1 INTRODUCTION

Construction projects often consist of superstructure and substructure components. Substructure refers to the part in contact with the soil, transferring superstructure loads to the bottom or surrounding soils and called the foundation. Foundation design requires close collaboration between structural, geotechnical, and construction engineers. The structural behavior of the underground structure and the foundation system needs to be adequately captured, and these, in turn, need to be based on the foundation response provided by the geotechnical engineer (Poulos, 2017). The analysis and design of foundations are iterative processes since the magnitude of imposed loads, the corresponding settlement, and the foundation geometry are interdependent and are affected by the geotechnical capacity, structural capacity, and settlement requirements (Fellenius, 2015). The primary criteria in the analysis and design of foundation systems are presented and emanated in load–displacement records (Eslami & Ebrahimipour, 2024).

Foundations have conventionally been divided into two categories: shallow and deep. Shallow foundations transfer loads to the bearing strata at a small foundation embedment depth ( $D_{\mathrm{f}}$ ) to width (B) ratio ( $D_{\mathrm{f}}$ /B), as depicted in Figure 1a. With the rapid growth of civilization, there has been a dependence on deep foundations ( $D_{\mathrm{f}}$ /B $\ge 10$ ) to construct infrastructures (Elhakim, 2005). Figure 1d shows a schematic view of sample deep foundations. The application of in situ testing for the geotechnical design of deep foundations is addressed and emphasized by Shirani et al. (2023).

Realizing the limitations of shallow and deep foundations, semi-deep foundations and a combination of shallow foundations together with ground modification are introduced as intermediate solutions (Eslami et al., 2020). Figure 1b,c depict examples of the two intermediate solutions. Semi-deep foundations are constructed in the B to 4B depth range for better load transfer and passing through soft layers (Rezazadeh & Eslami, 2017). Ground modification may be a viable alternative to costly foundations in conditions confronting problematic deposits (Eslami et al., 2024; Shakeran & Eslami, 2013). In such cases, the retrofitted mass of soil plays a significant role in geotechnical performance, and just a transition part is needed to transfer the superstructure loads. Apart from problematic soils, other geomaterials, including rock, can be treated via special measures, such as grouting practices for fractured zones (Kang et al., 2022).

The dimensions of foundations, embedment depth, surrounding soil properties, and load combinations affect the foundation geotechnical and structural performances. In small ordinary footings, $D_{\mathrm{f}}$ /B is a notable factor. In others, contact area, soil confinement, modified properties, and so on, affect load-settlement behavior in addition to the depth-to-width ratio ( $D_{\mathrm{f}}$ /B) (Rezazadeh & Eslami, 2017). Rui et al. (2023) have used this concept to categorize subsea pipeline end manifolds. Therefore, the $D_{\mathrm{f}}$ /B parameter must not be considered as the only factor for defining foundation type (Yun & Bransby, 2007). In this respect, and considering the advent of a variety of construction methods, different foundations' behavior, complexity in the type and conditions of projects, and the new criteria in foundation design, a new insight and more versatile approach for foundation systems classification seem necessary, and these have been the main objectives of the authors.

A new foundation categorization is introduced based on the theory of structures. Based on the form aspect, one-dimensional (linear), two-dimensional (planar), and three-dimensional (volumetric) foundations have been realized. Incorporating load transfer mechanisms, linear foundation systems are considered vector-acting, planar ones are divided into section-acting and surface-acting, and volumetric ones are recognized as block-acting. The mentioned concept applies to various geostructures under and above the ground, representing the necessity and significance of detailed assessment. A database of 22 case studies has been compiled to select and implement new foundations. It is composed of several offshore and onshore superstructures and different deposits. The concluded points have contributed toward evaluating foundations' alternative functions regarding geotechnical and practical aspects. Improved analytic hierarchy process (IAHP) methods have been applied for comparing, contrasting, and ranking the foundation alternatives qualitatively and quantitively. A perspective for building substructure implementation and selection is proposed, considering four prevailing groups of buildings and four typical levels of soil strength. The proposed algorithm is adapted through relevant case studies.

2 FORM AND LOAD TRANSFER ASPECTS OF FOUNDATION SYSTEMS

As an extension of structural engineering classification concepts, foundations can be classified based on their form. Three main categories can be recognized for foundations: one-dimensional or linear foundations, such as piles, and two-dimensional or planar foundations, such as spread footings and shell foundations. The third category includes box foundations and buckets, considered three-dimensional or volumetric (mass) foundations. Typical examples of form types of foundations and their prevalent transferred loads are depicted in Figure 2.

