Modelling the Mechanical Effect of Salt Weathering on Historical Sandstone Blocks through Microdrilling

Abstract

The durability of sandstones of historical building materials and geoheritage landforms is a major issue that requires an assessment methodology to follow salt weathering evolution. The building blocks of monuments support decorative carvings and reliefs that are outstanding testimonies of human activity. An evaluation based on quasi- and non-destructive testing is a reliable and generally accepted way of testing and inspecting historical building materials. Compression tests were performed on specimens of similar building sandstones extracted close to those of from St. Leonard’s Middle Ages Church, and microdrilling tests were carried out on adequate blocks of this monument. The locations of the latter tests were determined using the results of low-pressure water absorption tests, which contributed to finding a link between the sandstone specimens and the building blocks of the monument. This innovative methodology was used to generate simulated stress–strain diagrams of the building blocks of this church based on drilling strength results, avoiding the cutting of specimens from the façades with the sizes needed to ensure the mechanical validity of the results. A good agreement between the predicted and experimental stress–strain curves was achieved. The stress–strain curves of sound stones from historical building blocks and of their weathered envelopes are shown. The evolution of weathering profiles can be followed through the analysis of stress–strain diagrams, allowing an assessment of structural stability, which is essential to the study of the durability of historical building sandstones. This innovative methodology allows the adequate conservation of monuments and is a contribution to the knowledge of sustainable cultural tourism.

1. Introduction

Several authors have reported on stone degradation patterns in historic buildings [1,2,3]. Crack and deformation, detachment, features induced by material loss, discoloration and deposits, and biological colonization are the five types of stone deterioration patterns referred to in the International Council on Monuments and Sites—International Scientific Committee for Stone (ICOMOS-ISCS) glossary [4].

Material loss at cross-sections, aside fracture and strain damage, is most responsible for decreasing the stability of structural elements such as building blocks in walls, vaults and columns. The weathering of stone reliefs or carved details is very important, and a honeycomb pattern is one of the more visible features, also induced by material loss, in historic buildings.

Some of the most important sandstone monuments in the world with striking reliefs and carvings were studied by Fitzner et al. [5], who focused on Nubian sandstones of the Karnak and Luxor temples in Tebas, quarried in Gebel Silsila (Upper Egypt); Heinrichs [6], whose study object encompassed Cambro–Ordovician sandstone formations in Petra tombs and temples; Wadeson [7], who reported on Nabatean façade tombs in Petra and Hegra; Heinrichs and Fitzner [8], who investigated sandstone stelae of the Nemrud Dag sanctuary in Turkey; Ma [9] and Qiao et al. [10], whose studies concerned the sandstones of the red cliff carved with the Image of Leshan Grand Buddah; Stein [11], who worked with sandstones of the Kanchipuram temples and Khajuraho temples in India; Singh [12], who focused on the weathering of the Kailasanatha Temple at Kanchipuram; Deshpande et al. [13], whose study pertained to reliefs on walls and column carvings on yellow blocks of sandstones of Jaisalmer Fort in Rajasthan in India; Uchida et al. [14], Hosono et al. [15], and Siedal et al. [16], who highlighted the reliefs on the surface of the grey to yellowish-brown sandstones in Phnom Krom monuments (Angkor region) and their detachment; and Ashmore [17], who studied carvings on sandstone major stelae and some masonry structures in the Mayan city of Quiriguá in Guatemala.

The structural stability of medium-scale landforms (Mignón [18]) that are geoheritage, such as sandstone arches, sometimes depends on the integrity of the rock masses remaining after weathering evolution. Significant weathering patterns related to material loss are rendering-like erosion features. Important testimonies are the following: Rainbow Bridge in southern Utah [19,20], sacred to Indigenous Americans in the USA; Delicate Arch [20,21]; Marlong Arch and Looking Glass Arch in Carnarvon National Park in Australia [22]; and the Arch of Afazadjar, south of Akakus Massif in Libya [23].

In order to avoid jeopardizing these artistic or natural details, which are striking testimonies of human or natural activity, the structural stability of their supporting blocks must be assessed and monitored. Monitoring the progress of weathering on sandstones is required to allow the long-lasting existence of reliefs and carvings shown on these building or rock mass blocks, which can only occur if the integrity of the latter is maintained.

Mechanical behaviour can be assessed by compression parameters obtained from stress–strain diagrams; however, minimally intrusive tests and quasi-NDTs (non-destructive tests) are required for the sake of monument integrity, and its weathering progression must be assessed by these tests. The following authors carried out studies comprising microdrilling tests and recorded salt weathering profiles on stone samples and rock mass specimens.

The HardRock research project [24] developed an apparatus to study weathering profiles on historical building stones and the effectiveness of consolidation treatments on impregnation depth by means of measuring the downhole drilling strength and time. Ludovico-Marques and Delgado-Rodrigues [25] performed sodium chloride ageing tests on samples of volcanic tuffs inside a salt mist chamber and assessed the salt weathering effect through drilling resistance profiles on these samples. They also calculated the drilling energy needed to drill the holes downward from the recorded values of the strength and displacement of the drill bit. Further details of this Drilling Resistance Measurement Test (DRMT) are shown in Section 2 in the present study.

