Predicting the Mechanical Strength of Caliche Using Nanoindentation to Preserve an Archaeological Site

Abstract

During the processes of excavation, restoration, and conservation of archaeological sites, it is common practice to perform physical and chemical characterization of the site materials. This is carried out to determine the best methods and materials for conserving and preserving the site. For this reason, techniques such as infrared spectroscopy and elemental analysis by X-ray fluorescence (XRF) are primarily used for chemical characterization, while mechanical tests such as the uniaxial compression test and hardness tests are used for physical and mechanical characterization. However, a common limitation is obtaining samples for destructive physical tests, such as compression tests, due to their invaluable cultural value. To address this problem, this work proposes the mechanical characterization of the material through nanoindentation. This technique requires a smaller sample size and can be performed in a timely manner by observing the resistance of each mineralogical phase present in the material. Thus, a preliminary predictive model of mechanical resistance is proposed based on the composition observed in the samples from the archaeological site of Cerro de los Remedios, located in the municipality of Comonfort, Guanajuato, Mexico. The samples were characterized using infrared spectroscopy, XRF, XRD, and SEM-EDS. The results indicate that the stone (caliche) is formed from 95.6–93% micrite calcite; 2.51–0.42% aluminosilicate; 3.14–1.89% high-calcium aluminosilicate; and 3.43–2.39 quartz or amorphous SiO₂. The proposed correlation models were adjusted to a linear function, a second-order polynomial, and a logarithmic function. In the M2–linear model, the non-linear effects generated by variables such as texture, porosity, phase adhesion, cement type, and cracks or discontinuities were not considered. In this model the best prediction of the experimental data was obtained within a variation of ±15%.

1. Introduction

The conservation and preservation of archaeological and cultural sites require multidisciplinary knowledge, including history, culture, and technical aspects such as chemical composition, physical properties (density, mechanical strength, adsorption capacity, water permeability, etc.), as well as environmental factors that cause deterioration [1,2].

Therefore, it is crucial to determine the composition and mechanical resistance of materials to be preserved. This information is necessary to select the appropriate treatment and environmental conditions for conservation. For instance, if the material is susceptible to degradation due to humidity, water-repellent treatments may be chosen [3]. Alternatively, if the construction material is deteriorated and compromises the function of the monument, replacement may be necessary. In such cases, materials with similar composition and physical properties to the original are selected.

Currently, in the state of Guanajuato, Mexico, various pre-Hispanic settlements have been discovered in the Chumacuero valley area of the Laja Bajío. One of these sites is the ‘Cerro de los Remedios’ located in Comonfort, Gto. It is currently undergoing excavation, study, and conservation processes [4]; the determination of the chemical, physical, and mechanical properties of the different materials used during its building is very important for the selection of the best conservation method.

During the Epiclassic period, Cerro de los Remedios served as a civic ceremonial center in the ancient valley of Chamacuero in the Laja Bajío. The site is in the Dos Cerros, a mountainous massif that dominates the valley visually. It is situated at the beginning of the Bajío region of Comonfort, Guanajuato, Mexico. This site belongs to the Laja tradition in the archaeology of Guanajuato [4,5]. The site comprises four architectural ensembles, each with at least two structures. A large public square is located at the center of the settlement, with each architectural complex situated at the corners of the square. To the north of the settlement, a series of stepped terraces leads up to the rocks at the top of the hill. These complexes consist of rectangular platforms, pyramidal bases, sunken courtyards, enclosed courtyards, and stepped platforms. Currently, structures 1 and 2 of architectural complex A are being explored and restored [5].

The architectural complex was built with basaltic stone, using small decorative slabs of a carbonate rock “caliche”, which is present among the coating elements of the foundations and constructive bodies, as well as in various uses, such as floors, cobblestones, and constructive cores [4]. Caliche is a sedimentary rock with delicate conditions for its conservation; it is mainly composed of calcium carbonate of around 93–96% weight as micrite calcite phases, and other mineralogical phases, such as amorphous silica, quartz, and aluminosilicates, have been identified; on the other hand, this constructive material presents mechanical uniaxial compressive stress between 8 and 33 MPa, according to a previous report by Ahedo-Díaz and collaborators [5].

