Multiple-Criteria Decision Analysis Using TOPSIS: Sustainable Approach to Technical and Economic Evaluation of Rocks for Lining Canals

Abstract

One of the crucial projects underway in Egypt is the lining of watercourses to withstand the outflow of water through their beds and flanks. Various materials have been used in this project, including limestone, sandstone, basalt, and dolomite, along with other building materials. This study focused on the evaluation of rock characteristics to determine their suitability for the construction of a canal lining. All rock characteristics should be classified in terms of technical and economic concerns related to mining rock specifications, such as mechanical and physical properties, and evaluated according to their weights and ratings. As a rule of decision making, management stakeholders select the rock types. The primary purpose of canal linings is to reduce water loss due to seepage. Methodologically, we adopted the technique for order of preference by similarity to ideal solution (TOPSIS), and derived an improved TOPSIS method based on experimental testing. This study attempted the first application of TOPSIS to canal linings and relevant construction materials. The analysis shows that limestone L1 is the best rock-building material for canal linings in Upper Egypt. Limestone L1 has the shortest geometric distance from the positive ideal solution and the longest geometric distance from the negative ideal solution. The results provide decision makers with strategic indicators to select among different rock types based on the total points assigned to all rock specifications.

1. Introduction

Egyptian governorates plan to construct linings in all canals connected to the Nile River. Canal linings are generally constructed from earth materials, such as different rock types, and the selection of suitable natural rock materials is therefore very important. Rock types are classified into three categories—igneous, metamorphic, and sedimentary—which differ in their physical and mechanical properties. Because rocks have such different characteristics, selection of the best method for evaluating them is paramount. The evaluation must focus on not only the mechanical and physical specifications, but also economic factors.

Watercourse linings play a role in the sustainability of irrigation projects because they maintain the outflow features and maximize water conservation by reducing leakage. Thus, water can be used to expand and improve irrigation. Water canal linings in areas supplied by tube wells are particularly significant, because water supplied by pumps is comparatively expensive. Reduced water infiltration limits the rise in the subsoil water table, thereby increasing the vulnerability of the surrounding areas to water logging. Furthermore, due to the higher speed of the water in a lined canal, the width of the canal cross section can be reduced, which corresponds to reduced digging and stone work expenses. Linings help in retaining the canal shape and result in improved control and a larger working head for power generation.

Different materials contribute to constructing such linings, including cement, boulders, concrete, plastics, different types of stones and bricks, and compacted earth. The primary target of watercourse linings is the reduction of water loss caused by seepage. According to the strategic plan of the Egyptian Government, linings will be constructed in approximately 831 km of canals. A canal lining is an impermeable membrane that is added to the canal bed and sides to increase its life span and discharge capacity. Sixty to eighty percent of the water lost to seepage in an unlined canal can be saved by lining the canal. Watercourse linings are categorized into two major types according to the nature of their surface: earthen linings and hard-surface linings. Earthen linings are further divided into two categories: compacted earth linings and soil–cement linings. When appropriate earthen material is available close to the construction site or in situ, compacted earthen linings are the most suitable. However, if the appropriate earthen material is not available near the site, a compacted earthen lining is more expensive. Compactness undermines the soil pore volume by displacing air and water. The reduction of voids increases the density, compressive strength, and shear strength of the soil and reduces its permeability. Due to corresponding reductions in the volume and settlement of the surface, compactness is necessary to boost the stability and frost resistance, if needed. Moreover, erosion and seepage losses decrease. Soil–cement linings are made from mixtures of sandy soil, water, and cement, and are hardened to a concrete-like material. In general, for the construction of soil–cement linings, dry-mix and plastic mix methods are used. There are several lining methods that use cement concrete, such as a lining cast in situ, shotcrete lining, precast concrete lining, and cement mortar lining. In the case of a brick lining, bricks are laid using cement mortar on the sides and the canal bed. Thereafter, a smooth surface finish is added using cement mortar.

