Biophysical, Spatial, Functional, and Constructive Analysis of the Pre-Hispanic Terraces of the Ancient City of Pisaq, Cusco, Peru, 2024

Abstract

The aim of the research is to examine the biophysical, spatial, functional, and structural components of the pre-Hispanic terracing systems located in the ancient city of Pisaq, considering the impacts of tourism, geological instability, and cultural loss on the ecological and economic value of the terracing system. The methodology includes site analysis, climatology, and an examination of local flora and fauna, supported by digital tools such as QGIS 3.34, Google Earth Pro 2024, and Sun-Path. The results were primarily supported by the use of software tools such as QGIS, AutoCAD 2023, SketchUp 2022, 3D Sun-Path, D5 Render 2024, and Photoshop 2021. The findings include a biophysical analysis related to ecological and economic zoning (EEZ), which determines variables for preservation and reforestation; a spatial analysis measuring the cultivation terraces, with areas ranging from 4.89 ha to 110.20 ha; a functional analysis examining geophysical aspects such as seismic resistance and microclimate effects due to the greenhouse effect; and a constructive analysis that characterizes terrace typologies from an architectural perspective. In conclusion, this analysis evaluates the terracing system of the archaeological park to ensure its preservation and effective management. It also highlights that Inca culture has left a legacy of sustainable architecture, which aligns with the current Sustainable Development Goals (SDGs) (6, 11, 13, 15).

1. Introduction

The preservation and protection of cultural heritage are crucial for sustaining collective memory, promoting cultural diversity, strengthening national identity, fostering intercultural dialogue, and enriching the cultural experience of present and future generations [1]. Its importance lies in the fact that cultural heritage serves as tangible evidence of a society’s history and culture, allowing for the understanding of beliefs, customs, and technologies [2]. This international commitment highlights the fundamental importance of protecting cultural heritage, as it represents a shared legacy of humanity with exceptional value that enriches the lives of all generations [3].

The United Nations Educational, Scientific and Cultural Organization (UNESCO) carries out the task of designating and protecting archaeological sites recognized as world heritage through a dedicated committee. This committee maintains a list that includes cultural, natural, or mixed sites of significance to humanity [4]. Worldwide, there are 933 archaeological sites recognized as World Heritage Sites, each with diverse construction systems reflecting the cultures analyzed [5].

Figure 1 shows the location of various world heritage sites. In Figure 1A, the African continent is highlighted, specifically Egypt, where the Karnak Temple is situated. This significant site was constructed between 1554 B.C. and 313 B.C., serving as a religious center while also symbolizing power and authority in ancient Egypt [6].

The Karnak Temple is distinguished by its use of local materials, such as limestone, granite, and quartzite, which were shaped using advanced stoneworking techniques. Its architectural design reflects Egyptian cosmology and the importance of natural phenomena, incorporating elements that symbolize spiritual beliefs. The temple’s monumental structures include pylons, courtyards, hypostyle halls, and chapels, all adorned with reliefs and hieroglyphic inscriptions. These mythological representations and decorative elements enrich the temple’s religious and symbolic function [7].

Similarly, in Figure 1B located in the southeastern part of Europe, the Parthenon stands in Greece, a religious temple that manifested the power and prestige of the city-state of Athens. This significant monument, constructed between 447 B.C. and 438 B.C., served as a cultural and political center, representing the identity and splendor of Athens [8].

The Parthenon is characterized by its Doric architectural style, which is distinguished by robust columns and harmonious symmetry and proportions. It was built with limestone and marble from Mount Pentelicus, employing precise assembly techniques to form the columns. Its construction technique included the carving of notches and tongues on the surfaces of the blocks, ensuring a perfect fit. Additionally, the temple was adorned with sculptures and reliefs that depicted mythological and ceremonial scenes [9].

Also, in Figure 1C the archaeological site of Hampi is observed, located in southern Asia, India, which represents the importance of religion and spirituality in a center of devotion based on the symmetry and aesthetics of Vijayanagara culture [10]. This significant site, constructed between 1401 A.D. and 1500 A.D., made substantial use of clay and stone granite, which were intricately carved and assembled. Its trabeated style consisted of beams and columns, allowing for the creation of open spaces and elaborate ceilings. Furthermore, its geometric design in architectural elements such as shrines and porticos denote symmetry and proportion, emphasizing its intricate architecture, characterized by dome-shaped arches, parapets, and decorative capitals that serve a structural function [11].

Lastly, in Figure 1D the archaeological wonder of Machu Picchu is observed in South America, specifically in Peru. This citadel, constructed between 1450 A.D. and 1530 A.D., consists of agricultural terraces, temples, and ceremonial enclosures, reflecting a profound understanding of geography and astronomy [12].

The design of the citadel included the construction of retaining walls, platforms, and interconnected pathways. Large granite blocks were used, carefully selected and positioned to stabilize the terrain and facilitate effective drainage [13].

Figure 1. (A) Karnak, reprinted with permission from Ref. [14]. 2021, Clarín; (B) The Parthenon, reprinted with permission from Ref. [15]. 2014, Mark Cartwright and World History Encyclopedia; (C) Hampi, reprinted with permission from Ref. [16]. 2017, MADUR and Karnataka; (D) Machu Picchu; and construction timeline.

Figure 1. (A) Karnak, reprinted with permission from Ref. [14]. 2021, Clarín; (B) The Parthenon, reprinted with permission from Ref. [15]. 2014, Mark Cartwright and World History Encyclopedia; (C) Hampi, reprinted with permission from Ref. [16]. 2017, MADUR and Karnataka; (D) Machu Picchu; and construction timeline.

Throughout their historical development, cultures in Peru employed various techniques and materials that defined the construction systems characteristic of the pre-Columbian era. The technique of dry-stone assembly, evident in sites such as Machu Picchu and Saqsaywaman, is representative of Inca culture, which perfected this method to achieve solid and earthquake-resistant structures [17]. In contrast, the Chimú culture utilized adobe reinforced with river cobbles, as observed in the citadel of Chan Chan, adapting the material to the desert conditions of the coast. The Moche culture, for its part, distinguished itself through high-relief decoration, particularly visible in the friezes of the Huaca de la Luna, reflecting both their artistic skill and the ritual importance of their constructions [17].

In the realm of stone sculpture, the Incas developed precise stone-carving techniques in emblematic locations such as Ollantaytambo and Pisaq, a tradition rooted in Chavín culture, where it is evident in the cabezas clavas and the lanzón monolítico [17]. Finally, the use of ceramics and other hydraulic technologies is evident in Nasca culture, particularly in their irrigation canals, adapted to optimize water management in an arid environment. These practices, detailed in

Table 1. Innovative construction techniques compared to cultures in Peru [17].

Culture	Construction Techniques	Material Predominant	Building Typology or Name
Inca	Dry-stone assembly	Stone	Machu Picchu Saqsaywaman
	Stone sculpture		Ollantaytambo Pisaq
Chimú	Adobe reinforced with river cobbles	Adobe River cobbles	Chan Chan
Moche	High-relief decoration	Adobe	Huaca de la Luna
Chavín	Stone sculpture	Stone	Cabezas clavas Lanzón monolítico
Nasca	Structural cladding	Ceramic	Water channel systems and structures

, not only demonstrate the constructive ingenuity of each culture but also reflect their interaction with the environment and their vision of space and ritual in everyday life [17].

The construction systems employed by these diverse cultures can be attributed to several common factors that significantly influenced the choice and development of building techniques and materials. Firstly, the availability of resources such as adobe, stone, and ceramics was fundamental in establishing construction practices adapted to local conditions [18]. The climatic and geographical characteristics of Peru, marked by the aridity of the desert and the presence of seasonal rivers, propelled the development of irrigation systems and construction techniques designed to confront a dry environment. Additionally, technological innovation, which included advances in masonry, the use of mortar, and water channeling, played a crucial role in the evolution of buildings, being transmitted and shared among different cultural groups, allowing for mutual enrichment of knowledge and practices [18].

