractions of the wall. The height of the increased water content varies between 2 and 5 m above the ground depending on the hydraulic and structural properties of the masonry considered. The heterogeneous wall scenarios
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Fig. 8. Simulated steady-state fluxes of water through the exterior surface of the church wall determined for three alternative hydraulic properties of the masonry wall (corresponding to the three different sandstone samples). The results were obtained assuming homogeneous wall structure.
Fig. 6. Simulated water content distribution in the church wall consisting of two outer walls made of the masonry material corresponding to Sandstone 1 and the core filling material in between: a: steady-state distribution approximating the present state of the church masonry wall; b: projected state after 10 years since the closed drain installation; c: projected state after 10 years since the open drain installation.
Fig. 7. Simulated steady-state water content profiles in the church masonry wall resulting from six alternative numerical simulations assuming three different hydraulic properties (corresponding to the three different sandstone samples) combined with two possible wall structures (homogeneous structure vs. heterogeneous structure with outer sandstone walls and core filling in between). The profiles show water contents at a depth of 20 cm below the surface of the interior fac¸ade.
showed a consistently lower height of increased water content compared to the homogeneous wall scenarios. As expected, the process of evaporative drying significantly reduces the water content in a thin layer near the wall surface in all simulated scenarios (as shown for Sandstone 1 scenarios in
Figs. 5 and 6). This leads to a low hydraulic conductivity of the surface layer, which in turn limits the flux of water towards the wall surfaces. As a result, the second-stage evaporation prevails over the first-stage evaporation for the entire length of the wall surfaces exposed to evaporation under all steady-state and transient simulation scenarios except Sandstone 3 steady-state scenarios, in which the lower part of the wall surface above the ground remains under first-stage evaporation. This is caused by specific hydraulic properties of Sandstone 3 (namely by a low value of parameter ␣). In Fig. 8, the simulated steady-state fluxes of water through the exterior surface of the church wall are shown for the homogeneous wall scenarios. It can be seen that the evaporation rate declines significantly with the elevation above the ground. Evaporation flux equal to the prescribed potential rate is achieved only in Sandstone 3 scenario within 1 m above the ground. The prevailing evaporation conditions on the wall surfaces are strongly affected by the hydraulic parameters of the sandstone masonry. Hall et al. [26] showed that in their case the first-stage evaporation, controlled by weather conditions, dominated the process of evaporation from a masonry wall. Their results, seemingly contradicting our findings, can again be explained by a relatively low value of parameter ␣ in their study and a different wall configuration (narrow wall with a saturated source of water located directly at the soil surface). The results of the transient simulations, considering two different moisture-reduction measures, for the Sandstone 1 scenarios are presented in Figs. 5, 6 and 9. The predicted spatial distributions of water content after 10 years since the drain installation suggest that the open drainage system will substantially reduce the water content in the masonry, while the closed drainage system will be much less effective. It may seem surprising that there is not much change of moisture content for the closed drain scenario. This is caused by a continuous supply of water from the soil surrounding the foundation. The closed drain prevents flooding of foundations during episodic rainfall events, but does not insulate the foundation from the soil moisture. With the open drain, the water supply from the soil is cut off and replaced with evaporation (Table 2). Considering the flux between the subsurface masonry and the surrounding soil, its reversal from a short-lived exfiltration back to infiltration was predicted in all closed drainage system scenarios (as shown for homogeneous-wall Sandstone 1 scenarios in Fig. 9a). Directly after the drain installation, exfiltration of water from both horizontal and vertical faces of the subsurface masonry took place because of high pressure heads prior to the installation. After the
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Fig. 9. Simulated water fluxes through the wall boundaries for the homogeneous wall scenario with hydraulic properties corresponding to sandstone 1: a: after closed drain installation (negative fluxes indicate infiltration of soil water into the masonry while positive fluxes indicate exfiltration); b: after open drain installation. Table 2 Cumulative fluxes of water through the church wall boundaries (L m−1 ) and the corresponding changes of moisture storage (L m−1 ) predicted for the period of 10 years after the respective drain installation. The fluxes are positive outwards. Wall structure Homogeneous
Heterogeneous
Homogeneous
Heterogeneous
Drainage system
Sandstone 1 Foundation–bottom face Foundation–upslope face Above the ground 0–12 m Above the ground 0–1 m Initial moisture storage Initial minus final storage Sandstone 2 Foundation–bottom face Foundation–upslope face Above the ground 0–12 m Above the ground 0–1 m Initial moisture storage Initial minus final storage Sandstone 3 Foundation–bottom face Foundation–upslope face Above the ground 0–12 m Above the ground 0–1 m Initial moisture storage Initial minus final storage
Closed
Closed
Open
Open
–125 –576 843 761 5380 142
–105 –566 790 746 3770 119
49.5 102 192 118 5380 344
50.6 102 146 107 3770 299
101 –305 429 405 4440 225
85.8 –309 429 408 3150 205
115 94.5 100 76.4 4440 309
100 90.5 98.2 77.5 3150 289
–2711 –2550 5350 2990 3580 87.5
–2100 –2320 4480 3000 2500 53.8
35.8 186 664 321 3580 886
39.8 218 529 330 2500 787
pressure heads in the wall foundation decreased, the infiltration from the surrounding soil was restored. In contrast, the simulation scenarios involving the open drainage system predicted exfiltration from the bottom face of the wall foundation with gradually decreasing intensity over the whole simulated period (Fig. 9b). Predicted cumulative fluxes of water through the wall boundaries during 10 years after the drain installation are summarized in Table 2. Together with the initial and final storages of water in the masonry, these values represent a complete water balance over the period of interest. The fluxes are integrated along the boundaries of the vertical cross-section of the wall, i.e. the vertical unit-width strips of the wall surfaces. The flux values are positive outward–from the wall to its surroundings. The fluxes above ground, and for the open drain also below ground—on the upslope face of the wall foundation, are evaporation fluxes. Negative signs mean water supply from the soil to the wall.