Fitzner and Heinrichs, as referenced in Heinrichs [6], studied the salt weathering of the Umm Ishrin Sandstone Formation in the monuments of the Nabataean city of Petra. They determined drilling resistance–depth profiles using a device with drill bits 3 mm in diameter at constant pressure, supply of energy and rotation speed in a representative area with features such as contour scaling and granular disintegration. The drilling resistance was obtained as a ratio between values of drilling time and drilling depth. They found that halite was the representative salt mineral.

Siedal et al. [16] used the Durabo portable drilling system to carry out tests on a scale on the north wall of the Gopura building of Angkor Wat. They recorded, in a chart, the drilling resistance based on the values of the penetration depth of a drill bit with a 3 mm diameter, while the rotation and the pressing force were kept constant and determined the salt weathering profile. These results showed that the zone of detachment behind the scale has a thickness of approximately 1.5 cm.

Bruthans et al. (supplementary information of [21]) measured the drilling resistance as the drilling depth on samples of sandstone exposures in the Bohemian Cretaceous Basin and Colorado Plateau (Navajo, Wingate, Star Point, Kayenta and Hruba Skala sandstones and Crystal Peak Tuff) at constant pressure and rotation speed. This technique allowed them to correlate the drilling resistance with the tensile strength. They also found that the most durable sandstones against salt weathering cycles of NaSO₄ showed lower values of drilling resistance.

Dassow et al. [26] assessed artificial salt decay on a sample of Stanton Moor sandstone with ultrasonic-assisted drilling (UAD), recording the force applied and the power required to maintain the oscillation and amplitude while drilling with the drill bit developed for this device.

St. Leonard’s Church is a monument in Atouguia da Baleia, located in the western region of Portugal, about 3 km away from the Atlantic coast, and was built in the Middle Ages. Atouguia da Baleia was near a harbour on the shoreline of an ancient channel between this village and Peniche Island until the 15th century, when it started to be filled with sea and river sediments, and it has since disappeared. The façades of St. Leonard’s Church exhibit cavities in dimension blocks and capitals below the western vault, around 10 cm long and deeply connected, due to sodium chloride crystallization, the major source of these salts being seawater. The salt spray carries sodium chloride to the façades of St. Leonard’s Church and causes deposition and crystallization in the pores of the sandstone. Salt solutions are also absorbed by capillarity [27,28]. The salt effect is widely distributed and damaged the carvings of the portals of St. Leonard’s Church over a period of almost 800 years, inducing the loss of material in the motifs of the structural blocks, as highlighted on the main western façade (Figure 1).

Another important pattern of deterioration is biological colonization, highly developed on stone surfaces, with fungi and lichens being the most visible features. The latter is associated with the blistering and detachment of stone laminae.

The results of quasi-NDTs, such as DRMTs (Drilling Resistance Measurement Tests), carried out on stone monuments can be correlated with data from DTs (Destructive Tests), such as uniaxial compression. Expressions were obtained from a comparison between the DRMT data recorded from representative blocks of the monument St. Leonard’s Church and the results of compression obtained on similar specimens collected from built heritage in the vicinity. The latter specimens were validated by an intrinsic signature through a methodology based on finding similarities by carrying out a visual inspection and petrographic, physical (comprising the absorption of water under low pressure and porosity) and mechanical characterization (compression and DRM tests) [27,29]. Aside from size requirements for mechanical validity and the specifications required by the experimental apparatus, the compression test has no restrictions on the size of the specimens to maintain monument integrity, since it is not performed directly on its materials.

A detailed mineralogical, physical and mechanical characterization is presented concerning the four typologies of sandstone lithotypes found in the built heritage close to the monument in order to contribute to a better understanding of the physical and mechanical behaviour of these sandstone building materials.

An analytical model based on stress–strain diagrams, supported by microdrilling strength values of samples of sound and weathered sandstones, is shown, which allows the assessment of the structural stability of building blocks of monuments as a measure to ensure the long-lasting existence of striking artistic testimonies such as carvings and reliefs.

2. Experimental Work

More than 240 samples were extracted from different varieties of sandstone blocks of the Lourinhã Formation with 5 cm long cross-sections, corresponding to height-to-length ratios of 1 and 2. Three varieties of sandstones were detected on the façades of St. Leonard’s Church, identified as B, C and M. Variety A was not found in this monument, but it is present in the masonry walls located close to it. Varieties A and B belong to lithotype A + B, and varieties C + M constitute lithotype C + M.

Lithotype A + B’s macroscopic laminations and lineations were aligned parallel to the major axis. The prismatic specimens were randomly cut, as no well-defined macroscopic laminations were found in the C and M varieties of sandstone [27].

Archimedes’ principle was used to determine the porosity and the bulk and real densities of the sandstone specimens, according to the Recommendations of [30,31]; after saturation under vacuum at a minimum value of 15 mbar for 24 h, air voids were filled with trapped deionized water, lasting 24 h, and atmospheric pressure was reintroduced after 24 h. The drying of the specimens was carried out in an oven at a temperature of 105 °C and lasted 72 h.

Mercury intrusion porosimetry (MIP) was carried out in order to obtain the pore size distribution (PSD) of B, C and M sandstone varieties [27]. Mercury capillary pressures of up to 200 MPa were applied by an AutoPore IV9500 from Micromeritics Instrument Corporation. The Katz and Thompson method [32] was used to infer the permeability values.