The physico-mechanical properties of rock samples have a significant influence on their behavior in the application of canal linings. This study focused on the evaluation of different rock samples to determine an index and to classify the most suitable rock type with respect to a combination of their properties. Accordingly, ten samples of each type of rock were examined. A total of 140 samples were examined, and the following properties were measured: uniaxial compressive strength (UCS), tensile strength (TS), abrasion (Abr), and slack durability index (SDI), in addition to the physical properties of density (D), P-wave velocity (PWV), and water absorption (W). Furthermore, the material cost per cubic meter was included in the analysis. To determine the appropriate selection, we applied the technique for order of preference by similarity to ideal solution (TOPSIS). The principal concept of TOPSIS offers the best decision support, and thus leads to a solution that is close to the optimum. This technique is based on benefit criteria that are related to positive or negative ideal solutions. High and low solutions are compared to determine the distance between alternative solutions. This methodology has been widely applied in several fields, but to the best of the authors’ knowledge, this is the first application of TOPSIS to canal linings and relevant construction materials [1]. A mathematical model was adopted to calculate the distance between positive and negative alternatives; the authors made assumptions to define and create the rate and weight for each characteristic.

The remainder of this manuscript is organized as follows: Section 2 reviews the relevance of TOPSIS, its multiple uses in different scientific fields, and its increased efficiently relative to other methods. Section 3 describes the site investigations and documents the sites with photographs of actual canal linings. Section 4 illustrates and summarizes the laboratory test results of the mechanical and physical properties of the rock samples. Section 5 discusses material applications based on their properties for different purposes. Section 6 presents the methodology, data collection, constraints, problem formulation, raw material requirements, and implementation according to the analysis methods, including the relevant mathematical formalism. Moreover, it provides quality index calculations with respect to property weights and rates. Section 7 presents and discusses the results. Finally, the conclusions are drawn in Section 8.

Section 2 reviews the different uses of TOPSIS to direct decision makers toward sustainable and optimal alternatives among a list of options. This section highlights the relevance of the study as the first to focus on building materials and their use in canal lining.

2. TOPSIS: Relevance and State of the Art

TOPSIS has been broadly used in multi-attribute decision-making problems because of its ease of calculation, resilience of application compared with other methods, and acceptable results [2]. Similar to TOPSIS in its performance is the VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje) method, which was introduced academically in 1998; however, the VIKOR method has the major disadvantage of requiring a search for a compromise ranking order, such as a compromise between pessimistic and expected solutions [3].

In contrast, scholars have expressed great satisfaction with the TOPSIS method and have applied it in different fields. Based on TOPSIS, Kaveh et al. developed multi-objective decision making for a bi-objective decision. In addition, they offered a framework that includes tangible and intangible determinants to construct an integrated multi-objective framework [4]. The study reviewed scholarly interest in TOPSIS and its use in different arenas.

In an attempt to solve urban planning problems, Sharma and Singhal applied fuzzy TOPSIS [5]. In concrete manufacturing with siliceous materials, the fuzzy TOPSIS method was used to extend the concrete lifespan and reduce costs, thereby achieving sustainable development in the building sector [6].

Using possibility theory, Ye and Li [7] applied fuzzy TOPSIS based on fuzzy numbers to challenge multi-attribute decision making. Baykasglu and Golcuk [8] also used fuzzy TOPSIS and fuzzy cognitive maps to solve complicated decision-making problems. Maldonado-Macias et al. utilized an intuitive fuzzy TOPSIS to assess cutting-edge manufacturing technologies through numerical control of milling machines [9]. Luis et al. [10] developed a hesitant fuzzy linguistic term with TOPSIS to evaluate lean manufacturing and offer optimal alternatives to decision makers.

Cheng et al. proposed a heterogeneous TOPSIS for solving heterogeneous multi-attribute decision-making problems with deviation and fixation attributes. This proposal offered successful use of structural optimization of a high-speed press that considers multi-source uncertainties [11]. A hybrid fuzzy analysis network process based on TOPSIS has been used to select energy plant locations related to solid waste [12]. TOPSIS was improved to assess power quality by correlating indices that were ignored by other traditional methods, such as the analytic hierarchy process (AHP) and entropy weight (EW) [13].

3. Site Investigation and Data Collection

The various geological structural features and depositional environments of the Qena Governorate canals were evaluated for geotechnical characterization. Note that water did not penetrate cracks during the rainy season, as shown in Figure 1 and Figure 2. Dimensions of stone and thickness of boulder lining according to Egyptian code are also shown in

Table 1. Dimensions of stone and thickness of boulder lining according to Egyptian code.

