Life Cycle Cost Analysis and Deterioration Patterns of Limestone Paving

Abstract

Stone is a durable and high-performance paving material in standard and in intensive service regimes. Stone is thus a preferable material for sidewalk and promenade paving under intensive service regimes, such as touristic promenades and historic sites. Recent studies on the weathering and degradation of stones in buildings have revealed differing analytical approaches among geologists, geo-engineers, and civil engineers. The present research aims to develop a structured analytical–empirical methodology for the assessment of stone pedestrian pavements’ life cycle and life cycle costs. This study presents an integrated methodology that combines diagnostic field surveys, core laboratory tests, and the characterization of deterioration patterns. This approach allows for evaluating how faulty construction methods impact the durability and degradation of natural stone pedestrian pavements. It also assesses their effect on the pavement’s life cycle and associated costs. The diagnostic field survey concentrates on specific construction details, including: (a) Cracks in the paving stones. (b) Peeling of stone layers. (c) Subsidence and cracking at the paving edges. (d) Cracking of filler materials in joints between stone slabs. The laboratory tests focus on five core physical properties for the stone deterioration: (1) apparent density, (2) Water absorption, (3) Compressive strength, (4) Flexural strength, and (5) Abrasion resistance. This study proposes linear and exponential patterns for deterioration. A case study carried out on a Capernaum promenade revealed excessive deterioration patterns caused by the poor core properties of the paving stone and defective construction. The consequences of excessive deterioration on life cycle costs result in additional expenses of 73%, indicating a reduction in the life cycle. The novelty of this research lies in developing and delivering an integrated methodology that enables the assessment of how defective construction methods impact the durability, deterioration, life cycle, and life cycle costs of natural stone pedestrian pavements.

1. Introduction and State of the Art

Natural stone has been used in construction for centuries due to its durability and aesthetic appeal. However, modern practices utilizing thin stone slabs for cladding, flooring, and paving have sometimes led to premature deterioration [1,2,3]. The rate and extent of deterioration depend on various factors, including the stone’s geological origin, mineralogical composition, physical and chemical microstructure, and the environmental conditions to which it is exposed [4,5,6,7].

Different disciplines, such as architecture, geology, materials science, and civil engineering, often define and analyze weathering processes differently [2,8,9,10,11,12,13,14,15,16,17]. The recent studies have highlighted the contrasting analytical approaches between geologists and geo-engineers on the one hand and civil engineers on the other hand [18,19,20]. While geologists focus more on microstructural changes, civil engineers emphasize the impact on mechanical and physical properties. However, the holistic analysis of component performance within the overall structure is often lacking.

Despite the importance of natural stone paving in urban design, such as in tourist areas, public spaces, and historic sites, research specifically focused on this application is limited [21]. Developing diagnostic and analytical tools is crucial for the design and life cycle planning of modern stone paving. The recent studies have examined topics such as the structural design of cube stone pavements using advanced modelling [22], the life cycle benefits of incorporating stone waste in cement materials [23], and the use of hyperspectral imaging to assess pavements’ condition [24]. In [25] was investigated the impact of the hot and wet Eastern Mediterranean climate on the weathering of natural local sedimentary stones implemented in contact with cement mortars and concrete. The integration of weathering research with Life Cycle Prediction and life cycle costing (LCC) methodologies has also been discussed [26]. However, the holistic analysis of the components’ performance within the overall structure is often missing.

The reasoning and analysis of infrastructure systems is a meticulous topic. Pattern analyses for deriving the root causes of infrastructure failures, including design, the construction methods, execution, and external factors, which include unforeseen events or accidents was developed in [27]. The framework was validated on highway pavement construction. Research on pavement performance and the reliability domain indicates the need for performance and failure mechanisms criteria and life cycle assessment modeling [28,29].

Previous research into the critical success factors in pavement projects indicates the need for performance and life cycle assessment approaches for pavement materials [29]. Some researchers stressed the need for further research to quantify the environmental performance of construction materials and the methods used on sidewalk pavements to elucidate the most environmental pavement alternative and design guidelines by optimizing alternative materials and methods to improve the sidewalk performance [22]. In [30] was developed a stochastic framework for the assessment of pavement performance, emphasizing the pavement structure, the material, the traffic load, and the weather conditions. This model indicates the need for tools for the prediction of pavement performance under failure conditions. In [31] was emphasized the need for life expectancy estimates of pavement alternatives. This state-of-the-art review elucidates the gap in pavement materials’ service life expectancy models and life cycle cost modeling and designs guidelines for sidewalk pavements.

2. Standard Requirements for Pedestrian Design—Review

The structural design requirements for natural stone pedestrian pavements are outlined in [32]. The specific mechanical, physical, petro-physical, and durability requirements for natural stone paving slabs are detailed in [33]. Various national and international standards describe the test methods used to evaluate stone properties [34,35,36,37,38,39,40,41,42,43,44,45].