Cultural interaction, facilitated by trade, cultural exchanges, and territorial conflicts, also contributed to the diffusion of knowledge among different ethnic groups and regions, leading many communities to adopt similar approaches in their constructions. Finally, adaptation to the natural environment is reflected in the architecture and needs of each community, whether in agriculture, military defense, or social organization, resulting in construction systems that, although diverse, share common elements to face similar challenges [18].

In this context, Peru houses numerous archaeological sites registered by the Ministry of Culture, totaling 5090 and corresponding to various cultures and periods. These sites are not only testimonies to the cultural wealth of the country but also represent the diversity of construction techniques and materials used throughout its history [19].

Figure 2 shows the location of archaeological sites in Peru. In Figure 2A in the Department of Lima, is the archaeological site of Caral, a sacred city, ceremonial center, and the oldest settlement in the Americas with a complex social organization [20]. Its monumental architecture consists of pyramids with stepped platforms built from carved and fitted stones; its planned urban design includes plazas, courtyards, and ceremonial structures; and innovative features such as overlapping terraces and ceremonial halls with central hearths Its monumental architecture is composed of pyramids with stepped platforms constructed from finely cut and fitted stones; its urban design includes plazas, courtyards, and ceremonial structures, along with layered terraces and ceremonial halls featuring central hearths [21]. Similarly, in Figure 2B shows the archaeological site of Chavín de Huántar in Ancash, which corresponds to the Chavín culture. It was significant as a ceremonial and political center near essential trade routes and with access to natural resources [22]. Notable are its structures and spaces that suggest urban planning with designated areas for rituals, residences, workshops, and ceremonial activities; its architecture is evident in monumental structures such as the Lanzón Monolítico and Cabeza Clava, as well as in the use of drainage and ventilation systems and decorative reliefs on the structures [23]. On the other hand, in Figure 2C features the archaeological site of Kuelap, located in the Department of Amazonas, which was a significant fortified settlement of the Chachapoya culture and is characterized by its stone fortress with a strategic location atop a mountain [24]. Its construction system includes stone walls, circular elevated structures used for housing or domestic activities, and the use of platforms in special buildings such as the Tintero and the Torreón with Inca influence [25]. Additionally, in Figure 2D presents the archaeological site of Choquequirao, located in Cusco, which served administrative, religious, and residential functions, reflecting advanced Inca urban planning [26]. It comprises structures such as plazas, pachhas, qolqas, and temples, distributed in an organized manner adapted to the terrain, with horizontal stratigraphy in some structures indicating architectural renovations and progressive development [27].

These advanced plans not only reflect the Incas’ ability to develop complex territorial management and organizational strategies, but they were also crucial to the expansion and maintenance of an extensive and culturally diverse empire. Their efficiency and cohesion surpassed that of previous Andean civilizations, enabling them to establish a lasting legacy in the region [32].

To consolidate this infrastructure, the Inca civilization implemented advanced techniques, notably the Qhapaq Ñan, an extensive road network that facilitated communication, troop movement, and the transportation of goods throughout the empire [32]. Building upon the governance structures of previous civilizations like Wari and Tiwanaku, the Incas adapted and refined these systems, creating an even more efficient administration. This integration of infrastructure and knowledge allowed the Incas to effectively manage their vast territory, optimizing connections between distant regions and unifying the empire logistically and culturally [32].

Therefore, Inca buildings played a crucial role in the social and administrative organization of the empire. Palaces and elite residences not only served administrative functions but also acted as ceremonial centers, symbolizing the rulers’ power and their importance within the empire’s structure [33]. Likewise, the Acllawasis, where the acllas—women chosen by the Sapa Inca—carried out religious, ceremonial, and productive activities like textile and food production, and held significant roles in the Incan economy and religion [33].

The Incan architectural landscape included a variety of functional spaces, such as kallankas (large multipurpose buildings), ushnus (ceremonial platforms), fortresses, temples, and administrative centers. Each of these spaces contributed to the empire’s development and cohesion, reflecting architectural planning that combined practical functions with symbolic meanings, thereby consolidating the power and influence of the Incas in the region [33].

Moreover, the Inca construction system was distinguished by its complexity and adaptability, making the most of natural environmental features through the use of local materials like stone and earth. Their architectural technique combined crafted and natural stones, providing the buildings with notable structural flexibility and resilience. The structures included various forms, such as quadrangles, circles, and curves, organized into interconnected units forming harmonious and functional complexes, as clearly seen in the terraces [34].

Thus, the terraces served not only agricultural functions and soil stabilization for hillside constructions but also demonstrated a design that went beyond functionality. By aesthetically integrating settlements with the volumetry of the buildings, the terraces transformed the landscape into a sculptural work embodying the Incan worldview, which valued harmony between humans and nature. This balance between utility and beauty in Andean architecture is one of the most emblematic legacies of the Inca Empire [34].

Therefore, in the department of Cusco, significant terrace systems associated with Inca culture still persist in archeological sites, demonstrating their mastery in environmental adaptation and utilization. In these locations, one can observe not only agricultural terraces but also the precise stone assembly, sophisticated hydraulic systems, and the road network known as Qhapaq Ñan, which connected the vast territory of the Tawantinsuyu [35].

Figure 3 shows the location of archaeological sites in Cusco. In Figure 3A the archaeological site of Ollantaytambo is distinguished by its precisely carved stones; its agricultural terraces constructed on mountain slopes for soil retention and erosion prevention; and its hydraulic system, which facilitated irrigation by providing water for domestic and agricultural stands out for its precisely cut stones used in construction, agricultural terraces built on mountain slopes for soil containment and erosion prevention, and its hydraulic system, which provides irrigation for both domestic and agricultural purposes [36]. Conversely, in Figure 3B the archaeological site of Moray features locally sourced materials such as stone, limestone, and granite; a series of concentric circular terraces descending toward the center; terraces that allowed the control of various microclimates and experimentation with crops at different altitudes; and retaining walls that support the terraces and prevent soil erosion [37]. Additionally, in Figure 3C the archaeological site of Tipon is characterized by stone construction techniques, including the use of fixtures to join stone blocks; terraces with retaining walls adapted to the terrain, creating agricultural areas; ceremonial structures such as Intiwatana; and hydraulic engineering comprising aligned channels, ceremonial fountains, and water collection points [38].

These archaeological sites are part of the Valle Sagrado de Cusco, now located in the provinces of Urubamba and Calca. This valley is notable not only for its historical richness and cultural and archaeological significance but also as an outstanding example of advanced Incan agricultural engineering. It hosts a vast agricultural diversity and local communities, especially recognized for its extensive areas of Incan terraces [40]. These structures not only maximize agricultural production on sloped terrain but also embody a legacy of adaptation and sustainability that defines Incan civilization. The terrace system was essential for the agricultural development of the Inca Empire, as it allowed for effective adaptation to mountainous geography by creating flat surfaces suitable for the cultivation and care of various species [41]. This ingenious system also optimized soil water retention, improving growth conditions in areas with limited water availability. Consequently, the terraces not only met the food needs of the ayllus and llaqtas but also produced surpluses that supported urban growth and strengthened the socioeconomic structure of the Inca Empire [41].

In this context, the province of Calca, particularly the district of Pisaq, is home to the emblematic city of Pisaq, which stands as the Archaeological Park of Pisaq. This ppark is a cultural and historical treasure that reflects the rich heritage of the Incan civilization, evident in both its impressive landscape and ingenious architecture. The most remarkable feature of Pisaq is its extensive terrace system, developed by the Incas for agriculture—an eloquent testament to their exceptional adaptation to the Andean geography. This ensemble not only provides breathtaking panoramic views but also serves as a vital link between other important archaeological sites in the region. In addition to the terraces, the park houses a variety of architectural elements, including temples, plazas, and sophisticated irrigation systems, which illustrate the complexity and innovative vision behind Incan urban planning [42].