Canal Capacity, m3/s	Thickness of Lining, mm	Average Dimension along the Longest Axis, mm	Minimum Dimensions at Any Section, mm
0 < 50	150	150	75
50 < 100	225	225	110
>100	300	300	150

.

4. Mechanical and Physical Properties of Studied Samples

Middle Eocene limestone deposits have formed at sites throughout the Nile Valley, and have been studied by many researchers [14]. To date, all such investigations have focused on the mechanical properties of these deposits. These studies have reported that the strength increased with the degree of porosity, and accordingly, slightly porous fine-grained limestone was described as intermediate, whereas semi-porous coarse-grained limestone was described as crisp and very friable [15]. Aggregate degradation (AD) was studied to help decision makers select suitable materials for different purposes. Two types of experiments were performed to investigate the uniaxial compressive strength (UCS) and point load index (PLI). The AD properties of forty types of carbonate aggregate samples from Iran were studied. The results showed that the prediction of AD properties using rock strength tests based on rock types yields better correlations than tests using unclassified samples [16]. Cultrone (2005) studied the behavior of bricks under various conditions and their use in historical buildings. The mineralogy, texture, physical, and mechanical properties were investigated. This may be utilized in the pottery industry; however, these materials lack mechanical resistance to high temperatures [17]. Hence, the materials used in bricks do not seem suitable for canal linings.

Limestone samples were tested to evaluate their suitability for use in various applications based on their petrographic and technological features. Thus, it is possible to define the preferred use of each limestone sample to maximize its durability [18]. A comparison was conducted among the upper Cretaceous carbonates, which are strong and brittle, with a low modulus ratio. The highest electrical resistivity was recorded for the dry and saturated states of slightly porous weak stone faces, whereas the lowest value was recorded for semi-porous mudstone faces [19].

El-Tahlawi (1973) studied carbonate rocks of the Manfalout Formation in the Assiut area in Egypt. This formation was divided into two distinct limestones with flint and solidified concretion and a lower part made of a massive limestone, with few nummulites and significant flinty and cherty intercalation. The following features of the investigated samples were determined: (1) the average density was 2.33 gm/cm³, (2) the average porosity was 12.1%, and (3) the compressive strength varied from 199 to 352 kg/cm² [20]. Seyed et al. (2018) used these parameters to determine desirable engineering properties with resistance to exposure conditions. However, determining the aggregate sturdiness in a laboratory can sometimes be difficult. The mechanical and physical properties, water absorption, and Los Angeles abrasion coefficient were used to determine the specific durability of limestone aggregate in evaluating the model reliability. Certain performance indices, such as the correlation coefficient, variance account, and root mean square error, were calculated and compared for the two developed models [21].

Five locations in Nigeria were examined by Ola (1977) by adding lime to clay in order to enhance its mechanical behavior [22]. Vazquez et al. (2013) considered the construction of several types of buildings. To evaluate the merit of each stone for use as a masonry material, its petrographic characteristics and physical properties should be analyzed, because they affect its behavior when exposed to agents of decay. The travertine from Albox and crystalline dolostone from Bonar, both of which have relatively low porosity, are the highest-quality stones in terms of their hydric behavior and mechanical characteristics [23]. Ali et al. (2018) evaluated the chemical, petrographic, and engineering properties of these quarry limestones and assessed the determined parameters based on aggregate standards [24].

Table 2. Rock types: mechanical and physical properties.

Rock Type	Rock Class	Abbreviation	CS, MPa	TS, MPa	DIS, %	Water Absorption, %	Density, g/cm3	Abrasion, %	P Wave Velocity, m/s
Limestone 1	Sedimentary	L1	69.5	18.7	95.8	3.5	2.3	2.3	3655.6
Limestone 2		L2	72.8	19.3	98.2	4.04	2.2	2.22	3462.3
Limestone 3		L3	81.5	20.8	98.5	3.2	2.7	1.85	3125.4
Limestone 4		L4	78.6	18.9	98.1	3.6	2.6	0.98	3425.6
Dolomite 1	Metamorphic	D1	111.5	28.2	98.9	2.55	2.6	0.035	4560.5
Dolomite 2		D2	125.4	29.6	98.5	2.04	2.7	0.031	4897.6
Dolomite 3		D3	130.3	31.5	99.1	1.89	2.8	0.029	5001.2
Basalt 1	Igneous	B1	135.3	35.2	99.5	0.38	2.8	0.082	5050.8
Basalt 2		B2	145.5	34.6	99.6	0.39	2.9	0.078	4985.7
Basalt 3		B3	165.7	36.2	97.1	0.28	2.9	0.087	5010.4

summarizes the rock sample specifications according to the testing results obtained from the Faculty of Engineering at Al-Azhar University, Egypt.