The water absorption was measured in a low-pressure test [30] carried out using a Karsten tube fixed to removable putty on the top face of the sandstone samples. The top opening of the vertical pipe was filled with water dropped towards the tube top, with the graduation “0”. The slope of the linear part of the test curve was given by water absorption graphs of the mass of water per unit area as a function of the square root of time. The values of the water absorption coefficient, k, were then obtained. Figure 2 shows Karsten pipes puttied on a portal of the south façade.

A covered tray containing deionized water was used to carry out the capillarity tests on prismatic samples of sandstones [30]. These samples were introduced into a tray with a water-level thickness of 2 mm, which was kept constant during the test. The absorbed amounts of water were weighed at different times, and the values were divided per unit of cross area of the specimens. The values of this parameter were plotted as a function of the square root of time. The capillarity water absorption coefficient was obtained through the slope of the linear part of the test curve.

Drying tests were carried out according to the Recommendations of NORMAL 29/88 (1991) and RILEM (1980) [30,33] on cubic sandstone samples under laboratory environment conditions of a 20 ± 2 °C temperature (T) and 55 ± 10% relative humidity (RH). Drying occurred on the six faces of the cubic specimens of sandstone lithotype A + B and only on the top face of specimens of sandstone lithotype C + M. It was not possible on the other five faces of the latter samples because they were sealed with an epoxy resin impermeable to water.

The drying index (DI) of NORMAL 29/88 (1991) [33] expresses the drying behaviour of experimental curves and is given in Equation (1):

$$\mathrm{D}\mathrm{I}=({\displaystyle {\int }_{{\mathrm{t}}_0}^{{\mathrm{t}}_{\mathrm{f}}}\mathrm{f}({\mathrm{Q}}_{\mathrm{i}})})/({\mathrm{Q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathrm{t}}_{\mathrm{f}})$$

(1)

with f(Q_i) as the percentage of dry mass towards the end of drying (t_f), Q_max as the initial water content and t₀ as the initial time.

A Seidner servo-controlled press, model 3000D, with a load capacity of up to 3000 kN and a piston stroke of 50 mm was used in [34] to carry out monotonic uniaxial compression tests with an axial displacement control rate of 10 μm/s. Each LVDT was inserted on each side of the specimen between the plates of the compression testing machine, and the four LVDTs allowed the average axial displacement between platens to be determined. Stress–strain diagrams were obtained in order to determine the behaviour of 50 × 50 × 100 mm³ sandstone prismatic samples under uniaxial compression.

The Drilling Resistance Measurement Test (DRMT) was performed with a portable microdrilling device with a drilling head on a slide, which controls the stepper movement towards the stone building blocks on a façade or on a holder. Diaber tungsten drill bits with a 5 mm diameter and a triangular tip were used in this study to reach maximum drill hole depths of up to 25 mm through the measurement of a load cell. These drill holes were made on building sandstones of St. Leonard’s portal of the south façade (Figure 3) and on similar specimens collected close to this monument [27]. The drilling parameters were a speed of 200 rotations per minute (rpm) and an advancing rate of 20 mm/min, which were defined by preliminary tests. The power used to operate the DRMT device was electricity.

Tip wear due to abrasion was corrected on drilling strength profiles according to Singer et al. [35], based on linear dependence on the drilled depth. The correction factor was determined by linear regression on data recorded from a DRMTs performed on the same stone type at increasing drilled lengths with the same drill bit. The test results are given in graphs with drilling strength (σ_d) on the vertical axis and drilled depth (d) on the horizontal axis.

A balance was considered between respect for the integrity of the monument and the unknown time required for the preservation efforts for this heritage building. The maximum number of DRMTs carried out in the present study was only 2 to 3 per block of sandstone varieties in order to allow a future follow-up of weathering progression. Performing all of the DRMTs on the portal of the south façade, analysing their results and obtaining the drilled data took one working day.

3. Results and Discussion

3.1. Petrographic Study

Hand specimens of four varieties of sandstones were observed, and the classifications of their surface colour according to the Munsell colour system are the following: A HUE 5Y 5/3, olive; B HUE 5Y 6/4, olive; C HUE 2.5Y 7/2, light grey; M HUE 2.5Y 6/6, olive-yellow.

These samples of sandstones were collected from the Lourinhã Formation, which has been dated to the Late Jurassic, according to [36].

Thin sections of representative samples of the sandstone varieties were studied under a polarizing microscope (Figure 4), and a modal analysis was carried out based on thousand-point counting, allowing the composition to be obtained, as presented in

Table 1. The composition of the A, B, C and M varieties of sandstones obtained from modal analysis based on a thousand-point counting method (thin sections under a polarizing microscope, observations under crossed nicols).