One important aspect of the archaeological site of Cerro de los Remedios in Comonfort is the presence of ‘Caliche’, a non-endemic rock. Geologically, there are no settlements of this type of material, and there is a scarce amount of stone with composition, physical properties, and mechanical resistance like those of the archaeological site. This has hindered the conservation and restoration works of the site. Therefore, we opted for characterization techniques that require minimal sample usage, such as nanoindentation, to verify the material’s mechanical properties.

Nanoindentation (NIIT) is a technique used to determine the mechanical properties of materials on a micron scale [6,7]. The technique of nanoindentation (NIIT) is like that of hardness testing, but instead of measuring the deformation produced by an applied load, it involves a continuous recording of the indenter displacement (depth) and the applied load. This produces load–displacement (P-h) curves that allow the determination of material properties such as hardness, Young’s modulus, and maximum strength [7,8,9,10,11,12].

Zhaoyang et al. employed NIIT to investigate the mechanical properties of various rocks, including limestone, marble, sandstone, and claystone. This study revealed numerous advantages over conventional methods, such as minimal material requirements. However, it is important to note that certain disadvantages must be considered. For instance, external environmental factors can influence the mechanical properties of these materials [13]. Additionally, NIIT has been utilized for the characterization of carbonate rock, in which a micromechanical heterogeneity is observed. Consequently, the indentation can be made on the identified phase [14].

Therefore, this study aims to develop a preliminary predictive model for the mechanical properties of caliche based on its mineralogical composition, using nanoindentation as a non-destructive characterization method. For this purpose, previous studies [5] performed chemical and mineralogical characterization of the material using XRD, X-ray fluorescence spectroscopy (XRF), and petrographic analysis. The analysis was validated using uniaxial compression tests.

2. Materials and Methods

2.1. Caliche Samples

The caliche samples were collected around the sunken patio (CZA-1 and CZA-4), as indicated in Figure 1a; this material corresponds to the original caliche in the archeological zone. Additionally, caliche slab samples found on the surface close to the archaeological site (CZA-5) were collected as a possible restoration material for the Cerro de los Remedios (Figure 1b).

2.2. Chemical Characterization of Caliche

All caliche samples (sunken patio and caliche slab) were analyzed using ATR-IR spectroscopy with a TA Nicolet-iS-10 instrument (Thermo Fisher Scientific, Waltham, MA, USA). The measuring range was 4000–600 cm⁻¹, with an average of 32 scans and a resolution of 4 cm⁻¹. Additionally, mineralogical characterization was performed using powder X-ray diffraction (XRD) on a Rigaku Miniflex 600 diffractometer (Rigaku, Akishima, Japan) equipped with a Cu tube X-ray and kα radiation.

The mineralogical phases were observed through petrographic analysis using an Olympus BX41 petrographic microscope (Microscope Central, Willow Grove, PA, USA). For this study, the samples were cut into thin sections with a circular rock cutter and mounted on glass slides with epoxy resin. The samples were then ground and polished with carbide grit to a thickness of 0.3 mm. The caliche texture and minerals were characterized by microscopic analysis using both plane and cross-polarized light.

X-ray fluorescence spectroscopy (XRF) was used to perform elemental and oxide analyses of caliche samples with a Rigaku NEX CG (Rigaku, Akishima, Japan). Finally, the texture and morphology of the caliche samples and the caliche bench were observed using a JEOL JSM-6010 PLUS/LA SEM-EDS (JEOL Ltd., Akishima, Japan) scanning electron microscope at 15 kV and low vacuum.

2.3. Mechanical Characterization of Caliche

Nanoindentation (NIIT) is a technique used to determine the mechanical properties of materials on a micron scale [6,7]. The technique of nanoindentation (NIIT) is like that of hardness testing, but instead of measuring the deformation produced by an applied load, it involves a continuous recording of the indenter displacement (depth) and the applied load. This produces load–displacement (P-h) curves that allow the determination of material properties such as hardness, Young’s modulus, and maximum strength [7,8,9,10,11]. This method assumes that the indenter is subjected to a force P and moves into the material to a depth h until it reaches a maximum value of h_c. After the load is removed, the indenter moves to a depth due to elastic recovery [10]. The value of h_c is calculated by Equation (1), where ε is a constant that depends on the geometry of the indenter. For the Berkovich or spherical tip case, ε is 0.75, and for the conical tips, it has a value of 0.72. On the other hand, variable S represents the material stiffness, as determined by Equation (2) [12].