Figure 4 shows the Archaeological Park of Pisaq, which is divided into Figure 4A an agricultural zone, characterized by a terrace system designed for cultivation, and Figure 4B an urban zone, comprising ceremonial, residential, and defensive structures. One of Pisaq’s most prominent aspects is its historical significance as a ceremonial, administrative, and military center of the Inca Empire. The architectural skill and hydraulic engineering expertise of the Incas are evident in structures such as temples, plazas, aqueducts, tombs, and terrace systems [43]. Additionally, Pisaq is a popular tourist destination that contributes significantly to the local economy, creating jobs in the modern city. Archaeological research conducted within the park has expanded knowledge about the history and culture of the Cusco region, providing valuable insights into the societal evolution of this area [43]. Furthermore, the terraces in the Archaeological Park of Pisaq play a crucial role in agricultural production, enhancing water management and food security for communities over time. Their positive impact on environmental conservation is notable, as they help reduce soil erosion and optimize water retention, benefiting both agriculture and the local ecosystem [43].

Despite their remarkable historical and cultural importance, archeological sites like the Archaeological Park of Pisaq face various interrelated factors that compromise their preservation.

Figure 5 highlights the significant geological instability affecting the Archaeological Park of Pisaq. In Figure 5A, the park’s hazard map identifies high-risk areas, illustrating the vulnerability of the site and its terraces to processes such as Figure 5B gully erosion, and Figure 5C landslides [44]. It is important to emphasize that gully erosion occurs when the concentrated flow of runoff carves deep channels into the soil, progressively removing fertile layers and compromising the stability of adjacent structures. Landslides, on the other hand, involve the downward movement of soil or rock masses, typically triggered by intense rainfall, seismic activity, or disturbances to natural slopes. Both processes pose a significant threat to the integrity of archaeological and agricultural structures, with the potential to compromise access routes and endanger the preservation of cultural heritage, as well as the livelihoods of local communities. Furthermore, the presence of ravines exacerbates these risks, as they could trigger landslides that would severely affect both the terraces and circulation within the archaeological park. Furthermore, the lack of maintenance of drainage infrastructure and slopes exacerbates this instability, endangering structures vital for agriculture and local culture. Without adequate attention, these constructions could be severely compromised, affecting not only the archeological archaeological heritage but also the safety and well-being of surrounding communities [44].

On the social side, the implementation of public investment projects (PIPs) could have negative consequences, such as damage to the terraces, potential loss of agricultural lands, and alteration of traditional landscapes. Modernization and tourism development also pose risks to heritage conservation, as they may compromise the integrity of these ancient structures [45]. Therefore, there is an urgent need to raise awareness and provide training within the local community about the importance of the terraces, as well as their conservation and protection. Addressing these issues requires establishing a committee that includes various stakeholders, thereby ensuring effective management and sustainable use of the terraces. Globalization and tourism, while offering economic opportunities, may also lead to cultural loss, as they can result in the alteration of practices and traditions associated with these important spaces [45].

The tourism sector also faces various issues affecting the development of the archaeological park. First, inadequate infrastructure conditions limit access for people with reduced mobility, diminishing the quality of the tourist experience. Additionally, there is a notable lack of information and resources, reflected in the scarcity of updated tourist information, limited research efforts, and restrictions on information dissemination by public and private institutions. The lack of interest from authorities is also concerning; there has been a neglect by competent institutions in improving tourism infrastructure, which negatively impacts tourism activities and the destination’s image [46]. Furthermore, limitations in research hinder access to relevant academic work from Cusco universities, as human resources dedicated to research are often occupied with other academic and work responsibilities. Lastly, there is a lack of attention to a specific market segment: tourists with restricted mobility. This group has been overlooked, not only limiting their access to the park but also representing a significant loss of economic opportunities and tourist offerings in the region. Altogether, these issues present a significant challenge that must be addressed to ensure sustainable and equitable tourism development in the area [46].

Figure 5. (A) Hazard map, Ref. [47]. 2005, Hector Acurio and INDECI; (B) erosion, reprinted with permission from Ref. [44]. 2021. INGEMENT; and (C) landslides, reprinted with permission from Ref. [47]. 2005, Hector Acurio and INDECI.

Figure 5. (A) Hazard map, Ref. [47]. 2005, Hector Acurio and INDECI; (B) erosion, reprinted with permission from Ref. [44]. 2021. INGEMENT; and (C) landslides, reprinted with permission from Ref. [47]. 2005, Hector Acurio and INDECI.

Therefore, the objective of this research is to analyze the biophysical, spatial, functional, and constructive aspects of the pre-Hispanic terraces of the ancient city of Pisaq, Cusco, Peru, 2024.

2. Materials and Methods

2.1. Methodological Scheme

The analysis is divided into four phases as illustrated in Figure 6 and was carried out according to the detailed sections below.

2.1.1. Literature Review

In the first phase, an extensive collection of information was carried out to contextualize the biophysical, spatial, functional, and constructive analysis of the terraces in Pisaq. This process involved identifying and gathering various academic sources, scientific articles, and data from recognized governmental organizations such as UNESCO and WHO, providing a relevant theoretical and empirical framework for the study.

The review allowed for the identification of different construction systems and structures associated with the terraces, highlighting not only their agricultural functionality but also their architectural design and interaction with the surrounding landscape. This comprehensive approach facilitated a deeper understanding of how these elements integrate within the Inca’s geographical and cultural context.

2.1.2. Study Area, Climatic Analysis, Flora, and Fauna

Site analysis is essential for understanding the historical and cultural context, as it facilitates the comprehension of the historical and cultural characteristics of the location, which is crucial for the preservation and management of heritage. Additionally, it supports future research by providing a reference framework on the biophysical characteristics and conditions of the site [48]. The use of digital tools such as Google Earth Pro 2024 and QGIS 3.34 helps determine values such as the location and coordinates of the archaeological site, and spatial elements, defining its dimensions relative to the study area. Furthermore, scientific, academic, and governmental documents are reviewed to provide information on site placement, urban development, biophysical, spatial, and functional variables related to the terracing systems, as well as construction methods and materials, including the typology of existing terraces.

Climatic analysis is crucial for evaluating climatic effects, which are interrelated with the biophysical, spatial, functional, and constructive aspects of the archaeological site. It also provides a foundation for selecting adaptation and risk reduction measures, which are essential for the long-term preservation and sustainability of archaeological sites [49]. This procedure includes climatological analysis involving variables such as temperatures, relative humidity, precipitation, wind direction and speed, and radiation in the study area. The following is a description of the process:

• Collection of hydrometeorological data from the “Servicio Nacional de Meteorología e Hidrología del Perú” (SENAMHI) for the last 5 Years (2019–2023), including temperature (°C), relative humidity (%), and precipitation (mm) for maximum and minimum values.
• Collection of radiation and wind speed data (2019–2023): obtain data on radiation (kWh/m²; kWh) and wind speed (km/h; m/s) from Weather Spark and CBE Clima Tool.
• Processing and thorough evaluation of collected data.
• Creation of graphs visualizing climatic data.

Furthermore, the study of flora and fauna is fundamental for the formation of identities, as it is integrated into the narratives of humans, deities, and huacas, highlighting the interrelation between humans and their natural environment, which contributes to collective identity and the revelation of social and economic practices, as it identifies agricultural, ritual, and subsistence practices of ancient communities, providing insights into their interaction with their environment and the use of natural resources [50]. This analysis was conducted through scientific and academic articles and digital tools such as Geoservidor 3.0, which visualizes the distribution of flora and fauna species in the territory.

2.1.3. Results

The modeling process of the Pisaq Archaeological Park provides a detailed description of its geographic location and terrain, represented through a three-dimensional model. The primary objective of this analysis is to consolidate information to identify the spatial, functional, and constructive characteristics of the Pisaq terraces, aiming to gain a deeper understanding of their design, agricultural use, integration within the landscape, and the cultural practices of Inca society.