Minerals (%)	A	A ┴	B	B ┴	C	C ┴	M	M ┴	Ig1 #
Quartz	29.6	30.2	30.8	31.6	37.8	38.6	51.4	44.8	41.3
Feldspars *	14.6	13.2	15.6	15.1	17.9	17.0	15.2	17.0	18.0
Carbonates **	37.4	39.6	33.6	34.8	24.6	26.8	20.2	21.4	18.3
Micas/clinochlore ***	4.9	3.8	5.8	4.6	4.4	3.8	3.6	3.6	5.4
Matrix ****	6.7	6.8	7.8	7.5	7.3	5.8	3.2	4.8	8.8
Rock fragments *****	5.8	5.4	5.4	5.2	7.0	7.2	5.2	6.6	7.2
Opaque minerals	1.0	1.0	1.0	1.2	1.0	0.8	1.2	1.8	1.0
Total	100	100	100	100	100	100	100	100	100

┴ Perpendicular direction to lineations; # Ig1 is a sample collected on the south façade of St. Leonard’s Church and corresponds to C + M varieties regarding its composition; * feldspars: albite, microcline; ** carbonates: calcite prevails, and ankerite is rare; *** micas: muscovite and biotite; **** matrix: clay minerals, clinochlore, calcite, hematite/goethite; ***** rock fragments: sedimentary rock fragments, chert, carbonates, metamorphic rock fragments and polycrystalline quartz.

.

Table 2. Results of micropetrographic analysis of A, B, C and M varieties of sandstones.

Sandstones Variety		A	B	C	M	C + M (Monument)
Classification		Lithic arkose with carbonate cement (after [37]).
Major minerals		Quartz, calcite, feldspars, rock fragments.
Minor minerals		Micas, clinochlore, clays, opaque minerals, hematite, goethite, heavy minerals.
Fabric	Grain size (quartz and feldspars)	0.1 mm (average) 0.4 mm (maximum)	0.12 mm (average) 0.51 mm (maximum)	0.15 mm (average) 0.50 mm (maximum)	0.22 mm (average) 0.95 mm (maximum)	0.16 mm (average) 0.43 mm (maximum)
		Very fine sand (according to [38])	Very fine sand (according to [38])	Fine sand (according to [38])	Fine sand (according to [38])	Fine sand (according to [38])
		Grains with several sizes
	Sorting	Moderate.
	Roundness (quartz and feldspars)	Sub-angular to sub-rounded (after [39]).
	Grain contacts (quartz and feldspars)	Matrix-supported grains and rare direct grain contacts.		Matrix-supported grains and direct grain contacts (point contacts and waved sutures).
	Orientation	Micas and clinochlore present a dominant orientation	Not identified.	Micas and clinochlore present a dominant orientation	Micas and clinochlore present a dominant orientation	Micas and clinochlore present a dominant orientation
	Grain bonding	Matrix-supported fabric (carbonate as matrix mineral is predominant).		Matrix-supported fabric (carbonate as matrix mineral is predominant) and direct grain contacts (point contacts and waved sutures).
Mineral components	Quartz	Sometimes with overgrowths and inclusions.
	Carbonates	Carbonate, mainly calcite; ankerite is rare.
	Feldspars	Albite, anorthite, microcline; often weathered and sericitized or looking similar to quartz.
	Rock fragments	Sedimentary rock fragments, chert, carbonate rock fragments, metamorphic rock fragments, polycrystalline quartz.
Mineral components	Micas/ Clinochlore	Partly in large flakes; micas are biotite and muscovite; biotite is partly chloritized or occurs in combination with Fe-oxide (hematite); clinochlore occurs as single mineral or as fine-grained matrix mineral.
	Clay minerals	Kaolinite, sericite; partly in combination with Fe-oxide (hematite) and Fe-hydroxide (goethite).
	Opaque min.	Mainly ferrous.
	Oxides and hydrox of iron	Mainly hematite and goethite as opaque minerals and fine-grained as matrix minerals.
	Heavy minerals	Rare; mainly tourmaline, zircon, rutile; as single grains or inclusions.
Cement		Carbonates as cementing material, secondarily generated. Siliceous cementing material as contact cement. Secondarily generated and often mixed with fine-grained calcite are clay minerals, fine-grained clinochlore or hematite as contact cement on fine borders or as pore-filling materials.

shows the general results of this micropetrographic study including the observations made by scanning electron microscopy (SEM) and X-ray diffraction (XRD) analyses (Figure 4, Figure 5 and Figure 6). Quartz and feldspars are the major minerals, making up about 30–50% and 13–18% of the composition. The carbonates range between approximately 20% and 40% of the total amount and act as the cementing material, secondarily generated. The A, B, C and M varieties of sandstones were classified as lithic arkose according to [37], with the carbonate content playing an important role. These sandstone varieties were then classified as lithic arkose with carbonate cement, and two lithotypes were defined: A + B and C + M.

The properties studied and indicated in Table 2 show considerable similarities between the two lithotypes in terms of the following:

• The constitutive minerals are essentially the same in the grains, matrix and grain-bonding cement, although there are differences in their respective contents, as per the previous reference in Table 1.
• Micas present preferential orientations, except for the B variety, where there is a random distribution, and the M variety, which exhibits orientations in both directions. The macroscopic arrangement of the orientation of lineations in typology B is apparent, as microscopic observation revealed they were randomly distributed. In typology M, bedding was not observed macroscopically due to mica orientations in the two directions, according to microscopic observation.
• The cement of carbonate and silicious materials, which predominate, is of secondary origin.
• The rock fragments have the same origin, i.e., debris due to weathering, carried from Berlengas Islands in this specific subsector of the Lusitanian Basin, close to its western margin.
• Chemical weathering is frequently shown in feldspars, e.g., sericitization and the partial chloritization of biotite, which also occurs in association with iron oxides and hydroxides, with their dissemination in the matrix, and of clinochlore, which constitutes oxidized chlorite.