The foundation system comprises the embedded part of the structure and is surrounded by the underground soil of the lateral and underlying parts of the foundation unit itself. Indeed, the substructure can be considered a foundation system that comprises components such as walls, horizontal diaphragms, the surrounding soil, and the underground part of the structure. From a sustainability perspective, the most desirable geosystems with the least amount of artificial material and the largest volume of existing in situ geomaterials are involved in the foundation system.

Based on their load transfer perspective, structures can be divided into form-acting, vector-acting, section-acting, surface-acting, and hybrid. Form-acting structure systems are nonrigid, flexible, and secured by fixed ends, such as vertical hanger cables. Vector-acting structure systems comprising short, solid, linear members are structural components that can transfer only forces in their length direction, for instance, truss members. As fundamental elements of section-acting structure systems, beams can resist forces acting in the direction of their axis and those perpendicular to their axis via sectional stresses. Structural surfaces composed of elements forming mechanisms to redirect forces are surface-acting structure systems. Dissimilar structural systems can be connected to create a single operational construct with a new mechanism: hybrid structure systems. Examples of each structure system load transfer system are depicted in Figure 3 (Engel, 2013).

Figure 4 illustrates the load transfer mechanism of the above-mentioned foundation under imposed loads. In this regard, linear foundations bear the loads through shaft (side) and toe resistance as depicted in Figure 4a. Therefore, they are well recognized for transferring axial loads. The base resistance is the major resistant component of planar foundations. In shell foundations, which are considered planar foundations, the geometrical form contributes to the bearing process and enhances performance (as shown in Figure 4b). Volumetric or massive foundations, which can be realized as the geosystem (collection of soil and foundation unit), resist against a combination of loads via toe and shaft resistance. A comprehensive and interactive performance of various foundation elements, forming a block, can serve well in different conditions of superstructure and existing soil, as depicted in Figure 4c.

Considering their similarity to structural components and load transfer mechanisms, foundations can be realized similarly. The three main categories that were introduced based on form are divided into four types of foundation systems: vector-acting (e.g., single piles) as linear (1D), section-acting (e.g., mats) and surface-acting (e.g., shell foundations) as planar (2D), and block-acting (hybrid) (e.g., a mass-treated soil and piled raft foundation [PRF]) as volumetric (3D) foundation systems. A summary of the newly introduced categories is depicted in Figure 5.

2.4 Block-acting (hybrid) foundations

These foundations are among the most complete types of foundations in terms of soil and foundation interaction. Semi-deep foundations, especially marine ones, such as spudcans, buckets, and skirted ones, are the most prominent. For in-land projects, some typical instances are box foundations, PRFs, and foundations on the massively stabilized ground. Although the components may be vector-acting, section-, or surface-acting in a block-acting foundation system, they form a total hybrid system.

Skirted foundations, semi-deep circular foundations with thin skirts around the circumference (Figure 9a) and a retrofitted mass of soil, can act (see Figure 9b) as a block-acting (hybrid) foundation. Ground modification methods such as grouting or vertical and horizontal reinforcing can form a block-acting foundation. The retrofitted mass of soil bears the loads and the foundations implemented on or in it play only a transition role.

In box foundations, exceptional flexural stiffness is provided by using a block-acting (hybrid) foundation comprising floor and ceiling slabs and walls around the basement, as depicted in Figure 9c. Another instance of hybrid foundations is the PRFs. Like skirted foundations, the raft will perform as a section-acting foundation, and the piles are considered vector-acting foundations (Figure 9d).

3 DATA SET OF VARIOUS SUBSTRUCTURE SYSTEMS' CASE STUDIES

Twenty-two cases have been compiled from different countries to investigate the performance of each category of foundation systems on the basis of the reviewed design criteria. Information from different offshore and onshore projects, comprising various soil and foundation types, as well as remarks on the elaborated design, are encapsulated in Table 1.

The introduced foundation categories are focused on and addressed through reviewed case studies. Case studies 15 and 19 are examples of vector-acting foundation systems. Monopiles, realized as vector-acting, as mentioned in Cases 19 and 22, are the most common foundation alternatives for supporting offshore wind turbines (OWTs) (Bhattacharya, 2019). In such cases, dominant loads are horizontal loads and massive overturning moments (Amponsah et al., 2021); therefore, considerable foundation embedment depth is needed to resolve stability issues. Other loads, such as wave loads and ship impacts, may result in instability or failure of the monopile–soil system.