$$h_c=h_{max}-\epsilon {\displaystyle \frac{P_{max}}{S}}$$

(1)

$$S={\left({\displaystyle \frac{dP}{dh}}\right)}_{h=h_{max}}$$

(2)

Material hardness (H) is defined as the average pressure that the material withstands during loading. Equation (3) is used to determine this property, where A(h_c) represents the projected contact area at maximum load. The area is determined by a polynomial function (Equation (4)), where C_i are constants of each material and are determined experimentally [11].

$$H={\displaystyle \frac{P_{max}}{A\left(h_c\right)}}$$

(3)

$$\left(h\right)={\sum }_{i=0}^8{C}_{i-1}{h}^{2^{1-i}}=C_0{h}^2+C_{1}h+C_2{h}^{1/2}+\cdots +C_8{h}^{{\displaystyle \frac{1}{128}}}$$

(4)

The NIIT test also determines another property, the effective modulus E_eff, which is dependent on the material stiffness (S), as shown in Equation (5). The constant β is related to the indenter geometry. The effective modulus of elasticity (E_eff) differs from Young’s modulus (E) because the NIIT test involves elastoplastic behavior, where both elastic and plastic behavior coexist. The applied load P generates plastic deformation during indentation. In contrast, Young’s modulus (E) considers only the material’s elastic behavior. Equation (6) can be used to determine the value of E by knowing the E_eff of the material. The Young’s modulus and Poisson’s ratio for the indenter are represented by E_i and ν_i, respectively, while E and ν correspond to the test material [6].

$$E_{eff}={\displaystyle \frac{1}{\beta }}{\displaystyle \frac{\sqrt{\pi }}{2}}{\displaystyle \frac{S}{\sqrt{A\left(h_c\right)}}}$$

(5)

$$E_{eff}={\displaystyle \frac{1-{\nu }^2}{E}}+{\displaystyle \frac{1-{\nu }_i^2}{E_i}}$$

(6)

The purpose of the NIIT was to analyze the mechanical strength of each mineral phase present in the caliche by determining the microhardness of the material. Two thin films corresponding to each sample (sunken patio caliche and caliche slab) were tested using a CSM instrument TTX-NHT (CSM Instrument, Peseux, Switzerland) with a Vickers indenter. The maximum linear applied load was 10 mN at a loading rate of 20 mN/min with a 10 s pause. Finally, the mechanical strength of the caliche was measured by conducting uniaxial compression tests on a 3 × 3 × 3 cm sample of sunken patio caliche and caliche slab. The tests were performed in duplicate, using a Shimadzum-II Autograph AG-X-300KN (Shimadzu Corporation, Tokyo, Japan) at a test rate of 5 mm/min.

3. Results

3.1. Caliche from Archaeological Zone: Chemical and Geochemical Characterization

Figure 2 shows the infrared spectrum of the caliche samples obtained from the archaeological site. The CZA-4 caliche showed the highest moisture adsorption, while the slab collected around the archaeological site showed low moisture adsorption. All samples contained physisorbed water, which was identified at 3600 cm⁻¹ and 1600 cm⁻¹. Additionally, the intensity band at 2900 cm⁻¹ indicated that the organic matter (–CH₃) was negligible. The material signals show the presence of calcite (1422 cm⁻¹, 873 cm⁻¹, and 707 cm⁻¹) and a medium-intensity broad band at 1028 cm⁻¹ (Si–O–Si), which is attributed to the presence of silica or silicates such as amorphous silica, silicates, aluminosilicates, quartz, and various types of clays. The amount of silicate fragments varied among the samples, with CZA-4 having a higher amount and CZA-3 having a lower amount [15,16].

Figure 3a shows the XRD patterns for CZA-2 (caliche with low silicate content), CZA-5 (moderate silicate content), and CZA-4 (high silicate content). This characterizes the calcareous material with different possible silicate/calcite compositions present in the archaeological site, including the materials for restoration (CZA-5). Based on these results, the main mineralogical phases identified were calcite, quartz, and a small amount of amorphous silica, as confirmed by petrographic analysis (see Figure 3b). Micrite, ferromagnesian minerals, and banded texture were also observed. X-ray fluorescence spectroscopy was used to quantify the elements and oxides (see Figure 3c), revealing varying percentages of calcite in the caliche sample, ranging from 93 to 96% by weight.