5. Material Uses

5.1. Limestone

Limestone is more widely used in numerous applications compared to other rocks. Typically, limestone is crushed into stones and used as a masonry and construction material, such as a road foundation material, as aggregate in concrete, or as a raw material in the cement industry. In particular, strong and dense lime stones with minimal pores are suitable for these applications. These properties enable their resistivity to abrasion and freeze–thaw action.

Although limestone is less suited to these applications compared to some harder silicate rocks, limestone is extremely easy to mine and does not leave the same level of macerate on mining tools, screens, crushers, and the vehicle beds when being transported. In this study, we focused on lining watercourses using natural rocks, such as limestone. Limestone is used for numerous purposes, such as stair treads, facing stones, floor tiles, and windowsills. Furthermore, crushed limestone is employed as a weather- and heat-resistant coating on asphalt-impregnated shingles and roofing. In addition, general industrial limestone can be used in smelting and other metal-refining processes.

Under the heat of smelting, limestone liaises with impurities, can be removed from the process as slag, and can finally be used in cement manufacture. Limestone is only found in areas underlain by sedimentary rock but is also required in other areas. Moreover, buyers will pay several times the value of the stone in delivery charges so they can use it in their works, such as canal linings.

5.2. Dolomite

Dolomite is a widespread rock-forming mineral that is the elementary ingredient of sedimentary rock, dolostone, metamorphic rock, and dolomitic marble. It forms calcium magnesium carbonate with a chemical composition of CaMg (CO₃)₂. Limestone-containing dolomite was known as dolomitic limestone. Dolomite or dolostone is a carbonate sedimentary rock that contains more than 50% of the mineral dolomite by weight. Dolomite may precipitate from aqueous solutions (sandstones with dolomitic cement). Some dolomitic rocks are the so-called primary dolomites that were formed in lagoons where dolomite directly precipitated out of seawater, but such dolomites are much scarcer than previously believed. Few elementary dolomite deposits have been discovered from the Holocene age (the last 12,000 years). Seemingly, the elementary dolomites were common in the past, but this premise is difficult to confirm or deny, due to later diagenetic (processes affecting sediment after deposition) overprinting of the original material [25].

However, there is doubt that dolomitic rock formation is dominated by elementary dolomite deposits, because laboratory experiments have shown that dolomite never precipitates from aqueous solutions under atmospheric conditions (1 atm pressure, temperature <60 °C). When dolomite rock is replaced by pristine limestone, there are too many pore spaces. However, this exegesis concerning the higher porosity of dolomite rock has been resumed.

According to a paper published by the Geological Society of London, limestones become non-porous through compaction and cementation, whereas dolostones resist compaction and retain much of their porosity [26,27]. Dolostones are generally employed for construction purposes. They are crushed and sized for use as an aggregate in asphalt and concrete, a road foundation material, rip-rap, railroad ballast, or even fill. It is also calcined in the cement industry and cut into blocks of specific sizes known as “dimensional stone.” In addition, the reaction of dolomite with acid increases its applicability. It is used for acid neutralization in the chemical industry, stream restoration projects, and as a soil conditioner [28].

5.3. Basalt

Basalt is generally a black to gray-colored volcanic rock, and is usually fine-grained due to the fast cooling of lava on the Earth’s surface. It may be porphyritic, and contain large crystals in a fine matrix, vesicular, or frothy scoria. Unweathered basalt is black to gray in color. Basalt has a firm chemical definition. It is described as a total alkali silica (TAS) diagram. Basalt is an igneous rock that contains SiO₂ in the range of 45–52% and less than 5% of the total alkalis (K₂O + Na₂O)³. Neighboring rock types, such as basaltic andesite, basanite, picrite (picrobazalt), and trachybasalt, including more distant types such as phonotephrite or andesite, can appear similar and can be easily mistaken for basalt in many cases [29]. The mineralogy of basalt is characterized by the presence of calcic plagioclase feldspar and pyroxene. Olivine is a significant constituent. Additional minerals present in relatively minor amounts include iron oxides, such as magnetite and ilmenite; iron-titanium oxides, such as titanium-augite and sphene; and spinel.