The numbers listed in Table 2 reveal significant differences between cumulative boundary fluxes predicted for the two types of corrective measures considered (closed drain versus opened drain installation). This is caused by different hydraulic conditions on the soil—masonry interface of the church wall foundation—as explained in the previous paragraphs. There are also quite large differences in the masonry moisture regimes predicted for scenarios based on different sandstone hydraulic properties (denoted as Sandstone 1, 2 and 3). This is especially true for the Sandstone 3 closed-drain scenarios, which resulted in both greater intensity of infiltration from the soil to the wall foundation and more intensive evaporation from the wall surfaces above the ground than in the corresponding Sandstone 1 and 2 scenarios. This behavior is related to the significantly lower value of the hydraulic parameter ␣ of Sandstone 3, compared to Sandstone 1 and 2.
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The differences in cumulative fluxes and storages between the corresponding structurally homogeneous and heterogeneous wall scenarios are less prominent. Table 2 indicates large differences in moisture-reduction efficiencies predicted for the six alternative wall compositions and two projected drainage systems, highlighting the importance of the correct determination of hydraulic properties of the masonry for the adequate description of the moisture regime in the church wall. The shape of unsaturated hydraulic conductivity function (Fig. 4b) determines the intensities of fluxes through the wall. For the materials and conditions considered, a major fraction of the wall evaporation is realized through a narrow horizontal strip of the wall surface above the ground. This signifies the role of the sandstone retention curves (Fig. 4a), controlling the height of capillary rise above the ground (Fig. 7). 4. Summary and conclusions The performed finite element analysis provided an interesting insight into the moisture regime of historical sandstone masonry. The applied numerical model of capillary flow, based on the general concepts of mass conservation and Darcian flow in porous media, was parameterized and validated using data obtained through onsite survey, laboratory experiments and monitoring. An important finding of this study is related to the process of evaporation from the church wall surfaces. The modeling results confirmed our hypothesis that, in a long-term perspective, the second-stage evaporation, controlled by hydraulic properties of the masonry, prevails over the first-stage evaporation, controlled by atmospheric conditions. This finding has serious consequences for the predicted effectiveness of the corrective measures aimed at reducing the water content of the church masonry, as the secondstage evaporation rate is significantly lower than the atmospheric evaporative demand associated with the climate. Reduced evaporation may dramatically slow down the process of sandstone drying after the installation of a drainage system. It was determined that the long-term competition between first- and second-stage evaporation conditions on the wall surfaces is controlled by the combined effect of sandstone hydraulic properties, the structural composition of the wall, and the soil water status near the wall foundation. Of the two corrective measures considered in our simulation scenarios, i.e. closed drain versus open drain installation, the latter was found to be considerably more effective, leading to a greater reduction of moisture in the masonry. Acknowledgment The research was supported by the Ministry of Culture of the Czech Republic under the Applied Research and Development of the National and Cultural Identity Programme (NAKI II)–project DG16P02R049. References
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[2] E. Rirsch, Z. Zhang, Rising damp in masonry walls and the importance of mortar properties, Construct. Building Mater. 24 (10) (2010) 1815–1820, http://dx.doi.org/10.1016/j.conbuildmat.2010.04.024. [3] A.S. Guimarães, J.M. Delgado, V.P. de Freitas, Rising damp in walls: evaluation of the level achieved by the damp front, J. Building Phys. 37 (1) (2013) 6–27, http://dx.doi.org/10.1177/1744259112453822. [4] E. Franzoni, State-of-the-art on methods for reducing rising damp in masonry, J. Cult. Herit. 31 (2018) S3–S9, http://dx.doi.org/10.1016/j.culher.2018.04.001. [5] C. Hall, W.D. Hoff, Water transport in brick, stone and concrete, 1st ed., Spon Press, Taylor & Francis Group, 2002, http://dx.doi.org/10. 4324/9780203301708. [6] C. Hall, W.D. Hoff, Rising damp: capillary rise dynamics in walls, Proc. R. Soc. A 463 (2007) 1871–1884, http://dx.doi.org/10.1098/rspa.2007.1855. [7] W.H. Green, G. Ampt, Studies of soil physics, part I—the flow of air and water through soils, J. Agric. Sci. 4 (1911) 1–24. [8] L.A. Richards, Capillary conduction of liquids through porous mediums, Physics 1 (5) (1931) 318–333, http://dx.doi.org/10.1063/1.1745010. [9] D. D’Agostino, Moisture dynamics in an historical masonry structure: the Cathedral of Lecce (South Italy), Building Environ. 