The fundamental properties that influence the performance of stone pavements include apparent density, water absorption, compressive strength, flexural strength, and abrasion resistance [1,19,46,47,48,49]. While the European and American standards do not prescribe limits for these properties, the Israeli regulations are more prescriptive. However, the Israeli requirements need to be validated against long-term durability data [50,51]. Combining accelerated testing with reference service life data can provide a reliable basis for service life prediction and planning [52,53]. The typical values of limestone properties are summarized in

Table 1. Typical values of properties of limestone and standards requirements for building stones’ properties.

Property	Typical Values for Limestone [1,48]	Requirements for Building Stones [50,51]
Bulk density × [103 kg/m3]	1.9–2.65	Sample > 2.46; Average > 2.6
Total water absorption [mass %]	<1%–~20%	<1.5%
Water absorption coefficient [kg/(m2·hour1/2)]	n/a	<0.5
Compressive strength [MPa]	20–100	Sample > 56; Average > 60
Flexural strength [MPa]	5–25	>5
Abrasion characteristic [mm]	Capon (Wide Wheel) abrasion resistance: For intensive environment < 23	Amsler abrasion wear: For public places—Sample < 2.3; Average < 2.0

.

3. Aims of the Current Research

The primary objective of this research is to develop a structured analytical–empirical methodology for assessing the durability, deterioration patterns, and life cycle costs of natural stone pedestrian pavements under both standard and intensive service conditions. This study aims to provide tools for evaluating the impact of inadequate construction practices on the service life and life cycle costs of stone pedestrian pavements.

The research methodology encompasses six primary phases: (1) a state-of-the-art review, (2) a diagnostic field survey, (3) core laboratory tests, (4) the diagnosis of defects, (5) the characterization of deterioration patterns, and (6) life cycle cost assessments. Figure 1 depicts a graphical abstract of the methodology. The methodology proposes core criteria for the field survey, five laboratory tests, the development of deterioration patterns of stone pavement under failure conditions, and life cycle costs models derived from the deterioration patterns.

The novelty of this research lies in developing an integrated methodology that uniquely combines the following:

• Diagnostic field surveys;
• Core laboratory tests;
• The characterization of deterioration patterns;
• Life cycle cost (LCC) analysis.

This approach bridges material science, engineering practice, and economic assessment for natural stone pavements. It comprehensively evaluates how defective construction methods impact durability, deterioration, service life, and costs. By providing a reproducible framework that translates material properties and field observations into practical economic implications, this research advances sustainable infrastructure development, particularly for pavements under intensive service regimes.

4. Materials and Methods

This study was based on integrating the results obtained from experimental research on regression models developed for the prediction of deterioration patterns and the life cycle cost analysis of natural stone paving exposed to different decay and weathering agents.

(a) The one-year-long in-use exposure of limestone paving slabs in a pedestrian promenade built near Capernaum, the Sea of Galilee, Israel. These limestone slabs were imported from Jordan (an arid and hot climate) and exposed to service in Israel’s hot and wet climate. (For more information about the environmental conditions near the Sea of Galilee, see [54,55]. The selected limestone had no proven performance record or established service life in a hot and wet climate. The promenade designers chose Jordanian limestone based exclusively on aesthetic and architectural criteria. The contractor declared the compressive and flexural strength of the stone prior to the execution of paving works and found it met the standard requirements for building stones, see Table 1, and the maximal load scheme calculations. However, stone defects (decay) and failure (cracks) were observed in the promenade only one year after the implementation of Jordan limestone slabs; see Figure 2. This research adopted the definitions of “defect”, “failure”, and “defective performance”, which are recommended by [52,56]. The ratio of stones with defective performances (measured by the number of defective slabs) in the promenade was 15%. The chemical, physical, and engineering properties of the new (unaged) stones and one-year-long in-use aged stones were tested to reveal the causes and trends of stone deterioration upon the effect of particular environmental and service conditions.

(b) The accelerated short-term ageing of Jordan limestone and the reference limestone of proved long-term in-use service life was carried out by exposure to cycles of wetting/drying and UV radiation for 1000 h (QUV test [36]). The conditions during the QUV test were chosen under the natural regimes of rain cycles and the intensity of UV (ultra-violet) radiation in the area of the Sea of Galilee (Lake Kinneret), Israel [57]. This experimental stage was conducted to reveal the degradation trends of Jordan limestone under the effect of agents, characterizing the service conditions of external stone paving. The chemical, physical, and mechanical properties of the new and in-lab aged stones were tested, and the trends of deterioration of the stone exposed to ageing agent were revealed.