Figure 7 shows the steps of modeling the Pisaq Archaeological Park. Step 1 involves the collection and transformation of Geographic Information Systems (GIS), using vector data from reliable sources such as IGN, GEOCATMIN, and SIGRID. This phase is crucial, as it establishes the information base that will be used in the subsequent stages.

In Step 2, the terraces in the Pisaq Archaeological Park are digitized using QGIS 3.34 software, where the collected data are converted into accurate digital representations of the terraces. This process allows for the visualization and analysis of the spatial structure of the terraces based on their geographic layout.

In Step 3, once digitization is complete, the vector data are transformed into AutoCAD 2023 format, facilitating the creation of detailed and precise technical plans. Step 4 involves the three-dimensional modeling of the vector information in SketchUp 2021, which allows for the visualization of the terraces in a three-dimensional context, enhancing the understanding of their structure and design.

In Step 5, rendering is performed in D5 Render 2024 to create high-quality visual representations of the architectural model or landscape. This software generates photorealistic images that highlight details such as lighting, textures, and materials, providing a clear and appealing view of the terrace.

Finally, in Step 6, this render is used for the layout of the final figures. This last stage serves to effectively communicate ideas and concepts. The next step involves rendering the model in D5 Render 2024, generating high-quality images that showcase the architectural and landscape features of the terraces. Lastly, a graphic representation and post-production are performed in Photoshop 2021, where visual elements are integrated, and final images are laid out, achieving an attractive and comprehensible presentation.

2.1.4. Discussion and Conclusions

In the analysis of Pisaq, a comparison of findings is made with other Inca archaeological sites, such as Ollantaytambo, Moray, and Tipon. This comparison allows for the evaluation of both the similarities and differences in the design and construction strategies of the terraces, highlighting the Incas’ skill in adapting their terracing systems to various geographic and climatic conditions. This analysis reveals how these practices reflect a deep understanding of the environment and remarkable ingenuity in the construction of sustainable infrastructures, which not only met agricultural needs but also incorporated aesthetic and functional considerations.

2.2. Study Area

Figure 8 presents the location and placement of the study area, where Figure 8A identifies Cusco within the context of Peru; Figure 8B details the province of Calca, which includes the district of Pisaq; and Figure 8C shows the location of the ancient city of Pisaq (Pisaq Archaeological Park) [51]. It is situated 18.9 km from Cusco Main Square and 1.61 km from Pisaq’s Concession Square, with coordinates at an altitude of −13.408 and a longitude of −71.84 [52].

2.3. Climatic Analysis

In the Sierra region, between 1990 and 2020, a temperature variation between 12.6 and 14.4 °C has been recorded, along with precipitation fluctuations ranging from 570 to 834.3 mm [53].

Figure 9 illustrates the location and positioning of the Pisaq Archaeological Park. Over the past five years, temperatures have shown variability within a range, with a general trend towards increasing values. Humidity has progressively risen, while precipitation has been variable with a decreasing trend. The lowest average temperature occurs in July at 13.68 °C, and the highest average temperature is observed in November at 16.18 °C. Maximum humidity levels are seen in February at 46.77%, while the lowest humidity is in April at 31.20%. Precipitation is highest in January, February, and December, with January having the highest at 95.96 mm, and the lowest precipitation is in June at 0.95 mm [54]. Predominant winds blow towards the north at 5–10 km/h (18–36 m/s) [55,56,57]. Additionally, the year’s longest day occurs in December, lasting 12 h and 56 min [58]. The maximum solar radiation recorded is 5.4 kWh (450 kWh/m²) [56,59,60], and UV radiation is extremely high at 11:54 a.m. [61]. According to the WHO and other sources, the optimal ambient temperature for human comfort ranges from 18 °C to 29.5 °C with humidity between 19% and 80%. The temperature and humidity conditions in January and December approximate these comfort levels, making them the most comfortable months with variable rainfall and humidity [62,63,64].

2.4. Flora and Fauna

Figure 10 shows the territorial analysis of the Pisaq district, where the area is determined based on the predominant species of flora and fauna within a territory of 593 km².

The predominant flora includes the tunilla (Opuntia soehrensii), which covering 25% of the area; and the asiento de suegra (Oroya peruviana), representing 34% of the area; for fauna, the predominant species area the peregrine falcon (Falco peregrinus), which covers 70% of the area; the spectacled bear (Tremactus ornatus), occupying 16%; and the taruka (Hippocamelus antisensis), with a smaller area of 21%; for flora [65,66,67].

Figure 10. Distribution of flora and fauna in the district of Pisaq: (A) tunilla, reprinted with permission from Ref. [66], 2024, iNaturalist; (B) asiento de suegra; reprinted with permission from Ref. [66], 2024, iNaturalist; (C) peregrine falcon, reprinted with permission from Ref. [66], 2023, iNaturalist; (D) spectacled bear, reprinted with permission from Ref. [66], 2024, iNaturalist; and (E) taruka, reprinted with permission from Ref. [66], 2024, iNaturalist.

Figure 10. Distribution of flora and fauna in the district of Pisaq: (A) tunilla, reprinted with permission from Ref. [66], 2024, iNaturalist; (B) asiento de suegra; reprinted with permission from Ref. [66], 2024, iNaturalist; (C) peregrine falcon, reprinted with permission from Ref. [66], 2023, iNaturalist; (D) spectacled bear, reprinted with permission from Ref. [66], 2024, iNaturalist; and (E) taruka, reprinted with permission from Ref. [66], 2024, iNaturalist.

3. Results

3.1. Biophysical Analysis

3.1.1. Analysis of Place and Topography

Figure 11, shows the intervention area corresponding to the ancient city of Pisaq (Pisaq Archaeological Park), along with a topographic map that includes contour lines every 10 m. This map indicates a minimum altitude of 2960 m.a.s.l. and a maximum altitude of 4090 m.a.s.l. [68]. This layout facilitates a clear visualization of the topographic slope of the area. In this three-dimensional representation, the slopes exhibit inclinations ranging from 65.9% in section B–B′ to 73.4° in section A–A′. This variability in inclination allows for the construction of terraces that ingeniously adapt to the terrain conditions. This remarkable adaptation highlights how these structures not only integrate into the landscape but also optimize land use and water management in a mountainous environment [67,68].

3.1.2. Hydrogeography

Figure 12 shows the Alto Urubamba micro-basin, which is part of the Urubamba basin and covers an area of 21,173 km² [69]. This representation highlights the main river, Vilcanota, along with other tributaries within the delineated area, such as the Colipala River, which is 1.7 km long, the Pillatahuaygo at 1.51 km, and the Quilhuacocha at 0.56 km. These rivers are fundamental water sources that irrigate the terraces and supply the hydraulic infrastructure of the Pisaq terraces through evaporation processes influenced by wind and precipitation. This system is essential for agricultural development and the sustainability of communities in the region, thus enabling the prosperity of agricultural activities in a mountainous environment [67,69].

3.1.3. Species Distribution

In Figure 13, some dominant species in the delineated area are visualized. It presents flora such as species Figure 13A asiento de suegra (Oroya peruviana), which predominates at 65%, and fauna such as species Figure 13 B peregrine falcon (Falco peregrinus), which predominates at 100% of the delineated area [65,66,67]. Additionally, threatened flora species include Figure 13C Trompeta de angel (Brugmansia sanguinea) and Figure 13D Lobivia hertrichiana; fauna species include Figure 13E chinchilla (Lagidium viscacia). Other species of fauna include camelids such as the Figure 13F alpaca (Vicugna pacos) and the Figure 13G llama (Lama glama) [70,71].