63 (2013) 122–133, http://dx.doi.org/10.1016/j.buildenv.2013.02.008. [10] G. Facelli, Structural survey of St. Jacob’s Church and comparison with St. Ann’s Church (Broumov group of Churches) (MSc Thesis), Czech Technical University in Prague, Prague, 2014. [11] G.C. Topp, J.L. Davis, A.P. Annan, Electromagnetic determination of soil water content: measurements in coaxial transmission lines, Water Resour. Res. 16 (3) (1980) 574–582, http://dx.doi.org/10.1029/WR016i003p00574. [12] T. Vogel, H.H. Gerke, R. Zhang, M.T. van Genuchten, Modeling flow and transport in a two-dimensional dual-permeability system with spatially variable hydraulic properties, J. Hydrol. 238 (1–2) (2000) 78–89, http://dx.doi.org/10.1016/S0022-1694(00)00327-9 (ISSN 0022-1694). [13] H.H. Gerke, J. Dusek, T. Vogel, J.M. Köhne, Two-dimensional dual-permeability analyses of a bromide tracer experiment on a tile-drained field, Vadose Zone J. 6 (2007) 651–667, http://dx.doi.org/10.2136/vzj2007.0033. [14] J. Dusek, H.H. Gerke, T. Vogel, Surface boundary conditions in two-dimensional dual-permeability modeling of tile drain bromide leaching, Vadose Zone J. 7 (2008) 1287–1301, http://dx.doi.org/10.2136/vzj2007.0175. [15] M. Dohnal, J. Dusek, T. Vogel, Improving hydraulic conductivity estimates from minidisk infiltrometer measurements for soils with wide pore-size distributions, Soil Sci. Soc. Am. J. 74 (2010) 804–811, http://dx.doi.org/10. 2136/sssaj2009.0099. [16] J. Dusek, T. Vogel, Modeling subsurface hillslope runoff dominated by preferential flow: one- vs. two-dimensional approximation, Vadose Zone J. 13 (2014), http://dx.doi.org/10.2136/vzj2013.05.0082. [17] J. Dusek, T. Vogel, Hillslope hydrograph separation: the effects of variable isotopic signatures and hydrodynamic mixing in macroporous soil, J. Hydrol. 563 (2018) 446–459, http://dx.doi.org/10.1016/j.jhydrol.2018.05.054. [18] M.T. van Genuchten, A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J. 44 (5) (1980) 892–898, http://dx.doi.org/10.2136/sssaj1980.03615995004400050002x. [19] T. Vogel, M.T. van Genuchten, M. Cislerova, Effect of the shape of the soil hydraulic functions near saturation on variably-saturated flow predictions, Adv. Water Resour. 24 (2) (2000) 133–144, http://dx.doi.org/10. 1016/S0309-1708(00)00037-3 (ISSN 0309-1708). [20] Y. Mualem, A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res. 12 (1976) 513–522. [21] A. Klute, Water retention: laboratory methods. In: Klute, A. (Ed.), Methods of soil analysis, Part 1. physical and mineralogical methods. Monograph, vol. 9, Am. Soc. Agron, Madison, Wisconsin (1986) 635–660. [22] L.F. Cooling, The evaporation of water from bricks, Trans. Ceramic Soc. 29 (1930) 39–54. [23] J.F. Pearse, T.R. Oliver, D.M. Newitt, The mechanism of the drying of solids. Part I. The forces giving rise to movement of water in granular beds, during drying, Trans. Inst. Chem. Eng. 27 (1949) 1–8. [24] D. Hillel, Environmental soil physics, Academic Press, 1998 (771 p.; ISBN: 9780123485250). [25] V. Cnudde, et al., Multi-disciplinary characterization and monitoring of sandstone (Kandla Grey) under different external conditions, Q. J. Eng. Geol. Hydrogeol. 46 (1) (2013) 95–106, http://dx.doi.org/10.1144/qjegh2012-005. [26] C. Hall, A. Hamilton, W.D. Hoff, H.A. Viles, J.A. Eklund, Moisture dynamics in walls: response to micro-environment and climate change, Proc. R. Soc. A Math. Phys. Eng. Sci. 467 (2125) (2010) 194–211, http://dx.doi. org/10.1098/rspa.2010.0131.
[1] E. Franzoni, Rising damp removal from historical masonries: a still open challenge, Construct. Building Mater. 54 (2014) 123–136, http://dx.doi.org/10. 1016/j.conbuildmat.2013.12.054.
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Original article
Moisture regime of historical sandstone masonry — A numerical study Tomas Vogel ∗ , Jaromir Dusek , Michal Dohnal , Michal Snehota Czech Technical University in Prague, Faculty of Civil Engineering, Thakurova 7, 16629 Prague, Czech Republic
a r t i c l e
i n f o
Article history: Received 28 May 2019 Accepted 23 September 2019 Available online xxx Keywords: Sandstone masonry Rising damp Moisture-reduction measures Retention curve Unsaturated hydraulic conductivity Richards equation
a b s t r a c t Rising damp causes deterioration of masonry walls in many historical buildings. Although the phenomenon of capillary rise in porous structures is relatively well understood, reliable numerical modeling of the moisture regime, applicable to the assessment of current state as well as to the predictions of changes induced by various corrective moisture-reduction measures, remains a challenge. This paper presents the results of a numerical modeling study dealing with the moisture regime of a masonry wall of the baroque Church of All Saints in Heˇrmánkovice. The numerical approach used is based on general concepts of mass conservation and Darcian flow of capillary water in porous media. The model was parameterized and validated using experimental data obtained by on-site survey, laboratory analysis and monitoring. The modeling results confirmed our hypothesis that, in a long-term perspective, the secondstage evaporation—controlled by the hydraulic properties of the masonry—prevails over the first-stage evaporation—controlled by the atmospheric conditions—for most simulation scenarios conducted. Of the two corrective moisture-reduction measures considered, i.e. a closed drain versus open drain installation, the latter was found to be significantly more effective, leading to a greater reduction of moisture in the masonry. © 2019 Elsevier Masson SAS. All rights reserved.