The fundamental quality characteristics of basalt, such as compressive strength, high abrasion resistance, and chemical resistance, make it useful in industrial applications. Basalt can be converted into fine, superfine, and ultrafine fibers. Compared to other types of fibers, basalt fibers are deemed superior in terms of thermal stability, heat and sound insulation properties, vibration resistance, and durability. Basalt has replaced asbestos in almost all its applications and is three times more effective in isolating heat than reinforced plastic (1 kg of basalt provides equivalent reinforcement of 9 kg of steel). Typical basalt applications include crushed stone, concrete aggregates, railroad ballast, production of high-quality textile fiber and floor tiles, acid-resistant equipment for heavy industrial use, rock wool, basalt plastic pipes, basalt plastic reinforcement bars, basalt fibers, roofing felt, heat-insulating basalt fiber materials, and glass wool.

Crushed basalt ranging from 25 to 45 mm can be employed in the rock wool industry, and 30% of the product that is smaller than 25 mm is used as aggregates. The application of basalt as an aggregate is not preferred due to the availability of cheap alternative materials such as limestone, despite the fact that the physical engineering qualities of basalt are superior to those of limestone. Thus, basalt is considered a good option for durability. Moreover, basalt can be used as a dimensional stone for buildings.

Boulder lining materials were added as stones in the mortar mixture. Technical operations are required to exploit basalt stone and prepare for other operational requirements. When the lining is covered with stones, the surface imposes considerable resistance to flow; thus, the surface is sufficiently rendered, and the coefficient of rugosity is increased. Thus, stone linings are appropriate in situations where the loss of head is not an important factor and where stones are available at an affordable cost.

More extensive use of newly available nondestructive methods for testing the quality of completed work can provide independent backup for routine inspections during construction and can help minimize the number of inspections. A suitable rock type can be selected by applying the TOPSIS criteria. However, another issue involves the manner in which the methodology should be used to achieve high accuracy and easy application.

6. Methodology

In this study, we applied TOPSIS to determine a solution that is close to the ideal solution and distant from the non-ideal solution. This technique is based on determining the maximum or minimum benefit criteria that correspond to the positive or negative ideal solutions, respectively. TOPSIS compares positive and negative solutions to determine the distance between alternative solutions. Many researchers have developed TOPSIS methods [29]. These methods focus on creating a weight for each criterion, scoring the normalization for each criterion, and estimating the geometric distance between each alternative and the ideal alternative. Accordingly, the best value is determined for each criterion, and the concrete mixture is prepared depending on the physical and mechanical properties and the specific requirements for different purposes, especially in the canal lining, taking into consideration the economic factors (financial goals). The supply chain is an important factor in admixture techniques to overcome the gaps between production and requirements, and increase the product quality and efficient use of raw materials.

Table 3. Assignment of weights of to the tested rock samples.

Properties	L1	L2	L3	L4	D1	D2	D3	B1	B2	B3
CS, MPa	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4
TS, MPa	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4
DIS, %	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6
Water absorption, %	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8
Density, g/cm3	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3
Abrasion, %	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8
P wave velocity, m/s	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6
Cost, LE	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8
Cost, LE	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8

and

Table 4. Ratings assigned to different parameters [30,31].

Parameter	Rating
	0.2	0.4	0.6	0.8	1
Uniaxial compressive strength (MPa)	<250	250–500	500–750	750–1000	>1000
	Very low	low	Medium	High	Very high
TS, MPa	<25	25–50	50–100	100–150	>150
	Very low	low	Medium	High	Very high
DIS, %	<50	50–60	60–75	75–100	>100
	Very low	low	Medium	High	Very high
Water absorption, %	>0.75	0.75–0.5	0.5–0.25	0.25–0.1	<0.1
	Very high	high	Medium	low	Very low
Density, g/cm3	<2	2–2.3	2.3–2.6	2.6–2.9	>3
	Very low	low	Medium	High	Very high
Abrasion, %	>0.5	0.5–0.3	0.3–0.1	0.1–0.05	<0.05
	Very high	High	Medium	low	Very low
P wave velocity, m/s	<2750	2750–3500	3500–4250	4250–5000	>5000
	Very weak	Weak	Moderate	strong	Very strong
Cost, LE	<50	50–60	60–70	70–80	>80
	Very cheep	cheep	Moderate	Expansive	Extremely Expensive

present the weights and rates for all properties according to our assumptions. We estimated the weight values of the material properties that impact the performance of the canal lining using questionnaires and by interviewing professionals. This study modified the University of British Columbia (UBC) method by developing various economic, technical, socio-cultural, and environmental factors. Each of these factors was assigned a weight based on its impact on the application and purpose of the project.