(c) The comparison between the performance characteristics of the paving limestones tested after one-year-long in-use exposure and accelerated short-term ageing (Performance characteristic: the physical quantity that is related to the critical property [52]. This stage reveals if accelerated short-term ageing exposure is reliable for the performance evaluation of external paving stones used in hot and wet climates.

(d) The rate of Jordan limestone degradation upon the effect of different ageing agents was estimated compared to that of the reference limestone. This estimated result was then used for the mathematical regression models.

Figure 2. Paving limestones from Jordan. (High-resolution pictures can be seen in Appendix A of this paper).

Figure 2. Paving limestones from Jordan. (High-resolution pictures can be seen in Appendix A of this paper).

4.1. Field Survey

The contractor conducted regulatory tests of the stone’s mechanical properties (compressive and flexural strength and module of elasticity) and the stone’s bulk density prior to construction. These properties fully complied with the standard requirements [51]. However, the performance of the pedestrian promenade was defective and failed, as is shown earlier in Figure 2c,d.

A preliminary inspection was conducted along the Capernaum promenade (as shown in Figure 2b). During this initial visit, damage and wear to the promenade’s path were assessed since its handover. The identified damage included the following:

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Cracks in the paving stones (as shown in Figure 2d).

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The peeling of stone layers in some paving stones (as shown in Figure 2c).

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Subsidence and cracking at the edges of paving between limestone and basalt stones (as shown in Figure 2e).

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The cracking of filler materials in joints separating the stone slabs (as shown in Figure 2f,g).

A second visit took place one month after the first visit, during which samples of the paving stones were taken for testing.

The promenade, situated along the western road encircling the Sea of Galilee and to its east, is located in a sloping area. Therefore, a retaining wall varying in height between 1.20 and 2.50 m was designed on its eastern side. In some topographic regions, a retaining wall was also required on the western side of the promenade. The promenade is paved with hard limestone slabs, 4 cm thick, 30 cm wide, and of varying lengths. The edges of the paved path are lined with two strips of basalt stone (as shown in Figure 2b). The retaining wall is based on a foundation compacted with 94% AASHTO Mode A [58], topped with a Type A bedding layer compacted with 98% AASHTO Mode A [58]. The paving stones are laid on a 30 cm thick Type A bedding layer, compacted with 98% AASHTO Mode A [58].

The cross-section of the promenade includes a foundation compacted to 94% and an AASHTO Mode A [58], bedding layer compacted to 98%. The requirements for the AASHTO Mode A [58], bedding layer, according to the technical specifications, are as follows:

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Sieve #200 (upper limit)—within the range of 5–15%.

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Sand equivalent test—at least 27%.

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Atterberg limits [59]—maximum liquid limit of 25%, and a maximum plasticity index of 6%.

These specifications ensure the structural integrity and durability of the pavement, catering to the necessary engineering standards for such constructions.

Material testing for the pavement construction was conducted during construction. The test findings indicated that in most cases, the material met the requirements; for example, the compressive and flexural strength of paving limestone was tested during construction, and the strength results met the standard requirements. However, some tests revealed material properties that did not comply with the Type A (AASHTO Mode A [58]) bedding material specifications. For example, some tests during construction indicated that the material in the first layer of the beginning sections was suitable as Type B bedding [58]. This discrepancy could contribute to the observed sinkages in various locations. Despite the tests showing the non-compliance of the foundation and bedding materials with the stone slab paving requirements, these discrepancies were not recorded in the project’s work logs and were not resolved and addressed by the contractor on time.

4.2. Lab Experiments

In the present research, the following stones were laboratory tested:

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Reference paving hard limestone (RPHL)—Ramon Grey Limestone from Mitzpe Ramon, Negev Desert of southern Israel (https://www.stonecontact.com/ramon-grey-limestone/s7784, accessed on 30 October 2024).

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New (unweathered) paving limestone from Jordan (NUPL).

-

Used (one-year in-use weathered) paving limestone from Jordan (UWPL).

The experiments included tests of the stones’ chemical composition, the main physical properties used to characterize their pore structure, and the abrasion behavior of the stones used to estimate the performance properties of the pedestrian zone under discussion.

Chemical Composition:

-

The laser ablation ICP-MS method determined the chemical impurities’ content in the unaged RPHL and NUPL [60]. The chemical impurities in limestone (the minerals containing chemical compounds of aluminum (Al), magnesium (Mg), iron (Fe), manganese (Mn), and halite and sulfate salts) are the leading cause of color changes in limestone and may even cause the crumbling of limestone subjected to the impact of environmental agents [61].

Physical Properties:

The following physical properties were tested:

1.

Density and total water absorption;

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Tested following ASTM C97 [62].

2.

Surface water absorption;

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Checked according to the procedure described in [45].

3.

Water evaporation capacity;

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Tested according to the procedure described in [61].

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According to this procedure, the stones previously subjected to the surface water absorption test were then exposed to the lab environment (21 ± 3 °C/55% RH), and their weight loss was monitored during the next seven days.