1. Introduction Rising damp is one of the main problems affecting historical masonry structures all over the world as it endangers the integrity of construction materials and the performance of building envelopes [1]. Excess moisture is responsible for unsuitable indoor conditions, poor thermal insulation efficiency of building walls and decrease in the mechanical performance of masonry. Wet building materials may be exposed to frost decay and migration and crystallization of soluble salts. Damp walls cause high humidity of indoor air and may lead to growth of mold on cool surfaces. The extent of masonry affected by capillary rise is determined by a combined effect of infiltration into the wall foundations, evaporation from the above-ground wall surfaces and wall hydraulic properties. A dynamic equilibrium is established between the water uptake by capillary rise and the water loss by evaporation. A classical method for controlling rising damp in walls of historical buildings is the construction of subsurface drains along the masonry, limiting the supply of water from the ground. Drain ditches may be filled with soil or left open to enhance evaporation from the wall. Alternative methods for rising damp prevention,
∗ Corresponding author. E-mail address: [email protected] (T. Vogel).
such as the insertion of damp-proof membranes, injection of chemical liquids, or application of electro-osmosis, are rarely suitable for historical buildings. There is an extensive literature related to the description of rising damp phenomena in building materials [2–4]. However, many approaches reported are difficult to apply to historical structures, often built of nonstandard materials. Properties of these materials are unknown and their determination is complicated as the experimental, surveying and monitoring tools are limited by the requirement of preservation of historical authenticity. A well-established approach, enabling a simple quantitative analysis of rising damp in masonry walls, is the Sharp Front (SF) approach [5,6]. The SF approach combines the overall (nonlocal) mass balance equation with the Green–Ampt approximation of moisture front advancement in a homogeneous one-dimensional porous medium [7]. A more rigorous approach based on the Richards equation [5,8], combining the distributed (local) mass balance equation with the Darcy-Buckingham law, is used less frequently, perhaps because of inherent difficulties related to the numerical solution of the equation and experimental uncertainties associated with the determination of the required hydraulic characteristics of masonry materials. An important component of the rising damp analysis is the estimation of the wall surface evaporation. In most recent studies [9] the evaporation rate is evaluated based on the external atmospheric
https://doi.org/10.1016/j.culher.2019.09.005 1296-2074/© 2019 Elsevier Masson SAS. All rights reserved.
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Fig. 1. Church of All Saints in Heˇrmánkovice: a: north facade; b: church interior; c: location of the monitoring system.
conditions, which, however, control the wall surface evaporation only under high surface water contents. When the balance between below-ground infiltration and above-ground evaporation is studied over longer time scales and/or under lower wall surface water contents, the evaporation rate often becomes limited by the internal wall conditions, specifically by the unsaturated hydraulic conductivity of the masonry material. In the present study, we use a two-dimensional model of capillary flow, based on the numerical solution of the Richards equation, to study the distribution of water in sandstone masonry walls of the Church of All Saints in Heˇrmánkovice. The analysis involves two types of simulation scenarios: (i) scenarios considering the steady-state flow of water from the wet wall foundations towards the evaporative surfaces of the walls, thus approximating the present state of the church walls, (ii) transient flow scenarios, focused on the future long-term effects of the proposed moisturereduction measures—installation of open or closed drainage systems.
2. Material and methods 2.1. Church of All Saints in Heˇrmánkovice The Church of All Saints in Heˇrmánkovice (Fig. 1) is located in the northeast Bohemia, Czech Republic. The church was built in the period of 1722–1726, designed by Kilian Ignaz Dientzenhofer, a well-known Bohemian architect of the Baroque era. The church belongs to the so called Broumov Group of Churches—a unique complex of ten baroque churches built in the eighteenth century on the territory of the Broumov monastic estate. The church stands in the middle of a cemetery on inclined ground with an average slope of about 13%. The upslope wall, oriented towards the north, is significantly affected by rising damp (Fig. 1b). The church floor is about 20 cm below the soil surface at the north side of the building. The walls are made from sandstone from the local quarries, e.g. ˇ those located in Cerven y´ Kostelec and Boˇzanov. Some historical
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Fig. 2. Water content monitoring results: a: soil water contents in the soil pits; b: water contents in the sandstone masonry.
records report the presence of a quarry directly in Heˇrmánkovice [10]. Interior mortar is mainly made of limes and presents a thickness of about 3 cm. It appears layered in the typical three elements: a first protection thick layer in contact with the masonry made with coarse sand to fill the gaps and prevent stone degradation, a second layer meant to smooth the surface and permit the painting to attach, and a third finishing layer mainly made of gypsum to plaster the surface [10]. In the exterior, a thicker and rougher plaster, richer of small sand pieces covers the walls. Nowadays, the plaster layer on facades is lost or deteriorated on most parts of building (Fig. 1a). In the interior of the church, walls show a high level of surface deterioration due to rising damp and biological activity. Walls have been repainted many times—different colors are visible. Render and mortar are heavily damaged at the bottom part, wet and not cohesive. A biological attack is also affecting the first half a meter with mosses and algae, especially in the niches, where worse ventilation and thus higher relative humidity of air is present. The soil surrounding the church was classified as sandy loam (in average: 53% sand, 37% silt, and 10% clay). The natural layering of the respective soil type was heavily disturbed by burial activity at the cemetery. 2.2. Monitoring system For the purpose of this study, a system for continuous monitoring of water content and water potentials in the masonry of the upslope church wall and in two soil pits, positioned on the adjacent slope, was established (Fig. 1c). Water content reflectometers with 30 cm long rods (CS650, Campbell Scientific, Logan, UT, USA)
were installed in the pillar and the niche wall at heights of 10 and 60 cm above the church floor. The rods of the CS650 water content sensors were installed into pre-drilled holes of 4 mm in diameter. To avoid insertion error, we used purpose-made insertion guides (since the original insertion tool provided by Campbell Scientific was not intended for drilling). Thus, the drilled holes were as close to parallel as possible. Air gaps between the sensor and wall material were avoided by filling the space around the sensor by a mixture of water and fine sandstone material produced by drilling. The Topp equation [11], recommended by the manufacturer as a default method, was used to convert from relative dielectric permittivity, measured by CS650, to volumetric water content. The validity of the Topp equation for the conversion was verified by a three-point laboratory calibration experiment performed on a large sandstone sample taken from the Boˇzanov quarry. Water potential sensor (T8 Tensiometer, METER Group, Inc., Germany) was installed inside the wall foundation 28 cm below the floor level. Each of the two soil pits was instrumented with three tensiometers and two water content reflectometers. The monitoring system was completed with a heated tipping bucket rain gauge (MR2H-01m, Meteoservis v.o.s., CZ). The results of water content monitoring in the wall masonry and in the two soil pits are shown in Fig. 2. The water content data measured in the soil pit situated at 2.6-m distance from the wall (Fig. 2a) reveal high and relatively stable moisture levels throughout the period. The soil profile is nearly saturated most of the time with more dry conditions at the end of the period caused by the drierthan-average summer months of July and August 2018 (23 mm of rainfall over the period of July and August 2018 compared to 74 mm