Concerning the fabric, i.e., the geometric arrangement and the spatial distribution of the constituent elements, some differences are highlighted regarding the following aspects:

• Grain size: In the A + B lithotype, the average grain sizes of quartz and feldspars range between 0.1 and 0.13 mm, with maximum values between 0.3 and about 0.5 mm, while in the lithotype C + M, they vary between 0.15 and 0.24 mm, with maximum values between around 0.5 and 0.95 mm. The designation of very fine sands of the classification [38] is not adequate for the C + M lithotype, only fine sands. Variety M has grains with average dimensions slightly larger than those of variety C and maximum dimensions similar to those of coarse sands.
• Bonds and contacts between grains: In both lithotypes, the grains are supported by a predominantly calcite matrix, with direct contacts between them being rare in lithotype A + B, while in the C + M lithotype, there is a higher frequency of contacts.

The A + B lithotype is more compact than C + M.

Detailed micropetrographic observations carried out by SEM and XRD analyses are shown in Figure 4, Figure 5, Figure 6 and Figure 7. The minimum observable size of micropores obtained by SEM is less than about 0.5 μm (Figure 5e).

3.2. The Physical Study of Both Lithotypes of Sandstones of the Lourinhã Formation

Table 3. Physical parameters obtained by Archimedes’ principle.

Samples	Number of Samples	Porosity n (%) (Average ± SD (CV %))	Bulk Density (kg/m3) (Average ± SD (CV %))	Real Density (kg/m3) (Average ± SD (CV %))
A variety	34	4.1 ± 0.4 (9.8%)	2594 ± 13 (0.5%)	2705 ± 6 (0.3%)
B variety	35	6.9 ± 0.5 (7.2%) 6.3 (monument)	2510 ± 19 (0.8%) 2375 (monument)	2697 ± 8 (0.3%) 2533 (monument)
C variety	34	12.7 ± 0.4 (3.1%) 11.5 * (12.5 and 10.5)	2343 ± 25 (1.1%) 2350 * (2375 and 2324)	2684 ± 10 (0.4%) 2655 * (2714 and 2596)
M variety	140	18.5 ± 0.4 (2.2%) 17.1 * (18.3 and 15.9)	2179 ± 13 (0.6%) 2222 * (2202 and 2241)	2671 ± 6 (0.2%) 2682 * (2697 and 2666)

* Mean physical parameters obtained on monument samples Ig1 and Ig6 collected on south portal; SD is standard deviation; CV is coefficient of variation.

shows the values of porosity accessible to water and the bulk and real densities obtained on 240 specimens of sandstone A, B, C and M varieties and also on small samples of each variety from the monument, aside from variety A, which was not found. Water-accessible porosity values vary between about 3 and 5% for specimens of type A, 6 and 8% for the B variety, and 11 and 14% for the C variety, and for specimens of M-variety sandstone, the values range between approximately 16.5 and 19.5%. The average values of bulk density range from 2179 kg/m³ (variety M) to 2510 kg/m³ (variety B) and 2594 kg/m³ (variety A), with the values of the coefficient of variation generally lower than 1%. The average value of real densities of all specimens is close to 2680 kg/m³, i.e., the mean value of variety C, and the values of the coefficient of variation are lower than 0.5%. The average values of the properties measured regarding the tiny samples collected from the monument are generally within the narrow range of variation of 10% of each average value.

Figure 8 and Figure 9 show the PSDs of sandstones of varieties B, C and M obtained by MIP.

The PSD curves of sample M87 and monument samples Ig1 and Ig6 are similar.

The value of the distribution mode of samples B1, B7 and C4 is a radius of 54 μm (Figure 8) due to the measurement of only three values of radius (213, 54 and 36 μm). For higher values of injection pressure, corresponding to radius values lower than 10 μm, the variation in radius between measurements is about 1 μm or even lower, being about 0.5 nm for a radius value of 0.01 μm. So, the dimension of 54 μm does not represent more than 15% of the total volume of the pore space determined by MIP (Figure 9).

The percentage of micropore radii smaller than 7.5 μm [40] ranges between approximately 60% and 96%, and the median pore radius obtained at 50% of the total volume of mercury injected varies between about 0.1 μm in sample B7 and 5 μm in sample Ig1 (Figure 8 and Figure 9 and

Table 4. Physical parameters obtained by mercury intrusion porosimetry.

Samples	Porosity n (%)	Bulk Density (kg/m3)	Real Density (kg/m3)	Median of Pore Radius (µm)	Permeability (mD)
B1	5.8	2509	2665	0.31	56.8
B7	7.4	2472	2670	0.14	96.7
C4	12.4	2340	2671	0.84	2.8
C10	13.1	2333	2684	0.95	2.3
M87	17	2158	2591	3.57	30.1
Ig1 *	16.1	2139	2550	4.78	19.7
Ig6 *	16.2	2194	2616	3.20	24.6

* Ig1 and Ig6 are samples collected on south portal of monument.

). The value of the latter parameter is 96% in sample C10, reaching approximately 85% (samples B1, C4 and Ig6), more than 80% (samples B7 and Ig1) and around 80% (sample M87).