It is important to note that camelids played a fundamental role in Inca society, as their high-quality fiber was essential for textile production, a key resource in the empire’s economy [73]. In particular, llamas were vital as pack animals, facilitating trade and communication throughout the territory. Although their consumption was not common, they could also serve as a food source in times of scarcity. The possession of these animals not only represented wealth and social prestige but also held deep spiritual significance, being used in rituals and sacrifices [73].

The management of livestock in Pisaq, as part of the Inca Empire, was characterized by meticulous and structured organization. The michic (herders) were responsible for the care of the animals and were under the supervision of the llama-camayoc, who acted as the head shepherd. The management of herds also included the phattachiri, in charge of dividing the animals, as well as specialized personnel for taming llamas, known as yachachiri. The villages had cchuyhua or llamacancha (large corrals), and for separating the herds, specific corrals called cachicallanca were used [73].

The animals were marked through a procedure known as chimpuni, which involved piercing one or both ears and passing threads of wool of different colors to indicate their owner. This process was carried out in the presence of the phattachiri and had severe repercussions; any attempt to alter the mark could result in the death penalty. The marking was conducted during the month of Ccoya Raymi, which spans from 22 September to 22 October. It is worth noting that the harvested alpaca fiber was distributed among the ayllus, which were obliged to weave their own clothing. Additionally, specialized weavers, known as cumbi camayoc and ccacllas, who worked full-time, contributed to the textile production of the empire [73].

3.1.4. Life Zone

Figure 14 shows the predominance of the Lower Montane Dry Forest life zone [67,74]. This zone has several defining characteristics. Its extent covers the Meso-Andean valleys, including the Vilcanota River. Its climate, where the annual average evapotranspiration exceeds precipitation by one to two units, defines the region’s humidity [75]. Its relief and soils exhibit an edaphic pattern characterized by medium to heavy-textured soils with good drainage, classified as Kastonezems. The vegetation includes areas cultivated through irrigation or rainfall, with significant plant indicators such as retama (Spartium junceum), eucalyptus, maguey, capuli, and chamana [75]. Likewise, the current and potential use of land is limited by the low precipitation which restricts rain-fed agriculture and makes it necessary to rely on irrigation for crops [75]. This is evident in the irrigation systems of the terraces in Pisaq, which are distributed in parts of the Culispata ravine, near the Vilcanota Valley [69].

3.1.5. Ecological and Economic Zoning

Figure 15 shows the Mountain Slope Protection Zone, which presents physical, physicochemical, and biological characteristics [67,76]. Physically, the area receives an annual precipitation of 1200 mm and features mountainous slopes. Regarding physicochemical characteristics, the soils are slightly acidic, well-drained, and exhibit low fertility, making them unsuitable for agriculture. Biologically, the dominant vegetation consists of sub-humid shrubland found in inter-Andean valleys [77]. The recommended use indicates that the characteristics of the terrain limit its suitability for agriculture and logging at present [77]. However, these areas have significant economic value in terms of wildlife, landscapes, and tourism. Additionally, they serve as refuges for biodiversity, both plant and animal, represented in the distribution of species and life zones [71,74]. Therefore, the management approach focuses on conservation, afforestation, reforestation, and promoting applied research. In contrast to current management, in ancient times, these practices were integrated through the Andean worldview, reflected in the design and use of terraces as a harmonious adaptation to the natural and cultural environment [77].

3.2. Spatial Analysis

3.2.1. Accessibility

Figure 16 shows that Pisaq has two main access points. The first (1), from the south, begins at the city square of Pisaq and follows the collector road Ca. Intiwatana. This access is pedestrian in nature, with sloped stairs, allowing for the observation of the dryland terraces of Acchapata [78]. The second access (2) is located in the north and is made via the provincial road CU-112 and its annex CU-964, allowing vehicles to reach a parking area close to the K’allq’asa terrace [79].

Additionally, Pisaq has a strategic location that facilitates access to other important Inca centers, thereby reinforcing its connection to the Qhapaq Ñan, the Inca Road network that linked vast areas of the empire. This interconnection not only highlights its historical and cultural significance but also positions Pisaq as a key point in the exchange and communication system of the Inca civilization [33,67].

3.2.2. Site Analysis and Solar Orientation

Figure 17 shows how sunlight casts shadows over the terrace area from the east-facing slopes, where the first rays of the sun illuminate the Llaqta of Pisaq. This sunlight bathes the terraces before 6 a.m. throughout the year, which is fundamental for the development of crops on the terraces [80]. Prolonged solar exposure promotes optimal plant growth, thereby increasing the agricultural productivity of the site.

Moreover, a terrace and its solar orientation acquire special significance on key dates, such as 21 December, corresponding to the summer solstice, and 20 June, corresponding to the winter solstice. On these days, the solar position maximizes the incidence of light and heat, essential factors for the agricultural cycle of Pisaq [81]. The summer solstice coincides with the celebration of Capac Raymi or Hatun Raymi, a festival dedicated to Viracocha, the supreme god of creation in Inca mythology. This celebration symbolized creation and the fertility of the land, marking the beginning of the agricultural cycle and the planting season [81]. On the other hand, the winter solstice is associated with Inti Raymi, a period during which ceremonies and rituals were conducted, including dances, offerings, and the participation of the Inca, regarded as the Hijo del Sol (Intip Churin). This celebration not only honored the sun as a deity but also recognized its importance for plant growth and food production, serving as gratitude for past harvests [81].

3.2.3. Zoning, Distribution, and Circulation

The distribution of terraces is carried out in three zones, each composed of two or three terrace systems. These systems consist of cultivated terraces, which are divided by irrigation channels or steps.

Figure 18 shows the zoning of the terraces, organized into different areas. Zone 1 includes the terraces (1A) Ceremonial Terrace and (1B) K’allaq’asa terrace, located near the K’allaq’asa enclosure and the Amaru punku gateway. Zone 2 contains the terraces (2A) Qhosqa Qhosqa and (2B) P’isaqa terrace, which are located close to the P’isaqa enclosures and the Intiwatana enclosures. On the other hand, Zone 3 consists of the terraces (3A) Acchapta and (B) Rakiyoq, as well as (3B) Wanuwanupata, and (3D) Q’ente muyurina terrace situated near the Q’ente muyurina towers enclosure and other cultivated terraces. Additionally, the internal circulation is visualized, facilitating the connection between the terraces and the enclosures, which is useful for the mobilization of food and other agricultural activities [82,83]. This arrangement optimizes space usage and also reflects the strategic planning of the Inca civilization in managing its resources and organizing its territory.

Circulation in the area occurs through slopes with ups and downs, using paths of varying widths depending on the zone and the width of the terraces, as in certain sections the platforms also form part of the route. The paths that cross the buildings in Zones 1 and 2 reach a maximum width of 1.20 m, while in Zone 3, where the terrain is more complex, the paths are reduced to approximately 0.70 m and incorporate steps and sloped paths. This design variation facilitates transit adapted to the area’s topography, ensuring access without compromising the integrity of the archaeological environment. [83].

The management of zoning, construction, and maintenance of the terraces in the Inca civilization was the responsibility of the Apu, Kamachikuq, and other local authorities, who supervised the work through the mita system [84]. This mandatory system required the active participation of members of indigenous communities in agricultural projects, being essential in areas that demanded labor-intensive tasks for land preparation, sowing, and harvesting. They also played a crucial role in meeting the tax obligations established by the Inca state [85]. In contrast, the minka was a community work system that promoted cooperation and reciprocity among community members, allowing people to come together to carry out agricultural tasks, including those related to cultivation on the terraces [85]. This approach not only facilitated agricultural production but also strengthened social cohesion and mutual support within the ayllu, consolidating the bonds between its members and ensuring collective well-being [85].

3.2.4. Sizing and Architectural Elements

Figure 19 shows the dimensions of the terraces in all zones, and the total area of their extent, as well as the surface of the agricultural terrace platforms constructed by the Incas, is calculated. This analysis provides a detailed view of the spatial distribution and productive capacity of each terrace, facilitating a better understanding of their design and functionality within the Inca agricultural system. By evaluating these characteristics, it can be observed how the Incas optimized land use by creating terraces on gentle slopes in Zones 1 and 2, as well as in more rugged areas, such as in Zone 3. This strategy aimed to maximize agricultural production [67].