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for the same period in 2017). The small peaks on the water content graphs correspond to individual rainfall events. The water contents measured in the soil pit situated at 8.8-m distance from the wall reflect more natural water regime characteristic for the hillslope above the church. The soil profile at this location is significantly drier, with larger differences between the water contents measured at different depths. The deeper soil water content is less variable. The figure shows significantly elevated water contents in the soil pit situated near the wall, compared to the conditions observed in the pit situated further upslope—unaffected by the presence of the church wall. This confirms the findings of our preliminary soil survey, which ascribed the rising damp in the wall to water originating from the hillslope subsurface runoff, to which the church wall stands as a barrier, as well as water coming from the malfunctioning rain gutters draining the church roof. Based on the soil survey and laboratory analysis of soil samples, it was concluded that the difference in soil water regimes in the two soil pits is not related to different textural and soil hydraulic properties. The wall sensors show that the interior surface of the north wall is significantly affected by rising damp (Fig. 2b). The recorded water contents suggest only minor seasonal effects, with drier conditions in autumn, and insignificant short-term weather effects. Winter measurements resulted in erroneous data (not shown in the figure). The sensors inserted 10 cm above the church floor show consistently higher water contents than those at 60 cm with an average difference of about 0.01 cm3 cm−3 . The niche sensors suggest drier conditions than the pillar sensors. We note that the application of the water content reflectometer sensor (CS650) is well established in mineral soils but has not been thoroughly tested in construction materials. Therefore, the measured variations of water contents in the sandstone masonry (Fig. 2b) should better be interpreted in relative rather than absolute terms. 2.3. Numerical model of capillary rise We assume that the flow of capillary water in sandstone masonry is described by the Richards equation [8]. This equation combines two fundamental equations–the water balance equation and Darcy’s law. Richards’ equation can be written in the following general form: d ∂h = ∇ · (K (h) ∇ H) dh ∂t
H =h+z
(1)
where h is the water pressure head (m), H is the water potential (m) representing the potential energy associated with capillary forces and gravity, K is the hydraulic conductivity tensor (m s−1 ), is the volumetric water content (m3 m−3 ), z is the vertical coordinate—taken positive upward (m), t is time (s). Under isotropic conditions (assumed in this study), the hydraulic conductivity tensor is reduced to a scalar—further denoted by K. Equation (1) is solved numerically using the finite element code S2D developed at the CTU Prague [12]. The solution is based on the Galerkin finite element method with linear basis functions in the spatial domain, implicit finite difference scheme in the time domain, and adaptive time-stepping and iteration control to deal with the nonlinearity of the governing equation. The model was thoroughly verified and successfully applied to solve a number of water flow and solute transport problems [13–17].
linking the water content with the water pressure head h, and the hydraulic conductivity function K(h) or K(). The functional relationships describing the hydraulic properties of porous materials are usually approximated by simple analytical expressions. In this study, we use the modified form of the van Genuchten–Mualem model [18,19]. In this model, the water retention function is expressed as:
(h) = r + m − r
1 + (−˛h)
n −m
(2)
This formula is used to describe the retention curve in the unsaturated pressure head range (–∞, hs ). For pressure heads larger than the air entry value hs , the corresponding water content becomes equal to the saturated water content. The substitution of the retention function into the Mualem hydraulic conductivity formula [20] yields [19]:
K = Ks
− r s − r
1/2
2
1−F
1 − F s
F =
1−
− r m − r
m1 m
(3)
In the above expressions, Ks is the saturated hydraulic conductivity, r and s denote the residual and saturated water contents, respectively, ␣ and n are empirical fitting parameters. The parameter m is equal to 1–1/n and n is greater than 1. The parameter m is related to the air entry value hs through the relationship [19]:
m = r + s − r
1 + (−␣hs )
n m
(4)
2.5. Experimental determination of the sandstone properties To determine the hydraulic properties of the sandstone material, three samples of sandstone were taken to the laboratory (Fig. 3). The saturated water contents of the sandstone samples were measured gravimetrically based on saturated weight after 7 days of free capillary rise from open bath and dry weight after oven drying at 105 ◦ C to a constant weight. Main drainage branches of retention curves (Fig. 4) were determined using the standard sand box and pressure extractor methods [21]. The saturated hydraulic conductivity of the masonry was determined in situ using minidisk infiltrometer on a large sandstone block coming from the church wall. The determined hydraulic parameters of the sandstone samples are listed in Table 1. 2.6. Infiltration/exfiltration below the ground In situations where the masonry material (in our case the material of sandstone blocks) is in a direct contact with the surrounding soil, the water potentials inside and outside the masonry surface are equal, while the water contents differ according to the respective retention curves. This can be expressed as: hwall = hsoil
wall = wall (hwall )
soil = soil (hsoil )
(5)
where hwall and hsoil are the water pressure heads inside the masonry and in the surrounding soil, respectively. This relationship can be used as a boundary condition accompanying Equation (1) in the numerical simulations of capillary rise. Assigning specific values of hsoil , the model can represent either the infiltration of soil water into the masonry or the exfiltration of water from the masonry to the soil after the installation of a subsurface drainage system. 2.7. Evaporation from the wall surface
2.4. Parameterization of sandstone hydraulic properties The application of the Richards equation to model capillary flow in a porous medium requires the knowledge of the hydraulic properties of the medium. These properties are represented by two constitutive relationships: the water retention function (h),
Drying of masonry wall surfaces can be described as occurring in three distinct stages [22–25]: (i) a weather-controlled stage when drying is fully determined by external conditions, i.e. incoming radiation, air humidity, air temperature and air flow velocity, (ii) a capillary-flow-controlled stage when drying is limited by
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Fig. 3. Sandstone samples: Sandstone 1 (90.9 cm3 ), Sandstone 2 (106.4 cm3 ) and Sandstone 3 (146.1 cm3 ).