Section-acting foundations can be realized for Cases 4, 5, 9, 18, and 20. Two primary factors, suitable geotechnical conditions and low earthquake hazard, result in a planar foundation (raft foundation) instead of a massive PRF or a pile group (volumetric foundation). This issue clarifies the role of nonvertical load in combination with subsoil conditions in selecting the most appropriate foundation for a specific project. This issue arises from Cases 9 and 20.

Cases 2, 3, and 14 are among surface-acting foundations. Despite the typical assumption that deep foundations are essential for all tall structures such as communication towers, as in Cases 2 and 14, all horizontal and vertical loads are transferred through the raft or shell transition section to the subsoil. Moreover, uplift loads are tolerated via the gravity weight of the foundation and especially the transition structure. The considerable breadth of the raft provides resistant overturning moments against equivalent overturning moments and the foundation's weight supplies sliding resistance. Favorable existing soil conditions and the groundwater table in-depth contribute to the foundation for sustaining such a challenging structure without needing more complicated and massive foundations.

Block-acting foundation system instances are found in Cases 6, 7, 8, 13, and 21. Figure 10 presents different illustrations of various subsoil conditions chosen from existing cases. The foundation selection of the mentioned cases indicates the interactive role of the superstructure, foundation system, and the soil underneath in achieving efficient and favorable performance. Cases 11 and 21 are instances of soil improvement techniques being implemented as a complementary approach to typical foundation system solutions, leading to higher bearing capacity, more favorable stability, and lower settlement.

4 PERFORMANCE-BASED ASSESSMENT FOR VARIOUS FOUNDATIONS (NEW CATEGORIES)

Introduced Foundation system alternatives have been evaluated primarily based on two groups of factors: geotechnical and practical factors. Geotechnical issues generally involve considerations of bearing capacity, deformation, and stability. Practical aspects are mainly those factors relevant to ease and cost of construction and durability, along with sustainability and environmental aspects.

4.2 Practical aspects

The practical feasibility of a foundation refers to both constructability and sustainability issues. A foundation system's sustainability refers to its structure and the application of environmentally responsible and resource-efficient processes within the foundation life cycle: from planning to design, construction, operation, maintenance, renovation and rehabilitation, demolition, closure, and decommissioning. Overall, the following criteria are considered in this regard: construction cost (considering time and labor), durability, effective use of geomaterial, availability and possibility of reusing and recycling of the artificial material, ease of construction (degree of availability of equipment and straightforward construction and reinforcing methods), and construction environmental impacts. The general performance of each foundation system regarding the above-mentioned criteria is summarized in Table 3, based on evaluations proposed according to the experience of the authors.

Table 3. Assessment of foundation systems regarding practical aspects.

Criterion	Criterion ID	Vector-acting	Section-acting	Surface-acting	Block-acting (Hybrid)
Construction cost	P1	C	A	B	D
Durability	P2	B	C	B	A
Effective use of geomaterial	P3	B	E	B	A
Material reuse and recycling availability	P4	B	A	A	C
Ease of construction	P5	C	A	B	D
Construction environmental impacts	P6	C	B	A	D

• Note: Performance level: A = superior, B = remarkable, C = satisfactory, D = adequate, and E = inadequate.

Based on the material presented in Table 3, six factors, construction cost, durability, effective use of geomaterial, material reuse and recycle availability, construction ease, and construction environmental impacts, have been chosen for evaluating foundation systems. Based on the experience and investigations of the authors, the foundation system has been assessed from A to E. E is representative of the weakest and A is an indicator of the most favorable performance. The results obtained for each foundation system are depicted as radar charts in Figure 12. A similar approach has been used by Ebrahimipour et al. (2023).

The above-mentioned factors and the four alternatives for the foundation systems are evaluated using the IAHP method. The AHP deals with complex technological, economic, and sociopolitical problems. It attempts to unify the modeling of real-world problems and do away with existing fragmentation. The AHP approach to assess criterion weightings in multicriteria decision-making (MCDM) has become popular in different areas. There have been several previously published studies in geotechnical engineering that have applied the AHP approach as the primary tool in their analyses, particularly for landslide susceptibility assessment; among these are studies by Zangmene et al. ( 2023), Tri et al. ( 2024), and Liu et al. ( 2024). Due to limitations of the AHP method, such as rigorous consistency requirements and complex information extraction, the IAHP method has been proposed (Li et al., 2013) and is used here. In this method, after ordering the influential factors according to their importance using a discrete scoring scale from 1 to 10, the comparison matrix (CM) is constructed as follows:

  $$\text{If}{u}_i\ge u_j,\text{the matrix element} a_{\mathit{ij}}=\max \left(u_i-u_j,1\right).$$ (1)

  (2)

Where

$u_{i,j}$ scores from 1 to 10,

$a_{\mathit{ij}}$ comparison matrix elements.