Table 1. Mineralogical balance for caliche archaeological zone [5].

Minerals	Weight %
	CZA-2	CZA-4	CZA-5
Micritic calcite (CaCO3)	95.6	94	93.0
Alkqali feldspar; Plagioclase ((NaCa)SiAl3O8 and biotite (K(Mg,Fe)3AlSi3O10(OHF)2)	2.51	0.42	0.42
High-calcium aluminosilicates	1.89	3.19	3.14
Quartz/SiO2—amorphous	––	2.39	3.43

shows the mineralogical balance based on completed analyses (XRD, XRF, and petrographic analysis). The presence of calcium carbonate is observed as a micritic calcite phase, while silicate materials are common as aluminosilicate, calcium-aluminosilicate, quartz, or amorphous silica. This result has been previously reported [5].

3.2. Caliche NIIT Mechanical Characterization

Nanoindentation (NIIT) is a method for the mechanical characterization of materials that provides point-by-point information about their mechanical properties. In cases where the material has a uniform composition, the load–displacement curves (P-h) measured at different positions show similar behavior. However, when the composition is heterogeneous, the displacement of the curves may vary. Figure 4 shows that the analyzed samples have heterogeneous behavior based on the recorded displacement values for maximum load (h_max) and the load reached after release (h_f). Elastic recovery (%ε) can be calculated using Equation (7), which identifies three groups with different elastic recovery capacities: 3.52%, 10–16%, and recoveries greater than 20%, as presented in

Table 2. Displacements recorded by NIIT for the caliches of the archaeological zone.

		Maximum Displacement, hmax (nm)	Displacement After Unloading, hf (nm)	% Elastic Recovery
CZA-2	Group 1	1813.59 ± 356.58	1588.58 ± 331.71	12.44 ± 3.72
	Group 2	3145.23 ± 461.46	2826.07 ± 413.15	10.09 ± 2.59
	Group 3	6272.32 ± 250	6049.11 ± 174.11	3.52 ± 1.07
CZA-4	Group 1	943.39 ± 206.57	761.71 ± 212.55	20.16 ± 4.6
	Group 2	1841.44 ± 145.55	1605.59 ± 154.39	12.88 ± 2.98
	Group 3	2732.36 ± 409.21	2331.06 ± 368.36	14.74 ± 2.84
CZA-5	Group 1	1155.77 ± 415.96	989.58 ± 410.025	16.01 ± 6.45
	Group 2	1533.32 ± 210.53	1145.23 ± 153.29	24.906 ± 8.42
	Group 3	3232.24 ± 4.25	2784.48 ± 9.34	13.96 ± 0.401

.

$$\left({\displaystyle \frac{h_{max}-h_f}{h_{maz}}}\right)\times 100$$

(7)

The mineralogical phases identified by chemical and mineralogical analysis (calcite and micrite, quartz, and aluminosilicates) were associated with the different mechanical strengths observed by NIIT (see

Table 3. Mechanical properties calculated by NIIT for caliche samples from the archaeological site and their assignment to a mineralogical phase.

		Maximum Resistance O&P *, σ (MPa)	Young’s Modulus, E (GPa)	Vickers Hardness (HV)	Associated Material
CZA-2	Group 1	148.47 ± 57.52	8.28 ± 1.52	13.75 ± 5.33	Aluminosilicates
	Group 2	48.93 ± 6.88	3.76 ± 0.94	4.53 ± 1.04	Feldspars
	Group 3	9.80 ± 0.30	1.40 ± 0.06	0.908 ± 0.03	Calcite; Micrite
CZA-4	Group 1	312.30 ± 117	20.30 ± 3.6	28.9 ± 10.8	Quartz/Silica
	Group 2	125.56 ± 21.18	10.41 ± 1.93	11.63 ± 1.96	Aluminosilicates
	Group 3	325.07±	1.07 ± 7.41	34.08 ± 1.26	Quartz/Silica
CZA-5	Group 1	368 ± 13.61	17.38 ± 5.6	30.10 ± 6.97	Quartz/Silica
	Group 2	209.97 ± 6.24	12.14 ± 0.39	19.45 ± 0.58	Quartz/Silica
	Group 3	122.57 ± 15.47	36.22 ± 2.92	113.51 ± 14.24	Aluminosilicates

* The value is 325.07 ± 15.16.