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Water evaporation capacity was calculated as the ratio between the quantity of water evaporated by the stone in 24 h and the quantity previously absorbed in 168 h.

These properties were tested before and after the accelerated short-term ageing of the limestone (new (unweathered) stones, RPHL and NUPL, and in-use weathered stone, UWPL) using the QUV test for 1000 h [36,61].

Abrasion Behavior:

-

The Amsler abrasion wear of new (unweathered) and in situ weathered limestone was tested before and after the accelerated short-term ageing of limestone via the QUV test using the procedure described in ASTM C241/C241M-21 [37].

This structured presentation, including all the relevant references and explanations, provides a comprehensive overview of the experimental approach used in this study to evaluate the performance of the different limestone samples under various weathering conditions. The chemical composition tests focused on identifying the impurities that could lead to discoloration and deterioration. The physical property tests characterized the stones’ pore structure and water absorption/evaporation behavior, which are critical factors in weathering resistance. Finally, the abrasion tests provided insights into the stones’ performance under the wear conditions expected in a pedestrian zone.

4.3. Life Cycle Prediction and LCC Analysis

In the introduction of the current article, it was mentioned that throughout ancient history, stones have been employed in construction due to their physical and petrochemical properties, ensuring long-term durability in various environmental and service conditions on construction sites. In this context, it is noteworthy that in Israel, different types of limestone, namely chalk stones (karst) and hard limestone known as Jerusalem stone, as well as sandstone referred to as “Kurkar”, have been used in construction projects for millennia. In contemporary construction practices, these stones are no longer utilized as dimensional building blocks with thicknesses ranging from 40 cm to 1.5 m in wall construction because of insufficient waterproofing and capillary water absorption. Instead, they have evolved into elements primarily used for concrete wall cladding, paving, and flooring materials, typically with thicknesses ranging from 2 to 10 cm. Over the centuries of using these stones, they have demonstrated their exceptional resilience to local environmental conditions, contingent on their specific application and service regime in various projects.

One noteworthy example among these stones is Jerusalem Stone (hard limestone), which serves as a benchmark for assessing the long-term durability of these stones. Detailed information regarding the characteristics and evaluation of these stones can be found in these references [63,64]. The authors used Jerusalem Stone as a reference stone for life cycle assessment.

5. Results and Discussion

5.1. Properties of Unweathered and In situ Aged Paving Limestones

The contents of impure chemical elements in the stones are presented in Figure 3. Compared to the reference stone, RPHL, the limestone from Jordan, NUPL, has many more chemical impurities, Al, Fe, Cl, and SO₄ contents. These impurities are generally associated with clay mineral impurities in limestone. The clay impurities in limestone are prone to the impacts of high humidity and UV radiation and might cause the deterioration of the stone [1,61]. According to Winkler [1], the decay process in stones containing high amounts of impurities may take only a few years.

Figure 4 shows the general engineering properties of the studied paving stones. It can be seen that the bulk densities of the NUPL and RPHL are typical for limestone; see Table 1. However, the bulk density of NUPL is approximately 7% lower than the minimal limit recommended by [50,51] for building stone. The lower bulk density of NUPL is indirect evidence of higher porosity and water absorption than those of the reference limestone (see Figure 4). The Amsler abrasion wear of the NUPL is higher by 33% than that of the reference limestone, RPHL. The estimated wear resistances of the RPHL and NUPL, calculated using Equation (1), are 22 and 24 mm, respectively [42].

Wide Wheel = 17 + 1.7·(Amsler)

(1)

where

• Wide Wheel—Capon (“Wide Wheel Abrasion Test”).
• Amsler—Amsler abrasion wear.

Thus, NUPL is more appropriate for paving a promenade in an intensive pedestrian environment compared to RPHL (see Table 1).

Figure 3. Elemental analysis of minor chemical elements in paving stones. RPHL—reference paving hard limestone; NUPL—new (unweathered) paving limestone from Jordan.

Figure 3. Elemental analysis of minor chemical elements in paving stones. RPHL—reference paving hard limestone; NUPL—new (unweathered) paving limestone from Jordan.

Figure 4. Physical engineering properties of paving stones. RPHL—reference paving hard limestone; NUPL—new (unweathered) paving limestone from Jordan; +—positive error; −—negative error; CV—coefficient of variance.

Figure 4. Physical engineering properties of paving stones. RPHL—reference paving hard limestone; NUPL—new (unweathered) paving limestone from Jordan; +—positive error; −—negative error; CV—coefficient of variance.