Fig. 4. Retention curves (a) and hydraulic conductivity functions (b) determined for the sandstone samples and the wall core filling.
Table 1 Hydraulic properties of the sandstone samples and the wall core filling.
Sandstone 1 Sandstone 2 Sandstone 3 Core filling
r (cm3 cm−3 )
s (cm3 cm−3 )
␣ (cm−1 )
n (–)
Ks (cm d−1 )
hs (cm)
0.00 0.00 0.00 0.02
0.27 0.33 0.22 0.35
0.009 0.050 0.001 0.020
1.13 1.19 1.35 3.00
0.1 0.1 0.1 100
−10 −20 −20 0
the internal near-surface capillary water mobility, i.e. the water potential gradient and the unsaturated hydraulic conductivity of the masonry material, and (iii) a vapor-diffusion-controlled stage when drying is limited by near-surface pore vapor mobility, i.e. the vapor pressure gradient and the molecular diffusion coefficient of the masonry material. In the present study, we neglect the third stage and show that the second stage of drying is in our case the most relevant for the long-term rising damp analysis. Both the first- and the second-stage evaporation can be applied on the wall surface in a numerical model based on Equation (1). The first-stage evaporation is implemented using the Neumann (flux type) boundary condition in which the flux is determined based on the actual (instantaneous) or time-averaged weather conditions. The second-stage evaporation can be simulated using the Dirichlet (water potential) boundary condition, i.e. by setting the water potential at the drying wall surface to the hydric equilibrium with water vapor in the surrounding air. The hydric equilibrium water potential can be computed from the Kelvin equation [5], or estimated from the retention curve of the masonry material. 2.8. Model representation of the masonry wall The vertical cross-section of the church wall was represented by a 2.4-m wide and 13.2 m high rectangle rising 12 m above the
ground and 1.2 m below the ground. The computational domain was discretized using a triangular finite element mesh consisting of 71,942 elements. The wall is assumed to consist of a sandstone foundation below the ground and two outer sandstone masonry walls above the ground, each 0.8 m wide, with filling of looser material between the outer walls (perhaps a highly heterogeneous mixture of rough masonry and other porous materials available at the church construction site). The sandstone blocks of the wall allegedly originate from more than one local sources. As the exact origin of the stone was unknown, and systematic destructive sampling of the wall material was not acceptable, the three available parameter sets (denoted as Sandstone 1, 2 and 3 in Table 1) were used as equally probable alternatives characterizing hydraulic properties of the masonry. The differences among the parameter sets demonstrate the uncertainty associated with the determination of the wall hydraulic properties. Since this study is focused on long-term simulations of the masonry moisture regime without the intervention of short-term weather fluctuations, we assumed local water potential equilibrium between stones and mortar. Therefore, the effect of plaster and mortar on the hydraulic functioning of the masonry was neglected.
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The hydraulic properties of the filling material between outer walls are unknown. Therefore, two alternative representations of the filling material were considered in our analysis, assuming that: (i) the hydraulic properties of the filling are identical to those of the surrounding walls, i.e., the wall is hydraulically homogeneous; (ii) the filling resembles a coarse sand material with contrasting hydraulic properties (denoted as Core filling in Table 1). In both cases, the hydraulic parameters of the foundation were assumed identical to those of the above-ground masonry. Altogether, six variants of the wall configuration were considered based on the three alternative sets of hydraulic parameters of the sandstone blocks and two different assumptions about the structural composition of the wall (hydraulically homogeneous and hydraulically heterogeneous with coarse filling between the outer stone walls). 2.9. Steady-state simulations Steady-state simulations were performed to model the present state of the church wall. Along the contact line between the soil and the wall, the Dirichlet boundary condition was applied assuming full saturation at the bottom of the wall foundation, i.e. h = 0, and hydrostatically decreasing soil water pressure towards the soil surface, yielding h = –120 cm at the soil surface. These conditions are consistent with the observed soil water potentials in the nearby soil pit and confirmed by the water potential sensor inserted in the wall foundation. The wall surfaces above the ground were treated as evaporation surfaces, considering a possible coexistence of two different stages of evaporation on different parts of the wall surfaces (first-stage evaporation near the ground surface and second-stage evaporation further above). This approach is complicated by the fact that the vertical extents of these two parts of the wall surface are a priori unknown. Therefore, it was necessary to arrive at the steady-state flow regime through a long-term transient flow simulation starting with the first-stage evaporation along the entire height of the wall above the ground. The second-stage evaporation part of the wall surface then developed over time through a gradual transition of boundary nodes from Neumann to Dirichlet boundary condition. During the first-stage evaporation, the actual evaporation is equal to the potential evaporation rate. This rate was set equal to 0.1 cm d−1 , which is our estimate of the long-term average potential evaporation at the site of interest. During the second-stage evaporation, the actual evaporation is significantly reduced below the potential rate, being controlled by the unsaturated hydraulic conductivity of the drying wall surface. In this stage, the surface water potential drops to extremely low values approaching equilibrium with the air humidity. In our model, the second-stage evaporation of the wall surfaces is represented by the Dirichlet boundary condition assuming h = –15,000 cm. 2.10. Transient simulations Transient simulations were performed: (i) to confirm the hypothesis that the second-stage evaporation is the prevailing type of evaporation from the church wall surfaces after the installation of the projected moisture-reducing measures; (ii) to evaluate the long-term effects of open or closed drain systems installed along the church walls. Initial conditions for the transient simulations were derived from the steady-state distributions of capillary water. In scenarios simulating the effect of the open drainage system, the outer vertical face of the wall foundation (facing upslope) was exposed to evaporation (with a prescribed rate of 0.1 cm d−1 ). This corrective measure reduces the infiltration of water from
Fig. 5. Simulated water content distribution in the church masonry wall, assuming homogeneous hydraulic properties corresponding to Sandstone 1: a: steady-state distribution approximating the present state of the wall; b: projected state after 10 years since the closed drain installation; c: projected state after 10 years since the open drain installation.