3.2.5. Architectural Principles

The Inca terraces are analyzed through key architectural principles, such as the concept of axis, which connects two points in a symmetrical and balanced manner [86]. Additionally, symmetry organizes and distributes space harmoniously, while repetition is characterized by the reiteration of elements with subtle variations in details, size, or contour [86]. Another relevant principle is hierarchy, which assigns importance to a space based on its size, shape, or location relative to others. The datum is also considered, which structures spaces through lines, planes, or volumes, and rhythm, defined by the alternating or modulated recurrence of elements [86].

A.

Axis, Symmetry, and Repetition

Figure 20 shows terraces such as Figure 20 (3C) Q’ente muyarani terrace and Figure 20 (3D) Wanuwanupata, where the main axes marked by steps organized alongside the irrigation channel stand out. These axes are visible on specific platforms where primary circulation is established. The arrangement of these elements creates symmetry in the terraces, which in some areas is bilateral, contributing to a sense of balance in the expanse of the terraces by placing similar elements. Additionally, a central symmetry is observed where the platforms change angle based on the topography, adapting to the terrain and highlighting the functional and aesthetic integration in the design of the agricultural system [86].

This perspective visually groups elements in which repetition is apparent due to their proximity and shared characteristics, such as the stone structures and the cultivation terraces. This repetitive arrangement begins on the first platform and extends down the slope, adapting to the dimensions of the terrain and the topography, creating stepped platforms whose sizes and contours vary continuously. Furthermore, certain details, such as embedded stones, steps, and irrigation channels, are integrated into each terrace, reinforcing the visual cohesion of the whole [86].

B.

Hierarchy, Datum, and Rhythm

Figure 21 shows a clear spatial hierarchy of Figure 21(1A) Ceremonial terrace, distinguished by its square contour compared to the other terraces in the archaeological park, suggesting a distinct functionality, possibly of a ritual or ceremonial nature. Likewise, terrace Figure 21(2A) Qhosqa stands out for its architectural composition and large size; located in the eastern area of the archaeological park, it fully utilizes the topography to maximize the agricultural cycle, optimizing its relationship with the sunrise and integrating functional and symbolic elements into its design [86].

Both elements follow the principle of datum, much like Figure 21(1B) K’allaq’asa terrace, where topographic lines or contour lines serve as a visual basis, guiding the arrangement of the agricultural platforms. This organization creates a visual continuity in the terrace system, harmoniously integrating the agricultural structures with the natural relief of the land. Additionally, a rhythm is perceived in the design of the terraces, arising from the modulation of elements arranged at both regular and irregular intervals. The regular intervals, generated by variations in topography, give rise to well-defined geometries, as seen in Figure 21(1A) Ceremonial terrace. In contrast, the irregular intervals allow the terraces to integrate more organically with the surrounding terrain, adapting without significantly altering the topography, thus creating a continuity in the system that reinforces both the aesthetics and functionality of the agricultural landscape [86].

3.3. Functional Analysis

3.3.1. Geomorphological and Geophysical

Terraces allow agriculture in mountainous areas or steep slopes, where conventional agriculture is difficult or unviable, thus expanding the areas available for food production [87]. These terraces typically have rectangular or trapezoidal shapes and are designed with multiple levels of stepped terraces, adapting to geographical conditions [88].

Figure 22 shows the steep reliefs were artificially modified and adapted. The strata include E1, Controlled Inca Fill (RCI), composed of well-graded gravels (GW), and E2, Igneous Rocky Massif, formed by shoshonitic andesite with an average design resistance (RPD) of 714 k/cm² [89]. The RCI allows for leveling surfaces, uniformly distributing vertical loads, and directing rainfall to the subsurface for collection and drainage. This system was also applied in the Llaqtas, where terraces with retaining walls can be observed, evidencing the use of local and natural materials in their construction [89].

3.3.2. Hydrology

Figure 23 shows that the terrace system, constructed using ancestral agricultural engineering techniques, facilitates water infiltration into the soil, increasing its moisture and thus promoting crop development. These techniques, developed and perfected by Andean civilizations, reflect a deep understanding of the environment and the available natural resources [90]. By modifying the microtopography of the slopes, the terraces act as sinks, creating flat areas that not only allow for better water management but also reduce the velocity of water flow. This ingenious design not only optimizes water use but also contributes to soil stability, minimizing erosion and promoting a more balanced ecosystem [91]. Moreover, they are effective in reducing runoff by 75–80%, thanks to factors such as vegetation cover, soil depth, organic matter content, the presence of clastic rock and gravel, as well as the width of the terraces [92]. In terms of water use efficiency, the terraces allow for optimal distribution and control of irrigation, which is crucial for cultivating a wide variety of plants. This terrace system not only maximizes soil moisture retention but also facilitates the capture and storage of rainwater, thereby ensuring an adequate supply for crops [93,94].

This careful management of water resources underscores the importance of water in Inca culture, which was manifested in the celebration of Um raymi, a festival dedicated to the mountains and water, held in the eleventh month of the Inca calendar. This ritual sought to invoke the fertility of the land and ensure good harvests, showcasing the deep connection of the Incas with natural elements [95]. These ceremonies were fundamental within their worldview and religious practices, evidencing the integration of water management and their spiritual beliefs, both inseparable elements of the daily and productive life of Inca society [95].

3.3.3. Climatology

Microclimates are defined as areas where solar radiation and rainfall energy are received and dissipated, generating climatic conditions that differ from the general climate of a region. This phenomenon arises from the maximum interaction of frictional forces within these spaces, rendering them unique [96]. In a 24 h energy cycle, heat gain occurs from sunrise, approximately at 6:00 a.m., until 4:31 p.m. Subsequently, a period of energy loss begins, extending until the next solar cycle [97].

Figure 24 shows that the terraces are protected from the direct effects of the anabatic flow originating from the slopes [98]. This flow refers to the movement of warm, humid air ascending from lower areas to higher altitudes, which can impact local climatic conditions. By being shielded from this flow, the terraces can maintain a more stable microclimate [98]. The circulation flows within each terrace facilitate the ingress of heat and moisture while allowing for a controlled exit of water vapor and carbon dioxide (CO₂) from the system. This dynamic is crucial for optimizing growth conditions for crops and the sustainability of the agricultural ecosystem. These processes not only preserve the greenhouse effect within the microenvironment of the terraces but also mitigate energy loss through the anabatic flow, thereby generating more favorable microclimatic conditions [99]. Moreover, a reduced greenhouse effect increases energy loss, which in turn enhances energy availability in the terraces compared to natural conditions. This technique stands as a testament to Inca knowledge, reflecting a profound understanding of the interaction between microclimates and agriculture [99].

3.3.4. Edaphology and Ecology

The terrace system helps control erosion processes, reducing soil loss by up to 90% by decreasing both surface runoff and the erosive capacity of water [101]. Additionally, infiltration and reduced water erosion enhance soil moisture, organic matter content, and soil fertility [102]. By maintaining soil fertility and promoting sustainable agricultural practices, terraces contribute to the conservation of local biodiversity and ecological balance in the areas where they are implemented [103].

Figure 25 illustrates the food chain shown in Figure 25A, which includes producers, primary consumers, secondary consumers, and tertiary consumers, a system essential for sustaining the nutrient cycle and crop growth in the region. This chain, represented in Figure 25B, includes critical crops such as potatoes (Solanum tuberosum), cassava (Manihot esculenta), sweet potatoes (Ipomoea batatas), and broad beans (Vicia faba), whose interrelationships not only strengthen ecological resilience but also ensure the long-term sustainability of the agricultural system. Moreover, this diversity of crops highlights the importance of maintaining a balanced and healthy ecosystem, contributing to the overall well-being of the community [104,105].