It was found that the water absorption and evaporation characteristic values of the NUPL are six to fifteen times higher than those of the reference RPHL, as can be seen in Figure 5. The relatively small changes in capillary water absorption compared to the large increase in total water absorption suggest that most of the additional water uptake occurred in larger pores or microcracks formed during weathering, rather than through capillary action in fine pores. This indicates that environmental exposure primarily caused mechanical damage and structural fragmentation, increasing the total porosity, without significantly altering the fine-pored capillary network, which governs capillary absorption.

Furthermore, the evaporation capacity of the NUPL evaluated in terms of moisture residue in the stone after 168 h long in-lab exposure was about 15 times less than that in the case of the reference RPHL.

Thus, it could be considered that the intensive water absorption and sluggish water evaporation of the NUPL from Jordan, taken together with the high content of impurities in this stone (see Figure 3) might cause the advanced deterioration of the NUPL during one-year-long in-use exposure in the hot and wet climate near Capernaum, the Sea of Galilee (Lake Kinneret), Israel. Unfortunately, no tests of the chemical and physical/engineering properties of the NUPL were carried out by the contractor prior to paving the promenade. As was previously mentioned, the defects appeared in the paving after only one year. Therefore, the defective performance of the NUPL in the pedestrian promenade could serve as evidence of how disregarding the basic chemical/physical/engineering properties of paving stones and keeping up only with their aesthetical appearance and sufficient strength characteristics might lead to construction faults costing many millions of dollars. Hence, the chemical, physical, and engineering properties of specific building stones compared with those of a reference local stone of known lifespan should be considered as a necessary criterion for minimizing the probability of defects appearing in the external stone paving. It should be emphasized one more time that RPHL, chosen as a reference stone in the current research, is well known for its satisfactory long-term durability in different in-use exposures to the various environmental conditions in Israel. There is evidence about the lifespan of RPHL external pavements, which is up to 50 years [16]. In this research, a model for the prediction of the service life of claddings under standard conditions was developed, and the service life of stone under standard conditions was defined.

Figure 5. Water absorption and evaporation characteristics of paving limestones. RPHL—reference paving hard limestone; NUPL—new (unweathered) paving limestone from Jordan; +—positive error; −—negative error; CV—coefficient of variance.

Figure 5. Water absorption and evaporation characteristics of paving limestones. RPHL—reference paving hard limestone; NUPL—new (unweathered) paving limestone from Jordan; +—positive error; −—negative error; CV—coefficient of variance.

The one-year in-use exposure of paving limestone from Jordan to the hot and humid environment in the vicinity of the Sea of Galilee mostly led to an improvement in the water absorption characteristics of this stone and its abrasion wear (see Figure 6). The total water absorption and the surface absorption capacity of the NUPL have risen by 22% to 40% because of in-use weathering. The water absorption characteristics of the weathered (UWPL) and new (NUPL) limestone paving showed marked differences after one year of environmental exposure (Figure 6). The total water absorption and surface absorption capacity increased by 22% to 40% in the UWPL, indicating increased porosity due to weathering. However, capillary water absorption remained relatively stable, suggesting that the increased absorption occurred primarily in the larger pores and the microcracks rather than the fine capillary networks. The coefficient of variance (CV) for water absorption and evaporation was notably higher in the UWPL, pointing to non-uniform degradation across the stone slabs. This heterogeneous deterioration can compromise the overall durability of the paving. These changes—increased total absorption, stable capillary action, and high variability—collectively indicate accelerated wear in the UWPL after just one year. This rapid deterioration underscores the importance of proper material selection and maintenance of limestone paving in challenging environments.

The water evaporation capacity of the unused and used limestones from Jordan, the NUPL and the UWPL, respectively, was much smaller than that of the reference limestone, the RPHL; see Figure 7. The exposure of the stones to the cycles of UV radiation led to the decreased water evaporation capacity of all the studied stones. The water evaporation capacity of the limestone from Jordan after UV exposure became more insufficient, i.e., 41% vs. approximately 50% before UV exposure. Thus, 59% of the absorbed water was entrained in the NUPL and the UWPL after QUV ageing. A low water discharge might facilitate limestone decay processes [61] No difference was observed between the mean water evaporation capacity of the new and used limestones from Jordan, the NUPL and the UWPL, respectively, before and after their exposure to the QUV test. However, after the QUV test, the absolute variation in water evaporation capacity was much higher in UWPL than in NUPL, i.e., 25% vs. up to 7%, respectively. Thus, the QUV test could be adopted as a valuable method to reveal the discrepancies in the water discharge of paving limestones aged by different weathering agents.

The variation coefficients of the properties of limestones from Jordan, the NUPL and the UWPL, checked before and after the QUV test, are shown in Figure 8. Surface water absorption capacity is the property that was the most affected by ageing, with variation coefficients ranging from 28% to 38%. The water evaporation capacity during 24 h varied from 3% to 16%. Thus, the cycles of intensive wetting followed by short drying periods might cause substantial differences in the amount of water that remained in the adjacent stones implemented in the Capernaum promenade. Therefore, the stones from Jordan, the UWPL, being exposed during use to the mentioned wetting/drying cycles might undergo different rates of deterioration and decay because of the variances in the properties of the wet and dry limestones, i.e., the following:

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The variable kinetics of the phase transformations of minor minerals [61].