surrounding soil into the foundation and allows water to leave the foundation by evaporation. A free drainage condition (equivalent to the unit hydraulic gradient condition) was assumed at the bottom boundary of the wall foundation. No-flow condition was assumed on the inner vertical face of the foundation (facing downslope). The closed drainage system is assumed to bring the soil moisture conditions near the wall foundation to the state currently observed in the soil pit located 8.8 m from the church wall (unaffected by the subsurface water buildup near the church wall). For this scenario, a pressure head of –160 cm was assigned to the bottom boundary of the wall foundation (decreasing towards a soil surface value of –280 cm). 3. Results and discussion The simulated steady-state distributions of capillary water in the church wall (assuming hydraulic properties derived from the Sandstone 1) are shown in Figs. 5a and 6a. The distributions reflect dynamic equilibrium between the infiltration of soil water and the evaporation from the wall surfaces under current conditions. The figures indicate that the foundation of the church is close to saturation and the water content in the wall masonry above the ground is also significantly elevated. The core filling in the heterogeneous wall scenario (Fig. 6a) exhibits lower water content, which is caused by a limited capillary rise in the coarser material of the filling. Similar water content distributions were obtained for the Sandstone 2 and Sandstone 3 scenarios (not shown). In Fig. 7, vertical water content profiles, evaluated at a depth of 20 cm below the surface of the interior fac¸ade, are shown for all steady-state scenarios. It can be seen that the sandstone water content is significantly elevated for large fractions of the wall. The height of the increased water content varies between 2 and 5 m above the ground depending on the hydraulic and structural properties of the masonry considered. The heterogeneous wall scenarios
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Fig. 8. Simulated steady-state fluxes of water through the exterior surface of the church wall determined for three alternative hydraulic properties of the masonry wall (corresponding to the three different sandstone samples). The results were obtained assuming homogeneous wall structure.
Fig. 6. Simulated water content distribution in the church wall consisting of two outer walls made of the masonry material corresponding to Sandstone 1 and the core filling material in between: a: steady-state distribution approximating the present state of the church masonry wall; b: projected state after 10 years since the closed drain installation; c: projected state after 10 years since the open drain installation.
Fig. 7. Simulated steady-state water content profiles in the church masonry wall resulting from six alternative numerical simulations assuming three different hydraulic properties (corresponding to the three different sandstone samples) combined with two possible wall structures (homogeneous structure vs. heterogeneous structure with outer sandstone walls and core filling in between). The profiles show water contents at a depth of 20 cm below the surface of the interior fac¸ade.
showed a consistently lower height of increased water content compared to the homogeneous wall scenarios. As expected, the process of evaporative drying significantly reduces the water content in a thin layer near the wall surface in all simulated scenarios (as shown for Sandstone 1 scenarios in
Figs. 5 and 6). This leads to a low hydraulic conductivity of the surface layer, which in turn limits the flux of water towards the wall surfaces. As a result, the second-stage evaporation prevails over the first-stage evaporation for the entire length of the wall surfaces exposed to evaporation under all steady-state and transient simulation scenarios except Sandstone 3 steady-state scenarios, in which the lower part of the wall surface above the ground remains under first-stage evaporation. This is caused by specific hydraulic properties of Sandstone 3 (namely by a low value of parameter ␣). In Fig. 8, the simulated steady-state fluxes of water through the exterior surface of the church wall are shown for the homogeneous wall scenarios. It can be seen that the evaporation rate declines significantly with the elevation above the ground. Evaporation flux equal to the prescribed potential rate is achieved only in Sandstone 3 scenario within 1 m above the ground. The prevailing evaporation conditions on the wall surfaces are strongly affected by the hydraulic parameters of the sandstone masonry. Hall et al. [26] showed that in their case the first-stage evaporation, controlled by weather conditions, dominated the process of evaporation from a masonry wall. Their results, seemingly contradicting our findings, can again be explained by a relatively low value of parameter ␣ in their study and a different wall configuration (narrow wall with a saturated source of water located directly at the soil surface). The results of the transient simulations, considering two different moisture-reduction measures, for the Sandstone 1 scenarios are presented in Figs. 5, 6 and 9. The predicted spatial distributions of water content after 10 years since the drain installation suggest that the open drainage system will substantially reduce the water content in the masonry, while the closed drainage system will be much less effective. It may seem surprising that there is not much change of moisture content for the closed drain scenario. This is caused by a continuous supply of water from the soil surrounding the foundation. The closed drain prevents flooding of foundations during episodic rainfall events, but does not insulate the foundation from the soil moisture. With the open drain, the water supply from the soil is cut off and replaced with evaporation (Table 2). Considering the flux between the subsurface masonry and the surrounding soil, its reversal from a short-lived exfiltration back to infiltration was predicted in all closed drainage system scenarios (as shown for homogeneous-wall Sandstone 1 scenarios in Fig. 9a). Directly after the drain installation, exfiltration of water from both horizontal and vertical faces of the subsurface masonry took place because of high pressure heads prior to the installation. After the