Based on the concluding points of Sections 4.1 and 4.2 and using Equations (1) and (2), the general performance of foundation systems is realized. Comparison matrices are presented in Table 4 and 5. It should be noted that the scores written in parentheses are out of 10, and w is the weight, indicating the priority (average performance) of each choice, such that their sum will be equal to one. The scores are allocated based on the average performance of each foundation system alternative that was presented qualitatively in Tables 2 and 3. A to E have been considered 9 to 1, respectively, and the average scores are determined.

Table 4. Sorting comparison matrixes of geotechnical aspects.

Geotechnical aspects	Vector-acting (7)	Section-acting (3)	Surface-acting (5)	Block-acting (8)	w
Vector-acting (7)	1.000	4.000	2.000	1.000	0.350
Section-acting (3)	0.250	1.000	0.500	0.200	0.083
Surface-acting (5)	0.500	2.000	1.000	0.333	0.158
Block-acting (8)	1.000	5.000	3.000	1.000	0.409

Table 5. Sorting comparison matrixes of practical aspects.

Practical aspects	Vector-acting (7)	Section-acting (8)	Surface-acting (9)	Block-acting (6)	w
Vector-acting (7)	1.000	1.000	0.500	1.000	0.201
Section-acting (8)	1.000	1.000	1.000	2.000	0.281
Surface-acting (9)	2.000	1.000	1.000	3.000	0.367
Block-acting (6)	1.000	0.500	0.333	1.000	0.151

For calculating amounts of w, first, each value in a column is divided by the summation of values in that column, and then the summation of values of each row will be calculated as w of the foundation system in that row. The data provided in Table 4 and 5 are visualized in Figure 13a as a bubble chart. The coordinates of the bubbles are the weight of each foundation system type determined using the IAHP method for geotechnical and practical issues. The situation of each kind of foundation system compared to others is illustrated, which results in the fact that typically, higher technical performance is achieved along with lower practical performance. In this regard, engineers play an essential and artistic role in the efficient and optimum application of each foundation system alternative in different projects.

Based on the geotechnical assessment results, presented in Section 4.1, and the practical-based evaluation results presented in Section 4.2, the four different foundation systems have been compared generally and relatively, as depicted in Figure 13b.

The general trend for the interactive performance of different foundation systems can be compared in Figure 13b. It can be concluded that section- and surface-acting foundation systems have poorer geotechnical performance but are favorable regarding constructional aspects. On the other hand, despite the high geotechnical performance, hybrid foundation systems are not desirable regarding constructional aspects. The performance of vector-acting foundation systems is moderate considering both aspects.

5 CASE-BASED ADAPTATION FOR BUILDINGS' SUBSTRUCTURES

The height, type, and location of the superstructure are among the most influential factors in the pattern and magnitude of imparted loads on the substructure. Based on a comparison by Poulos (1988) of two offshore and onshore structures with the same height and weight, the vertical design load of the offshore structure was 35% larger than the onshore high-rise. Significant horizontal load and moment, 1600% and 500% larger, respectively, have been reflected in around 150% expansion in the foundation area.

The data from the site investigation are applied for the successful design of the foundation, choice of site, selection of foundation type, and operational integrity of the structure (ISSMGE, 2005). Lunne (2001) and Randolph (2004) reviewed the application of in situ testing for offshore sites. Subsurface soil conditions dictate the type and characteristics of the foundation system in many cases. Problematic geomaterials, also known as surprising or challenging, are prone to geotechnical problems such as bearing failure, large settlements, instability, liquefaction, erosion, and water seepage (Coduto et al., 2016; Han, 2015; Holtz et al., 2023).

Apart from problematic geomaterials, circumferential conditions may lead to geotechnical challenges, induced naturally, such as earthquakes, sinkholes, and floods, or human activities like adjacent construction and pile driving may make geotechnical conditions more severe (Han, 2015). The adjacency and its effect on the geotechnical performance of the foundations have been studied by Moghadasi et al. (2023) and Eslami et al. (2023).

Supplementary considerations are divided into issues relevant to construction and sustainability. Factors such as availability of material and utilities, net cost and time, transportation, and involvement of experienced human sources are the most crucial regarding practical and constructional feasibility. Optimum design concepts incorporating efficient material and utility consumption are recommended. The sustainability evaluation of foundations is performed by considering environmental (planet), economic (profit), and social (people) aspects. Future designs should focus more on pollution reduction and effective material consumption, as addressed through several studies, such as Basu et al. (2013) and Cho (2016).