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The inconstant degree of thermal and hydric expansion [1].

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The differences in load-bearing capacity and abrasion wear (ibid).

Therefore, the failures that appeared very soon after paving works began on the Capernaum promenade might also be explained by the large differences between the properties of the different limestone slabs from Jordan.

Thus, the variation coefficient of limestone’s total surface water absorption could serve as a helpful performance characteristic for estimating the life cycle of external pavement. According to Bortz and Wonneberger an average lifespan of a 1 mm, completely unweathered, hard limestone slab in a humid climate is 33 years [65]. No proven data are available for the lifespan of limestones subjected to solar radiation. As previously mentioned, there is evidence about the lifespan of RPHL external pavements of approximately 35 years. Thus, for the limestone from Jordan, the lifespan calculated based on 28% and 38% variation coefficients is likely to range from 25 to 30 years, correspondingly.

Figure 6. Changes in physical and engineering properties of paving limestone from Jordan after one year of in situ weathering. NUPL—new (unweathered) paving limestone. UWPL—used (one-year in situ weathered) paving limestone; +—positive error; −—negative error; CV—coefficient of variance.

Figure 6. Changes in physical and engineering properties of paving limestone from Jordan after one year of in situ weathering. NUPL—new (unweathered) paving limestone. UWPL—used (one-year in situ weathered) paving limestone; +—positive error; −—negative error; CV—coefficient of variance.

Figure 7. Water evaporation capacity of paving limestones. RPHL—reference paving hard limestone; NUPL—new (unweathered) paving limestone from Jordan. UWPL—used (one-year in situ weathered) paving limestone; +—positive error; −—negative error; CV—coefficient of variation.

Figure 7. Water evaporation capacity of paving limestones. RPHL—reference paving hard limestone; NUPL—new (unweathered) paving limestone from Jordan. UWPL—used (one-year in situ weathered) paving limestone; +—positive error; −—negative error; CV—coefficient of variation.

The coefficient of variance (CV) of the laboratory tests presented in Figure 4, Figure 5, Figure 6 and Figure 7 aimed to assess the dispersion and uncertainty in the stones’ physical and mechanical properties. The CV shows that the genuine stone’s physical and mechanical properties were initially more widely dispersed compared to that of the standard reference stone, expressing the trend of the NUPL toward accelerated deterioration comparing to that of the reference stone (RPHL). The physical properties of the stones after exposure to the site service regime (UWPL) were found with a high ratio of properties variance, as depicted by the coefficient of variance.

Figure 8. The variation coefficient of the properties of the limestone from Jordan. NUPL—the new (unweathered) paving limestone from Jordan. UWPL—the used (one-year in situ weathered) paving limestone.

Figure 8. The variation coefficient of the properties of the limestone from Jordan. NUPL—the new (unweathered) paving limestone from Jordan. UWPL—the used (one-year in situ weathered) paving limestone.

5.2. Assessment of the Life Cycle Costs of Paving

5.2.1. Life Cycle Cost Modeling Approaches for Stone Pavements

The life cycle costs of natural stone paving detail comprise three elements: the initial construction cost (C), the annual maintenance costs (M), and the end-of-life replacement costs (R). Figure 9 illustrates the sequence of costs over a single life cycle of natural stone paving in detail. This figure illustrates annual maintenance costs of 1% of the construction costs and assumes that the pavement will be used for one more service life cycle; therefore, the end-of-life replacement costs are avoided. The maintenance of pedestrian pavement is carried out continuously based on periodical inspections (twice per annum) and the assessment of the condition; the deteriorated slabs are replaced, and the sinking slabs are replaced after the repair of the bedding pavement layer. The annual costs of this procedure are estimated at 1% of the construction cost.

Considering the conducted tests, it is estimated that the paving and structures covered with Jordanian stone exhibit an accelerated deterioration pattern. The life cycle of the paving components is expected to range from a minimum of 1 year (as observed in the promenade case study) to a maximum of 20 years, instead of the original 24 [66]. Staged replacement work will be necessary, with the current requirement to replace 15% of the stone slabs and to seal the cracked joints with suitable cement mortar. It is also assumed that the dismantling costs will be 0.12C—12% of the construction costs (where C is the reinstatement cost per square meter of paving).

The research method uses field surveys designed to identify the financing needs and sources. Subsequently, a model for estimating the costs was developed, distinguishing between various financing sources, as demonstrated through two typical projects: a residential construction project for sale and an office building construction project for rental purposes (a “yielding” project). Running the model on these typical projects allowed for the comprehensive characterization of the life cycle costs flow, their scope, and their dependency on various parameters.