Table 4 shows the permeability values inferred by the Katz and Thompson method [32], ranging from around 2 to 100 mD. The higher values of permeability obtained on the B samples are due to the value of the distribution mode of the radius being 54 μm. The software used by the equipment to calculate permeability assumed the maximum hydraulic conductance for this pore radius value, overvaluing these permeabilities.

The results of the tests of absorption of water under low pressure (pipe method) obtained on prismatic specimens and on monument façades are shown in

Table 5. Values of coefficient of water absorption, k, obtained on all varieties of sandstones.

Variety	Samples (Prisms)	Water Absorption, k (kg/m2/√h)	Water Absorption, k (kg/m2/√h) Average ± SD (CV %)
A	AP38	0.7	0.9 ± 0.2 (21)
	AP39	0.7
	AP53	0.8
	AP96	0.7
	AP1	1.3
	AP5	1.1
	AP6	1
	AP9	0.9
	AP11	0.8
B	BP6	2.4	2.4 ± 0.3 (14.4)
	BP27	2.4
	BP32	3.2
	BP45	2.5
	BP72	2
	BP3	2.4
	BP13	2.4
	BP	2
C	CP18	7.6	6.2 ± 1.1 (17.5)
	CP24	7.4
	CP50	5.3
	CP40	5.3
	CP87	5.3
M	MP1	26.4	25.6 ± 3.4 (13.3)
	MP2	23.7
	MP3	22.8
	MP5	23.2
	MP6	31.8
C + M	T1	5.6	-
	T3	6.0	-
	T4	28.5	-
	T6	21.7	-

SD is standard deviation, and CV is coefficient of variation.

, i.e., the values of the coefficient of absorption of water, k.

The curves of capillarity water absorption are presented in Figure 10, and the corresponding values of the coefficient of water absorption are shown in

Table 6. Values of the coefficient Cc of capillarity water absorption obtained on sandstone varieties.

Variety	Samples	Cc (kg/m2/√h)	Average ± SD
			(CV %)
A	P1	0.4	0.4 ± 0.1 (24.5)
	P2	0.5
	P5	0.3
	P6	0.3
B	P3	0.6	0.6 ± 0.1 (9.2)
	P8	0.6
	P11	0.5
	P13	0.7
C	P4	2.5	2.1 ± 0.5 (25.0)
	P12	2.2
	P14	1.5
M	P1	5.7	5.9 ± 0.8 (13.6)
	P2	6.2
	P3	5.1
	P4	5.3
	P5	7.1

.

The potential correlation between surface wettability measurements and water absorption rates in historical building materials is also an important area of research contributing to the understanding of the physical behaviour of sandstone materials in monuments [41].

The drying behaviour of both sandstone lithotypes is shown in Figure 11 and Figure 12.

In Figure 11, the occurrence of a high retention of water content at the end of the tests, compared to the initial water content, is approximately 20% in the specimens of variety B and more than 1/3 in type A samples.

In Figure 12, the complete drying of sandstone variety M was achieved at around 550 h. In variety C, this time around, 10% of the initial water content remained, and drying was not completed after about 1100 h.

The curves of sandstone varieties A, B and C stabilized and would not benefit from longer tests (Figure 11 and Figure 12).

Although the results for the two lithotypes are not directly comparable, given the different conditions of the experimental procedures, it is evident that the values of the final retained water content show a decreasing trend from the A + B to the C + M lithotype.

The drying index (DI) is less affected by the experimental conditions and was measured following [33], which states that the characterization of drying is carried out by this index. In

Table 7. Values of drying index of lithotype A + B.

Variety	Samples (Prisms)	Drying Index			Drying Index Average ± SD (CV %)
		DI1	DI2	DIt	DI1	DI2	DIt
A	AP1	0.01	0.37	0.38	0.01 ± 0.00 (0.00)	0.36 ± 0.02 (5.56)	0.37 ± 0.02 (5.41)
	AP2	0.01	0.33	0.34
	AP5	0.01	0.37	0.38
	AP6	0.01	0.38	0.39
B	BP3	0.02	0.18	0.20	0.02 ± 0.00 (0.00)	0.18 ± 0.01 (5.56)	0.20 ± 0.01 (5.00)
	BP8	0.02	0.16	0.18
	BP11	0.02	0.18	0.20
	BP13	0.02	0.18	0.20

and

Table 8. Values of drying index of lithotype C + M.

Variety	Samples (Cubes)	Drying Index			Drying Index Average ± SD (CV %)
		DI1	DI2	DIt	DI1	DI2	DIt
C	C60.1	0.02	0.16	0.18	0.02 ± 0.00 (0.00)	0.18 * ± 0.07 * (38.89) * 0.15 ± 0.01 (6.67)	0.20 * ± 0.07 * (35.00) * 0.17 ± 0.01 (5.88)
	C85.2	0.02	0.13	0.15
	C79.1	0.02	0.14	0.16
	C78.1	0.02	0.16	0.18
	C47.2	0.02	0.16	0.18
	C87.2	0.02	0.33 *	0.35 *
M	M103	0.06	0.06	0.12	0.05 ± 0.01 (20.00)	0.05 ± 0.01 (20.00)	0.10 ± 0.01 (10.00)
	M104	0.05	0.05	0.10
	M105	0.05	0.05	0.10
	M106	0.06	0.05	0.11
	M107	0.05	0.04	0.09
	M108	0.05	0.04	0.09

* Higher values.