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Fig. 9. Simulated water fluxes through the wall boundaries for the homogeneous wall scenario with hydraulic properties corresponding to sandstone 1: a: after closed drain installation (negative fluxes indicate infiltration of soil water into the masonry while positive fluxes indicate exfiltration); b: after open drain installation. Table 2 Cumulative fluxes of water through the church wall boundaries (L m−1 ) and the corresponding changes of moisture storage (L m−1 ) predicted for the period of 10 years after the respective drain installation. The fluxes are positive outwards. Wall structure Homogeneous
Heterogeneous
Homogeneous
Heterogeneous
Drainage system
Sandstone 1 Foundation–bottom face Foundation–upslope face Above the ground 0–12 m Above the ground 0–1 m Initial moisture storage Initial minus final storage Sandstone 2 Foundation–bottom face Foundation–upslope face Above the ground 0–12 m Above the ground 0–1 m Initial moisture storage Initial minus final storage Sandstone 3 Foundation–bottom face Foundation–upslope face Above the ground 0–12 m Above the ground 0–1 m Initial moisture storage Initial minus final storage
Closed
Closed
Open
Open
–125 –576 843 761 5380 142
–105 –566 790 746 3770 119
49.5 102 192 118 5380 344
50.6 102 146 107 3770 299
101 –305 429 405 4440 225
85.8 –309 429 408 3150 205
115 94.5 100 76.4 4440 309
100 90.5 98.2 77.5 3150 289
–2711 –2550 5350 2990 3580 87.5
–2100 –2320 4480 3000 2500 53.8
35.8 186 664 321 3580 886
39.8 218 529 330 2500 787
pressure heads in the wall foundation decreased, the infiltration from the surrounding soil was restored. In contrast, the simulation scenarios involving the open drainage system predicted exfiltration from the bottom face of the wall foundation with gradually decreasing intensity over the whole simulated period (Fig. 9b). Predicted cumulative fluxes of water through the wall boundaries during 10 years after the drain installation are summarized in Table 2. Together with the initial and final storages of water in the masonry, these values represent a complete water balance over the period of interest. The fluxes are integrated along the boundaries of the vertical cross-section of the wall, i.e. the vertical unit-width strips of the wall surfaces. The flux values are positive outward–from the wall to its surroundings. The fluxes above ground, and for the open drain also below ground—on the upslope face of the wall foundation, are evaporation fluxes. Negative signs mean water supply from the soil to the wall.
The numbers listed in Table 2 reveal significant differences between cumulative boundary fluxes predicted for the two types of corrective measures considered (closed drain versus opened drain installation). This is caused by different hydraulic conditions on the soil—masonry interface of the church wall foundation—as explained in the previous paragraphs. There are also quite large differences in the masonry moisture regimes predicted for scenarios based on different sandstone hydraulic properties (denoted as Sandstone 1, 2 and 3). This is especially true for the Sandstone 3 closed-drain scenarios, which resulted in both greater intensity of infiltration from the soil to the wall foundation and more intensive evaporation from the wall surfaces above the ground than in the corresponding Sandstone 1 and 2 scenarios. This behavior is related to the significantly lower value of the hydraulic parameter ␣ of Sandstone 3, compared to Sandstone 1 and 2.
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The differences in cumulative fluxes and storages between the corresponding structurally homogeneous and heterogeneous wall scenarios are less prominent. Table 2 indicates large differences in moisture-reduction efficiencies predicted for the six alternative wall compositions and two projected drainage systems, highlighting the importance of the correct determination of hydraulic properties of the masonry for the adequate description of the moisture regime in the church wall. The shape of unsaturated hydraulic conductivity function (Fig. 4b) determines the intensities of fluxes through the wall. For the materials and conditions considered, a major fraction of the wall evaporation is realized through a narrow horizontal strip of the wall surface above the ground. This signifies the role of the sandstone retention curves (Fig. 4a), controlling the height of capillary rise above the ground (Fig. 7). 4. Summary and conclusions The performed finite element analysis provided an interesting insight into the moisture regime of historical sandstone masonry. The applied numerical model of capillary flow, based on the general concepts of mass conservation and Darcian flow in porous media, was parameterized and validated using data obtained through onsite survey, laboratory experiments and monitoring. An important finding of this study is related to the process of evaporation from the church wall surfaces. The modeling results confirmed our hypothesis that, in a long-term perspective, the second-stage evaporation, controlled by hydraulic properties of the masonry, prevails over the first-stage evaporation, controlled by atmospheric conditions. This finding has serious consequences for the predicted effectiveness of the corrective measures aimed at reducing the water content of the church masonry, as the secondstage evaporation rate is significantly lower than the atmospheric evaporative demand associated with the climate. Reduced evaporation may dramatically slow down the process of sandstone drying after the installation of a drainage system. It was determined that the long-term competition between first- and second-stage evaporation conditions on the wall surfaces is controlled by the combined effect of sandstone hydraulic properties, the structural composition of the wall, and the soil water status near the wall foundation. Of the two corrective measures considered in our simulation scenarios, i.e. closed drain versus open drain installation, the latter was found to be considerably more effective, leading to a greater reduction of moisture in the masonry. Acknowledgment The research was supported by the Ministry of Culture of the Czech Republic under the Applied Research and Development of the National and Cultural Identity Programme (NAKI II)–project DG16P02R049. References
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Please cite this article in press as: T. Vogel, et al., Moisture regime of historical sandstone masonry — A numerical study, Journal of Cultural Heritage (2019), https://doi.org/10.1016/j.culher.2019.09.005