This fact shows that during the time of the Incas, agriculture in Pisaq thrived through a carefully maintained balance throughout the entire agricultural cycle. During this period, the Kamachikuq supervised specialists such as the Chakra kamayuq, who were responsible for the cultivated lands and played a crucial role in organizing and managing activities, from harvesting to various tasks associated with agricultural production, as shown in

Table 2. Calendar of Agricultural Activities [84].

Months	Agricultural Tasks	Specialists
January	Zara papa ballamy mita: The turn to clean, weed, and hill the corn and potato fields	Chakra kamayuq
February	Chaqmay mita: The turn to break the virgin soil. Zara tuta qaway mita: the turn to tend the corn.	Pisqu kamayuq
March	Zara qaway mita: The turn to tend the corn.	Arariwa paryan pachaqa Paryan arariwa
April	Zara puquy zuwamanta waqaychay mita: The turn to mature the corn and protect it from thieves.	Pachaqa arariwa
May	Zara kalchay arkuy mita: The turn to cut the corn and stack it.	Kallchaq
June	Month of abundance and festivity. Tilling of the land.	Pachaqa
July	Zara papa apaykuy aymuray mita: The turn to store potatoes and corn.	Qullqa kamayuq
August	Haylli chakra yapuykuy pacha: The time to joyfully plow the fields.	Apu, Kamayuq
September	Zara tarpuy mitan: The turn to plant corn.	Zara tarpuq Kamayuq
October	Chackramanta pisqu qarquy pacha: The time to drive away the birds from the fields.	Paryan arariwa pachaqa
November	Zara qarpay, yakuy muchuy, rupay pacha: The time to water the corn, during the water scarcity and heat.	Zillkiwa
December	Papa uqa tarpuy pacha: The time to plant potatoes and oca.	Zillkiwa

[84].

It is important to highlight that for the Incas, agriculture was not just a means of subsistence but a sacred act honoring Pachamama, Mother Earth. By designing the terraces to respect and integrate natural flows, the Incas demonstrated a deep understanding of nature’s cycles and a strong commitment to sustainability [84]. This integrated system ensured not only the sustainability of crops but also fostered a harmonious relationship with the environment, guaranteeing the constant availability of essential resources for the sustenance of the ayllus residing in Pisaq [84].

3.4. Constructive Analysis

3.4.1. Constructive Elements and Materiality

Figure 26 shows a detailed cross-section of the structure, highlighting the main construction elements. Prominent is the retaining wall composed of large stones, followed by the foundation of the cultivation terrace, which includes a layer of large stones topped with smaller ones [106]. Above this base lies a fill consisting of layers of soil mixed with small stones and gravel, culminating in the upper layer, which corresponds to the arable soil. This structural arrangement ensures stability and optimizes moisture retention, thereby facilitating cultivation on terraces. Another important element is the tuycos or taca, which are stones embedded in the wall that serve as steps for circulation [106,107,108].

3.4.2. Typology of Terraces

According to Kendall, there are four types of terraces, among which Terrace Types 1 and 2 are identified.

Figure 27 shows two types of terraces. In Figure 27A terrace type 01 is depicted in a cross-section, showcasing its typical structure with variations such as the wall’s inclination, which has a projection ranging from 5 to 15°, in addition to a stepped intermediate foundation for the terrace and an irrigation channel. Conversely, in Figure 27B terrace type 02 is observed, which, while sharing the characteristic of a stepped intermediate foundation, features a vertical wall with a projection of 90° [106]. These structural variations illustrate the specific adaptations of the terraces to their environment and the irrigation needs in each instance, as presented in

Table 3. Types of terraces in the Archaeological Park of Pisaq [106].

Type	Platform Profile	Retaining Wall	Irrigation System	Distinctive Factors
1	Horizontal	Inclined	Yes	Stratigraphic fills of stones and soils
2	Horizontal	Vertical	Yes and No	Backfill of some stones behind the foundation or base

.

A.

Type 1 terrace

Figure 28 shows the terrace referred to as Terrace 1A (Ceremonial terrace), characterized by steeply inclined retaining walls and an irrigation system. Circulation is facilitated through steps and taca (embedded stones in the wall). Currently, its condition is satisfactory, owing to the maintenance conducted on the terraces, which includes controlling weed growth and clearing the irrigation channels.

Figure 29 shows the terrace 3C (Q’ente muyurina terrace) and the terrace 3D (Wanuwanupata) are presented, both characterized by vertical retaining walls and an irrigation system situated alongside the steps. Circulation is facilitated through these steps and by tuycos (embedded stones within the walls). Currently, part of the circulation is still maintained via the steps of the terraces.

B.

Type 2 terrace

Figure 30 the terrace 3A (Acchapata) is illustrated, characterized by its vertical retaining walls and the absence of an irrigation system, which restricts cultivation to dryland farming. Movement within this terrace is facilitated by steps, tacas (embedded stones within the walls), and a platform. In contrast, the terrace 3B (Rakiyoq) features an irrigation system and provides circulation through platforms and embedded stones integrated into the wall structure. Although both terraces are in good condition, access to them is limited due to geological instability and other factors.

3.4.3. Terrace Morphometry

Table 4. Morphometry of terraces in the Archaeological Park of Pisaq [67].

Zone	Code of Terrace	Length (m)	Width (m)	Wall Height (m)	Rock Diameter (mm)	Max. Slope (%)
1	A	Min.: 17.26	Min.: 3.22	Min.: 3.50	Min.: 220	44.5
		Max.: 60.86	Max.: 12.89	Max.: 4.05	Max.: 290
	B	Min.: 135.83	Min.: 1.63	Min.: 3.10	Min.: 210 Max.: 270	48.5
		Max.: 355.69	Max.: 33.2	Max.: 4.00
2	A	Min.: 5.73	Min.: 1.28	Min.: 2.60	Min.: 230	52.4
		Max.: 192.52	Max.: 38.98	Max.: 3.15	Max.: 250
	B	Min.: 5.40	Min.: 1.22	Min.: 2.40	Min.: 240 Max.: 260	70.4
		Max.: 115.47	Max.: 6.52	Max.: 3.20
3	A	Min.: 33.25	Min.: 2.19	Min.: 2.10	Min.: 250	66.5
		Max.: 78.66	Max.: 14.34	Max.: 2.40	Max.: 600
	B	Min.: 11.31	Min.: 2.14	Min.: 2.60	Min.: 290 Max.: 400	69.1
		Max.: 86.11	Max.: 6.37	Max.: 2.90
	C	Min.: 23.66	Min.: 2.42	Min.: 2.40	Min.: 210 Max.: 320	67.8
		Max.: 101.05	Max.:4.10	Max.: 2.80
	D	Min.: 32.07	Min.: 2.52	Min.: 2.10	Min.: 180 Max.: 260	65.5
		Max.: 121.61	Max.: 5.65	Max.: 2.40

presents the morphometry of the terraces in the archaeological park, including dimensions such as length, width, rock diameter, and slope [67].

4. Discussion

The pre-Hispanic terraces of the Inca civilization represent an innovative and effective solution for agriculture in mountainous terrains, transforming steep slopes into flat and fertile surfaces, thereby increasing cultivation capacity [41]. Under the administration of figures such as the Apu and Kamayuq, who managed collective labor through the mita and minka systems, the agricultural cycle was regulated with precision, adapting to the complexities of the Andean landscape and optimizing the use of natural resources [84]. This system not only ensured efficient water retention, which is essential in regions facing water scarcity, but also facilitated agricultural diversification across different ecological zones, allowing for a rich and varied diet [109]. In emblematic sites such as Pisaq, Ollantaytambo, Moray, and Tipon, the Incas demonstrated their vast agricultural knowledge, organizational capabilities, and respectful connection with the environment; by integrating social, economic, and cultural elements, they established a sustainable model that continues to be admired today for its harmony with nature and its ingenious use of microclimates for food production [109].