, the results of the drying index are presented. This parameter was calculated for all parts of the evaporation curves, considering two evaporation regimes. Thus, the total drying index (DIt) was decomposed into the index obtained in the constant flow regime (DI₁) and in the non-linear flow regime (DI₂).

The values of the drying index obtained on the specimens of the two lithotypes are also not comparable, given the differences in the final drying times, around 500 h in the A + B and 1100 h in the C + M lithotype samples. Longer drying times in the first lithotype were not allowed for the reasons explained above.

The values of the drying index shown in Table 7 and Table 8 generally exhibit acceptable deviations.

The mean values of the DI_t and DI₂ indices provided in Table 7 decrease by around half from the A to the B variety, while DI₁ doubles. In Table 8, a similar situation is shown in terms of DI_t from variety C to M. The mean value of DI₂ of variety M is one-third of the average value of DI₂ of type C, and the mean DI₁ value of variety M is more than twice the average DI₁ value of variety C. An important change in variety M is shown: the average values of DI₁ and DI₂ are equal, which means a significant increase in the contribution of the constant flow regime to the drying process.

The analysis of the results leads to the conclusion that the increment in the contribution of the constant flow regime in drying occurs with the increase in porosity of each lithotype, meaning easy drying.

While the evaporation kinetics of the constant flow regime are essentially based on external parameters, in the non-linear flow regime, they depend on the characteristics of the pore space.

The increment in values of retained water content in the vapour phase of drying (non-linear flow regime) is related to the lower dimensions of microporosity, with a wide distribution of more than 80% of the pore space of the samples investigated by MIP. As the pore space dimensions decrease, the adhesion forces between the water molecules and the pore walls increase, along with the tendency for small air bubbles to trap water droplets.

The coefficient of absorption by capillarity and drying index data are only shown because they allow a better characterization of monuments through similar samples that were tested.

3.3. The Mechanical Study of Both Lithotypes of Sandstones of the Lourinhã Formation

The mechanical behaviour was assessed by stress–strain curves obtained from compression tests on more than forty prismatic specimens of varieties A, B, C and M [34], and the physical behaviour was evaluated from porosity, PSD, water absorption and drying tests carried out on the samples investigated in this experimental work.

In the present study, the mechanical characterization of sandstones on the monument’s portal on the south façade was performed by DRMTs on the same blocks of varieties B, C and M on which water absorption under low pressure tests were done previously (Figure 2 and Figure 13 and Table 5). The use of the results of the latter physical tests guided the authors to perform the DRMT on adequate locations. The link between compression and DRMT results is due to the similar values of water absorption under low pressure shown by the monument blocks and sandstone specimens. In one block of the B variety, this link was achieved through a porosity value because it was the available result of a physical parameter. The methodology described limited the number of drilling tests to what was required, allowing the monument’s integrity to be respected. From the comparison between the DRMT results obtained on the monument blocks (Figure 14) and the stress–strain diagrams of the corresponding sandstone specimens collected in the vicinity of the monument, direct correlations between compression parameters and drilling strength are given in Section 4.

Drilling depths of up to 20 mm were deep enough to obtain strength values for an outer envelope with a weathering thickness of up to 9 mm on blocks of the south portal. Values of peak strength recorded at approximately 1 and 8 mm drilled lengths are due to higher-resistance grains.

4. Analytical Modelling of Stress–Strain Curves from DRMT Data

In the present study, a non-linear regression equation, Equation (2), was determined from the correlation between the compressive strength (σ_C) obtained on representative prismatic specimens of sandstones extracted in the vicinity of the monument and the drilling strength (σ_d) recorded on corresponding sandstone blocks of the south portal (Figure 15).

$${\mathsf{\sigma }}_{\mathrm{c}}=10.751{\mathrm{e}}^{1.161\mathsf{\sigma }\mathrm{d}}$$

(2)

The results of deformation at failure (ε_R) determined by compression tests carried out on sandstone specimens and σ_d results obtained on similar sandstone blocks of the south façade are shown in Figure 16.

Equation (3) correlates the deformation at failure (ε_R) and the drilling resistance (σ_d):

$${\mathsf{\epsilon }}_{\mathrm{R}}={\displaystyle \frac{8.186-0.571\mathsf{\sigma }\mathrm{d}}{1000}}$$

(3)

The coefficient of determination R² = 1.

However, no specimens with low-pressure water absorption coefficients of around 21.7 kg/m²/√h were obtained in order to compare compression and DRMT results, and it was not possible to correlate deformation at failure with the drilling strength value from the IgII test.

Equation (4) describes the compression behaviour of sandstones of the south portal through the compressive strength (σ_C), given by Equation (2), and the deformation at failure (ε_R), given by Equation (3).

The prediction of stress–strain curves for monument sandstones based on Equation (4) is dependent on the drilling strength (σ_d) obtained on the monument blocks of varieties B, C and M.

$$\mathsf{\sigma }=\left[-{\left({\displaystyle \frac{1000\mathsf{\epsilon }}{8.186-0.571\mathsf{\sigma }\mathrm{d}}}\right)}^3+1.47{\left({\displaystyle \frac{1000\mathsf{\epsilon }}{8.186-0.571\mathsf{\sigma }\mathrm{d}}}\right)}^2+0.5\left({\displaystyle \frac{1000\mathsf{\epsilon }}{8.186-0.571\mathsf{\sigma }\mathrm{d}}}\right)\right]\times 10.751{\mathrm{e}}^{1.161\mathsf{\sigma }\mathrm{d}}$$

(4)

Figure 17 presents experimental curves and predicted stress–strain curves generated through the use of Equation (4). The comparison between the former and latter diagrams of varieties of sandstones tested revealed that they are similar to each other.