To consider the conditions encountered in actual projects, under vertical loading and for routine conditions, four categories of superstructures comprising low-rise, up to 20 stories; mid-rise, 20–40 stories; high-rise, 40–80 stories; and tower, over 80 stories, are examined. The soil underlying the superstructures is assumed to be clay, and for the analyses, undrained conditions are assumed. Furthermore, four different levels of soil strength (Su), comprising soft ( $S_{\mathrm{u}}\le 50\mathrm{kPa})$ , medium ( , hard ( , and very hard ( , are considered for the clay. The average imposed stress from the superstructure on the foundation has been assumed to be 10 kPa for each story (Eslami, 2013). A raft foundation ( $D_{\mathrm{f}}=0)$ , an inverted cone shell foundation ( $D_{\mathrm{f}}=1\mathrm{m})$ , single piles (0.6 m in diameter and 20 m in length), and a PRF (combination of the assumed raft and one pile per ${\mathrm{m}}^2$ ) are assumed for the evaluation. The bearing capacity of the assumed foundations has been assigned via static analysis methods under undrained conditions. For raft and shell foundations, $q_{\text{ult}}=5.14S_{\mathrm{u}}+{\sigma }_{\mathrm{z}=D_{\mathrm{f}}}^{\prime }$ have been applied. For the shaft resistance of piles, $r_{\mathrm{s}}=\alpha S_{\mathrm{u}}$ , in which $\alpha$ varies with $S_{\mathrm{u}}$ and, for toe resistance, $r_t=9S_{\mathrm{u}}$ have been used (Eslami, 2013). The suggested general trend for the foundation system option for each data pair, which consists of soil strength and superstructure height, is determined. The results are depicted in Figure 14. The intersection of a vertical line from the soil type axis and a horizontal line from the superstructure height axis is the recommended option from the four categories of foundation systems.

The proposed illustration in Figure 14 can be adjusted to the cases listed in Table 1. In the Torre Latino project, Case No. 1, an office tower, realized as a high-rise, located on soft clay, a combination of floating foundation and deep foundations is applied, forming a block-acting system, as suggested by Figure 14. Similarly, for Messeturem Tower, Case No. 6, PRF as a block-acting foundation system is applied as recommended in Figure 14.

For Case No. 3, Nonoalco Tower, which has 25 stories located on a soft clay overlying sand and hard clay, section- or surface-acting foundation is recommended, the same as the shell foundation implemented in the project.

One Shell Plaza, Case No. 4, is a high-rise underlain by overconsolidated (OC) clay and is supported by a raft. Based on Figure 14, a section- or surface-acting foundation is the optimal choice. For a mid-rise superstructure, up to 40 stories, on very hard soil, a section-acting foundation system is suitable and compatible with the foundation system option used in Case No. 9, the Al Faisaliah project, as well as Case No. 20, the Le Royal Hotel Complex.

Due to medium dense to very loose conditions of soils near the ground surface and the type of superstructure of a tower similar to Case No. 16, the Burj Khalifa project, the implementation of block-acting (hybrid) foundations such as a PRF is undeniable. This issue is also valid for Shanghai Tower, with 128 stories, which is supported by a PRF surrounded by soft to medium mixed deposits, and is compatible with what is suggested by the proposed approach in Figure 14. Figure 15 demonstrates some actual cases that have complied with the procedure illustrated in Figure 14.

The recommended general trend shown in Figure 14 should be used only in a normal condition of vertical load for safe design. Due to the underlying soil conditions (very hard or dense) in the projects considered, there may be no concerns about excessive bearing capacity or settlement problems in these projects, and foundation systems such as section- or surface-acting will be appropriate options. Nevertheless, in cases involving high lateral loads such as winds or seismic loads and a considerable height-to-breadth ratio of a building, selecting more profound foundation systems that provide higher stability against lateral loads, such as vector-acting foundation systems, would be more appropriate. High liquefaction potential is another abnormal condition in which the choice of appropriate foundation systems must be made more insightfully and carefully. It is worth mentioning that the proposed foundation alternatives and foundation selection framework are not limited to the building projects and can be applied to various geostructures implemented under or above the ground.

6 SUMMARY AND CONCLUSIONS

For a more comprehensive and detailed assessment and screening of foundation alternatives and employment for projects apart from the buildings, more cases must be analyzed based on challenging criteria, such as energy, economy, and environmental issues, leading to sustainable development.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.