From a biophysical perspective, the archaeological centers of Pisaq, Ollantaytambo, Moray, and Tipon exhibit ingenious, sustainable, and efficient agricultural adaptations, each designed to maximize productivity in its particular environment, demonstrating the profound Inca knowledge in natural resource management. In analyzing location and topography, Pisaq features slopes ranging from 34° to 61°, configuring terraces that optimize land use by controlling erosion and enhancing water retention. Ollantaytambo, with an average slope of 42.5%, illustrates the Inca ability to manage resources in mountainous terrain sustainably [67]. Similarly, Tipon, located in areas of steep incline, benefits from its terraces to create microclimates that retain water, thereby facilitating cultivation in a mountainous environment [38]. In contrast, Moray stands out for its concentric layout, generating temperature variations at each terrace level, which enables the cultivation of diverse species in confined spaces, effectively utilizing the site’s topographical uniqueness [37].

In terms of hydrogeography, these four sites showcase advanced approaches to water management. Tipon is notable for its intricate hydraulic system of channels and springs, which ensures water distribution across each terrace, even during drought periods, primarily sourced from the Apurímac River [37]. Pisaq also has a channel system that facilitates the irrigation of the terraces, harnessing water from tributaries that feed the Vilcanota River [43]. Ollantaytambo benefits from its proximity to the same river, employing aqueducts to irrigate its terraces and ensuring a constant water supply [36]. subtle although the irrigation system is more subtle in Moray, the concentric terraces capture and retain moisture, taking advantage of the microclimates created at each level and situated within the Urubamba River basin [37]. Each site demonstrates Inca knowledge in adapting irrigation systems according to their specific geographic conditions.

Additionally, the ecological and economic zoning in Tipon, Pisaq, and Moray reflects a territorial organization focused on sustainable productivity. In Tipon, the zoning is designated for producing tubers and grains, complemented by areas for grazing and gathering [39]. Pisaq exhibits integrated zoning with specific areas for cultivation, housing, and storage, ensuring community self-sufficiency [43]. Ollantaytambo’s zoning emphasizes agriculture and trade, with agricultural terraces near the valley and exchange zones [36]. Moray, with its experimental approach, divides the area into concentric terraces to analyze the effects of microclimates on the growth of various crops [37]. The zoning in these centers underscores the Inca’s ability to integrate ecological and economic planning into their agricultural practices, ensuring the sustainability of their resources.

Furthermore, spatial analysis of the terraces in Pisaq highlights a remarkable variability in dimensions, ranging from 4.89 hectares to 110.20 hectares [67]. This diversity not only demonstrates the flexibility of Inca agricultural practices but is also complemented by a network of paths that effectively connect these structures, facilitating the movement of people and products within the agricultural area [43]. Similarly, in the archaeological site of Moray, the terraces are organized in circular and concentric formations, capturing crucial microclimates for the growth of diverse crops [37]. In Pukará Alto, within Tipon, advanced Inca hydraulic engineering is evident with 43 interconnected terraces linked by paths that enhance accessibility and reflect the detailed planning of this civilization [38].

The functional analysis of the Pisaq terraces encompasses a multidimensional perspective. From a geomorphological standpoint, the strategic placement on the terrain facilitates slope control, while from a geophysical perspective, the RCI (Inca Constructions) emerge as key components for structural stability [87,88,89]. Hydrology reveals how the terrace system mitigates runoff and optimizes water use [92]. Climatologically, the microclimates created by the terraces and their small-scale greenhouse effect benefit the cultivation of a variety of plants, while in terms of edaphic and ecological factors, biodiversity in crops and soil organisms sustains a trophic pyramid that balances the agricultural ecosystem [96,104]. Complementarily, in Moray, the terraces in circular formations control microclimates, allowing for crop diversification according to each level and enhancing agricultural productivity [37]. With a system of stone channels efficiently distributing water, the terraces of Moray and those in Sectors 1 and 2 of Pisaq demonstrate similarities in their advanced engineering [37,43]. Moreover, the terraces in Ollantaytambo play a crucial role in preventing erosion by controlling water velocity on the slopes, which contributes to preserving soil fertility [36].

Finally, the constructive analysis of the archaeological sites reveals reveal significant similarities in their structural systems, highlighting the use of granite blocks of various and sizes, selected and placed with precision to ensure terrain stability and effective drainage [34]. These designs integrated both worked and natural stones, providing structural flexibility and allowing for better adaptation to environmental conditions. The arrangement of these elements in quadrilateral, circular, and curved configurations, organized into interconnected units, favored the creation of harmonious and coherent sets that reflect a remarkable level of planning and architectural skill characteristic of the Incas [36,37,38,43].

5. Conclusions

The pre-Hispanic terraces of the Inca civilization represent a significant achievement in agricultural engineering, demonstrating their extraordinary ability to adapt agricultural practices to mountainous terrain. This system transformed steep slopes into fertile and productive spaces, facilitating food production under challenging geographic conditions. The management of collective labor, led by figures such as the apus and kamayuq, optimized the use of natural resources and ensured efficient water retention, thereby promoting the diversification of crops across various ecological zones.

Moreover, the ecological and economic zoning observed in these sites reflects the Incas’ skill in organizing territory sustainably, thereby ensuring the self-sufficiency of communities through a balanced use of resources.

Spatial analyses of the terraces at Pisaq and other archaeological sites reveal the remarkable diversity and adaptability of agricultural practices within the Inca civilization. The dimensions of the Pisaq terraces, which range from 4.89 hectares to 110.20 hectares, highlight the flexibility in agricultural design, while the network of pathways interconnecting these structures facilitates the movement of people and products, optimizing operational efficiency in the agricultural zone. Additionally, the terraces, combined with advanced hydraulic engineering, demonstrate meticulous planning that maximizes space utilization and captures essential microclimates for the growth of diverse crops.

In functional analysis, the Pisaq terraces represent an ingenious agricultural system adapted to the characteristics of the mountainous terrain. Their strategic placement enables effective slope control and optimal water management, mitigating runoff. The generated microclimates promote crop diversity, while soil biodiversity sustains a balanced ecosystem. Although they share similarities with other sites such as Moray and Ollantaytambo, the uniqueness of Pisaq lies in its multidimensional approach, integrating geophysical, hydrological, and climatic factors, thereby ensuring the sustainability and success of Inca agricultural practices over time.

In terms of constructive analysis, the Pisaq terraces reveal the use of granite blocks of varying dimensions, selected and positioned with precision to ensure terrain stability and effective drainage. The combination of worked and natural stones provides structural flexibility and allows for efficient adaptation to the environment. The arrangement of these elements in quadrilateral, circular, and curved configurations, organized into interconnected units, results in harmonious sets that reflect the architectural planning and skill of the Incas in Pisaq.

The Inca agricultural works in Pisaq not only reflect the ingenuity of this civilization but also serve as a model of sustainability and respect for the environment, whose legacy continues to be admired and studied today. This complex and functional agricultural system positions Inca practices as a fundamental pillar of their civilization, exemplifying their adaptability and resilience in the face of environmental challenges. Additionally, it reflects a profound respect for local cultures and a design meticulously adapted to the climate, embodying a community-centered approach that resonates with contemporary sustainable architectural projects [110].

It is crucial to note that Inca culture has left a legacy of sustainable architecture through its terrace systems, which align with current Sustainable Development Goals (SDGs). Significant similarities can be observed with several of these goals, such as SDG 11, which promotes sustainable cities and communities; SDG 13, which focuses on climate action; SDG 15, which centers on the conservation of terrestrial ecosystems; and SDG 6, which seeks to ensure access to clean water and sanitation. This connection between Inca agricultural principles and the SDGs underscores the relevance of ancestral practices in the contemporary context, emphasizing the importance of learning from the past to address current environmental challenges [111].