Figure 10 depicts the actual field survey datapoints gathered. Two deterioration patterns were suggested to characterize the deterioration progress: linear deterioration and exponential deterioration. Both the patterns have a high correlation coefficient with time, despite the small number of datapoints available for similar failure conditions of natural stone pavement. This methodology was developed and validated in prior research [15,16,17].

In light of this, a comparison was made between the costs to the owner under normal wear conditions (without replacements until a life cycle of 24 years) and costs under accelerated wear conditions in two wear patterns (Figure 9):

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A linear wear pattern (uniform wear rate).

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An exponential wear pattern (initially rapid wear rate that decelerates over time).

Figure 10. The linear versus exponential wear patterns in the paving of the Capernaum promenade.

Figure 10. The linear versus exponential wear patterns in the paving of the Capernaum promenade.

5.2.2. Cost of Paving Under Standard Wear Conditions (Without Failure)

Equation (2) expresses the present value of the LCC under standard wear, where the maintenance costs remain constant, assuming preventive and condition-based maintenance. The deterioration rate for this equation was taken from the reference stone’s deterioration (RPHL) and was assessed at 1% per annum, [16].

LCC₁ = C + M × rp(i, LC₁)

(2)

where

• LCC₁ = The life cycle costs under standard wear conditions.
• C = The initial construction cost per square meter.
• M = The annual maintenance costs (a typical value for stone paving is 1% per year).
• M = The annual maintenance costs (a typical value for stone paving is 1% per year).
• M = The annual maintenance costs (a typical value for stone paving is 1% per year).
• rp = The present value factor of a payment series at an annual interest rate of i [%] over LC₁ years.
• i = The annual interest rate [%].

Based on the two examined accelerated wear patterns, two LCC flow scenarios were estimated:

Under “linear” wear conditions—at a constant rate.

Under “exponential” wear conditions, the rate decelerates over time (Figure 11).

Under both the wear patterns, it is assumed that 15% of the Jordanian stone slabs need to be replaced immediately.

Figure 11. Life cycle cost Flow for paving stones with linear deterioration pattern (with failure conditions).

Figure 11. Life cycle cost Flow for paving stones with linear deterioration pattern (with failure conditions).

5.2.3. Linear Wear Pattern

The cost flow under linear wear conditions is presented in Figure 11. In these conditions, the cost to the owner for the component is

LCC₂ = C + M × rp(i,LC) + R₁ × sp(i,1) + R₂ × [rp(i,20) − rp(i,1)]

(3)

where

• LCC₂ = The life cycle costs under “linear” wear conditions.
• R₁ = The replacement costs in the first year.
• sp(i,n) = The present value factor of a single payment in year n (in this case n = 1) at an annual interest rate of i = 6%.
• R₂ = The replacement costs from the second year up to the twentieth year, which is the maximum life cycle for Jordanian stone slabs, as determined by the accelerated wear tests.

Equation (3) expresses the present value of the life cycle costs under linear accelerated deterioration pattern, as expressed in Figure 10. The maintenance costs were taken from the Capernaum field survey, with observed wear of 15% after 1 year and 4% in the remaining life cycle of the stone according to the linear wear patterns acquired by the linear deterioration pattern shown in Figure 10.

Subtracting Equation (2) from Equation (3) yields the marginal cost incurred by the owner due to defects in the quality of the paving stone and the coverings under linear wear conditions (Equation (4) below):

∆LCC₁₋₂ = R₁ × sp(i,1) + R₂ × [rp(i,24) − rp(i,1)]

(4)

where

• ∆LCC₁₋₂ = The marginal life cycle costs under “linear” wear conditions.
• R₁ = The replacement costs in the first year.
• sp(i, n) = The present value factor of a single payment in year n (in this case n = 1) at an annual interest rate of i = 6%.
• R₂ = The replacement costs from the second year up to the twenty-fourth year, which is the maximum life cycle for Jordanian stone slabs, as determined by the accelerated wear tests.
• rp(i, n) = The present value of the series of equal payments during n years, where n = 1.

The value obtained is given in terms of the present value.

Plugging the values into Equation (3) where i = 6%, a lower interest rate than the long-term market rate in Israel, yields the following result:

$$\mathbf{\Delta }LC{C}_{\mathbf{1}-\mathbf{2}}=\mathbf{1.12}\times \mathbf{0.15}C\times sp\left(\mathbf{6},\mathbf{1}\right)+\mathbf{1.12}\times {\displaystyle \frac{\mathbf{0.85}}{\mathbf{19}}}\times \mathbf{C}\times \left[rp\left(\mathbf{6},\mathbf{20}\right)-rp\left(\mathbf{6},\mathbf{1}\right)\right]$$

(5)

By plugging the values into Equation (5), the following value is obtained:

That is, the additional cost incurred by the owner due to defects in the quality of the stone and the joints is about 69% of the original paving price (in terms of the present value).