Table 9. Comparison between predicted and experimental values of compressive strength and strain at failure obtained through drilling strength simulation.

Specimen/Test	AP11	BP3	Bpt(n = 6.3%)	CP24	T3	MP1	T4
k (kg/m2/√h)	0.8	2	2	7	6	26	28.5
σd (MPa)	2.25 *	-	1.9	-	1.2	-	0.5
σc (MPa)	136.2	95.0	-	45.7	-	18.7	-
σc pred DRMT (MPa)	146.5	-	97.6	-	43.3	-	19.2
εR	6.3 × 10−3	7.2 × 10−3	-	7.4 × 10−3	-	7.9 × 10−3	-
εR pred DRMT	6.9 × 10−3	-	7.1 × 10−3	-	7.5 × 10−3	-	7.9 × 10−3
∆σc pred − σc specimen (%)	7.6	2.7		5.3		2.7
∆εR pred − εR specimen (%)	9.5	1.4		1.4		0

* Predicted value.

shows a comparison between the predicted values of compressive strength (σ_{Cpred. DRMT}) and the strain at failure (ε_{Rpred. DRMT}) of sandstone blocks of the portal of the south façade and the corresponding experimental values for samples obtained near the monument (σ_{Csample i} and ε_{Rsample i}). The absolute differences (∆) between them are lower than 5%, aside from variety-A values, which are lower than 10%.

This analytical modelling allowed simulated stress–strain diagrams to be generated based on the drilling strength values obtained on sandstone samples. It was also possible to predict the drilling strength (σ_d) from the compressive strength and the strain at failure of the variety-A sample and generate the simulated stress–strain diagram based on drilling strength, even without the previous experimental results of the DRMT on this sandstone variety.

Figure 18 highlights the simulation of stress–strain behaviour of two sound blocks of sandstones of lithotype C + M and of the corresponding salt-weathered envelopes with a depth of up to 9 mm from the DRMT results. These weathered envelopes developed over a period of almost 800 years.

Over a period of around 800 years, the compressive strength decreased by approximately 20% for sandstone blocks of variety C and around 30% for sandstone blocks of variety M on the south façade of St. Leonard’s Church. These general rates of the compressive strength decrease are about 0.025% for the former and approx. 0.0375% per year for the latter blocks in the outer weathered envelope. Its thickness of up to 9 mm translates to a size increment of more than 10 µm per year. These data provide insight regarding the determination of a time range for the weathering of the outer envelopes of blocks of the south portal, reaching lower stable values of half the compressive strength that can ensure that they last for more than 130 to 200 years, assuming that similar environmental conditions occurred up to the current time.

However, future research will be carried out to contribute to a better understanding of the long-term effects of the simulated stress–strain diagrams on the durability of historical building materials.

Stress–strain diagrams allow the assessment of the stability of sandstone building blocks or rock mass blocks by following the evolution of salt-weathered envelopes. The methodology described in this work is essential to the study of the durability of blocks that support carvings, reliefs of cultural heritage and features of medium-scale geoheritage landforms, assuming that the time at which salt weathering began is known.

Adequate conservation works based on this innovative methodology for following the weathering of historical building materials and geoheritage rocks are essential to ensuring sustainable cultural tourism, which plays a key role in the sustainable development of such regions.

The methodology and findings of this study can be applied to other historical buildings or geoheritage sites facing similar durability issues, once a nearby non-heritage source similar to heritage stone materials is available to cut an adequate number of specimens with sizes that ensure the physical and mechanical validity of the test results. Laboratory facilities are required to carry out all tests used in this study, and authorized access to heritage sites should be given to perform the referenced NDTs and quasi NDTs.

5. Conclusions

The façades of Saint Leonard’s Church show important decorative reliefs and carvings. The building blocks that support these Middle Ages’ artistic testimonies are arkose sandstones with carbonate cement from the Lourinhã Formation. A broad characterization was carried out, comprising studies on rock composition, physics and mechanics, which allowed a better understanding of the physical and mechanical behaviour of these stone materials in order to obtain a match between the building blocks of this monument and the specimens extracted from masonry walls close to it.

A methodology was used to generate simulated stress–strain diagrams of the building blocks of this church based on compression tests carried out on similar building stones collected in its vicinity and DRMTs performed on the actual blocks of this monument. These predicted stress–strain curves have good agreement with the experimental diagrams obtained.

An assessment of the structural stability based on the stress–strain curves of the sound stone and weathered envelope of these building blocks allows researchers to monitor the mechanical behaviour of both and to gain knowledge about their durability to ensure the long-lasting existence of relevant art elements shown, ensuring the development of sustainable cultural tourism.

Further research avenues will come from data obtained on other historical buildings or geoheritage sites with the use of this innovative methodology in order to extend its application and to increase the knowledge about structural stability related to durability issues.