). This association was based on the mechanical strength reported by Kilic in 2008 [17,18] for different rocks. The strength of quartzite, a metamorphic rock rich in quartz, was reported to be 210 MPa. Calcites have a strength between 112 and 163 MPa, tuffs have a strength between 6 and 37 MPa, and andesite has a strength of 56 MPa. Studies on the mechanical properties of soils treated with calcium carbonate have found low compressive strengths ranging from 0.66 to 1.2 MPa [19,20,21].

The correlation between chemical composition and mechanical strength was analyzed under two conditions: M1 and M2. In M1 (Equation (8)), the mechanical strength is calculated as the sum of the mechanical strength of each phase (σ_i) multiplied by its fraction or content in the sample (x_i). In condition M2 (Equation (9)), the material strength was determined by the mechanical strength of the carbonate (majority component) and the component with the highest mechanical strength (SiO₂–quartz; σ_q) where the non-linear effects generated by variables such as texture, porosity, phase adhesion, cement type, and cracks or discontinuities were not considered.

$$\sigma ={\sum }_{i=1}^n{x}_i{\sigma }_i$$

(8)

$$\sigma =x_{CaC{O}_3}{\sigma }_{CaC{O}_3}+\left(1-x_{CaC{O}_3}\right){\sigma }_q$$

(9)

The models proposed were validated using experimental data from uniaxial compression tests (see Figure 5a). As shown in Figure 5b, the mechanical resistance measured for uniaxial compression is presented, according to the content of micrite calcite, which was quantified for chemical and mineralogical analysis. A minor carbonated material with greater resistance was observed.

Table 4. Correlation between mechanical strength and carbonate content in caliche samples.

	Equation	R2
M1–linear	y = −367.33x + 364.26	0.996
M1–polynomial	y = −3504.1x2 + 6242.7x − 2752.6	1
M1–logarithmic	y = −346.3 ln(x) − 2.477	0.995
M2–linear	y = −718.61x + 693.22	0.952
M2–polynomial	y = −23,447x2 + 43,511x − 20,163	1
M2–logarithmic	y = −677.2lnx − 24.216	0.951

shows the models obtained using the M2 value for each. The predicted mechanical strength for the material is represented by y, while the CaCO₃ content in the caliche sample is represented by x. Figure 6 shows the predicted mechanical strength of caliche as a function of the carbonate content in the sample. The experimental data of caliche strength obtained by uniaxial compression test was compared with these values. A better fit was observed for the linear function that calculates the strength according to M2. This function considers the strength of the two materials that contribute to this property, the one with the higher percentage and the stronger phase. While M1 considers the contribution of all components, it does not consider their distribution, resulting in a poorer fit to the experimental data.

Figure 7 compares the measured and predicted data for the two models, highlighting the measured mechanical strength in comparison to that predicted by the proposed model correlations. The results are in good agreement, with an error band of ±15% for the M2 models (linear, polynomial, and logarithmic). While M1 considers the contribution of all components, it cannot account for their distribution, resulting in a poorer fit to the experimental data due to factors such as phase distribution and orientation. This is because the stones exhibit anisotropic behavior.

4. Conclusions

This paper proposes the use of the NIIT test to develop a predictive model for the mechanical properties of materials found in archaeological and cultural sites, taking into consideration their mineralogical composition. The advantage of this method is that it is less invasive than current alternatives. Therefore, the following conclusions can be drawn:

Nanoindentation is a mechanical test that allows the determination of the mechanical behavior of materials, such as caliche, while reducing the amount of sample required for testing in comparison to compression testing. It is an alternative method for characterizing materials with limited sources, such as the material under study.

The model developed correlates the compressive strength with the material composition, considering only the two main phases in the material. The M2 model was found to provide a better fit to the experimental data within ±15%. To improve the model’s behavior prediction, it is necessary to include each component of the rock and a factor that relates to its distribution and sedimentation type and others.

The model enabled a comparison of the mechanical behavior of sample CZA-5 (slab caliche) with samples from the archaeological site, achieving a more precise characterization of the material. This characterization allowed the selection of the material as restoration material for the archaeological site.