5.3. Exponential Deterioration Pattern

Under exponential wear conditions, the costs incurred by the client for defects according to the exponential wear pattern are

$$\mathit{L}\mathit{C}{\mathit{C}}_{\mathbf{3}}=\mathit{C}+\mathit{M}\times \mathit{r}\mathit{p}\left(\mathit{i},\mathit{L}\mathit{C}\right)+{{\displaystyle \sum }}_{\mathit{j}=\mathbf{1}}^{\mathbf{20}}{\mathit{R}}_{\mathit{j}}\times \mathit{s}\mathit{p}\left(\mathit{i},\mathit{j}\right)$$

(6)

where,

• Rj is the rate of cracked stone slabs in year J, derived from Figure 12.

Subtracting Equation (2) from Equation (6) yields the additional cost incurred by the client due to defects under exponential wear conditions, as presented in Figure 10 (Equation (7) below):

$$\mathbf{\Delta }\mathit{L}\mathit{C}{\mathit{C}}_{\mathbf{1}-\mathbf{3}}={{\displaystyle \sum }}_{\mathit{j}=\mathit{1}}^{\mathbf{20}}{\mathit{R}}_{\mathit{j}}\times \mathit{s}\mathit{p}\left(\mathit{i},\mathit{j}\right)$$

(7)

where i represent the annual interest rate on the capital.

By plugging the values into Equation (7), with the Ri values derived from the function in Figure 9, the following value is obtained:

$$\mathbf{\Delta }\mathit{L}\mathit{C}{\mathit{C}}_{\mathbf{1}-\mathbf{3}}=\mathbf{0.73}\mathit{C}$$

That is, the additional cost incurred by the client due to defects in the quality of the stone according to the exponential wear pattern is 73% of the original paving price (in terms of present value).

Therefore, the present value of the paving is between 0.31C and 0.27C, where C is the reinstatement value of the stone paving per square meter.

Figure 12. The cost flow assuming an exponential deterioration pattern.

Figure 12. The cost flow assuming an exponential deterioration pattern.

6. Discussion

This research delivers a novel approach to natural stone pavements’ life cycle analysis, incorporating the material properties, the deterioration patterns, and consequent life cycle costs and planning. The tested standard properties of the paving stone have been incorporated into the life cycle cost analysis model in the following ways:

• The core laboratory tests of the paving stones, including apparent density, water absorption, compressive strength, flexural strength, and abrasion resistance, provided decisive criteria for the assessment of the natural stone pavement’s wear and tear trends. The coefficient of variance of the laboratory tests shows that the genuine stone physical properties were initially more widely dispersed compared to those of the standard reference stone. The physical properties of the stone after exposure to the site service regime were found to have a high ratio of variance, as depicted by the coefficient of variance, and intensive accelerated deterioration worsened these properties.
• The diagnostic field survey focused on construction details, such as cracks in the paving stones, the peeling of stone layers, subsidence and cracking at the edges, and the cracking of joint filler materials. These observations helped characterize the deterioration rate of the stone pavement.
• Based on the laboratory tests and field observations, two deterioration patterns were developed: a linear deterioration pattern and an exponential deterioration pattern.
• These deterioration patterns were then used for life cycle cost analysis. The LCC model compared the costs under standard wear conditions (without failure) to the costs under the two accelerated wear patterns.
• The natural stone pavement LCC approach developed in this research further enhances the state-of-the-art methodologies [21,23], that focus on life cycle assessment and do not discuss the deterioration patterns under intensive service regimes and the outcomes of failure mechanisms.

7. Conclusions

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An integrated framework is proposed for assessing natural stone pavements’ durability and life cycle costs. This framework incorporates laboratory testing, field surveys, and deterioration pattern analysis. This study highlights the adverse influence of substandard construction practices on pavement performance, leading to premature degradation and increased costs.

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Essential laboratory tests were conducted to establish the material properties, including density, water absorption, compressive, flexural, and abrasion resistance. A comprehensive field survey was implemented to identify the deterioration patterns. Statistical analysis revealed two distinct patterns: linear and exponential. The exponential pattern, characterized by rapid initial deterioration, substantially impacted the life cycle costs.

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Life cycle cost analysis demonstrated that defective construction practices can result in losses from 69% to 73% of the initial paving value. These findings underscore the critical importance of adhering to the established mechanical parameters during natural stone pavement planning and construction phases.

This methodology is reproduceable in any project provided that a diagnostic field survey is carried out, the performance of the stone pavement is assessed according to the ratio of damaged and cracked stones, and the degradation mechanisms are identified according to the framework provided in this research.