TOPSIS assumes that monotonic criteria increase or decrease according to normalization as a basic factor, although an odd dimension is considered in multicriteria cases. TOPSIS is an effective method for comparing criteria that are considered to have poor results in other aspects. Such results provide us with a more realistic form of modeling, compared to the results of other methods, considering the related alternatives to include or exclude alternative solutions [1,32].

The discussion and illustration of the UBC method are clarified in the previous section and the modifications are discussed in this section. The primary criterion for this technique is to measure the stratification of all mechanical and other properties of the bedrock so they can be added to a new Excel sheet and linked with phenomena that correspond to all mining methods using TOPSIS, which can easily connect all the rock type characterizations (e.g., mechanical properties such as UCS, TS, and abrasion; physical properties such as density, water absorption, and wave velocity; and economic factors related to cost). Figure 3 illustrates the integration of all parameters and properties applied to this technique.

All methods were formulated according to the UBC method, which was developed and adjusted for application in this study. All equations were formulated and linked using cells in an Excel sheet that represented all properties, assuming that the property was considered in determining an alternative. Referencing to the value assigned to the jth criterion of the ith alternative, where x_ij is the decision matrix, the equivalent weight of the property is expressed as w₁, w₂, …, w_n, and the TOPSIS processes are expressed in five steps using Equations (1)–(5).

• Normalize the decision matrix. This can be calculated by

  $${\overline{X}}_{ij}=\frac{X_{ij}}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{X}_{ij}^2}}$$

  (1)

  r_ij = x_ij__m_k = 1 × 2k_j, i = 1, …, m; j = 1, …, n, where r_ij denotes the normalized value of the jth criterion for the ith alternative Ai.
• Calculate the weighted normalized decision matrix. $V_{ij}$ can be calculated as

  $$V_{ij}={\overline{X}}_{ij}\times W_j$$

  (2)

  v_ij = w_j r_ij, i = 1, …, m; j = 1, …, n (2), where w_j is the weight of the jth criterion or attribute.
• Determine the ideal positive and negative solutions $S_i^{+}$ which can be calculated by

  $$S_i^{+}={\left[{\displaystyle \sum }_{j=1}^m{\left(V_{ij}-V_j^{+}\right)}^2\right]}^{0.5}$$

  (3)
• Calculate the Euclidean distance from the ideal worst condition. $S_i^{-}$ can be described as

  $$S_i^{-}={\left[{{\displaystyle \sum }}_{j=1}^m{\left(V_{ij}-V_j^{-}\right)}^2\right]}^{0.5}$$

  (4)

  where Vij = weighted and normalized decision matrix (Vij),
  S⁺ = the Euclidean distance from the ideal best,
  S⁻ = the Euclidean distance from the ideal worst.
• Calculate the performance score and ranking $P_i$ This can be calculated by

  $$P_i=\frac{S_i^{-}}{S_i^{+}+S_i^{-}}$$

  (5)

Many researchers have studied the relationships between physio-mechanical properties and the behavior of limestone and other materials during general evaluations (Edet, 1992). Quality indices have been applied for different properties such as porosity, swelling, and compressive strength. The final results indicated that compressive strength decreased with increased porosity and swelling indices, and the swelling index increased with an increased porosity index [33]. Mostafa et al. (2009) studied suitable materials for building, cement manufacture, and road pavement with respect to their physical and mechanical properties in the Sohag and Qena quarries near the Nile River; their results indicated quality indices of very good, good, fair, and poor for samples tested for different purposes [34]. Nigerian limestones were studied by Teme (1991), who determined that the suitability of limestone in highway pavement depends on the index properties of strength, chemical properties, petrographic properties, and resistance to attrition. Recommendations were made for the use of selected limestones as pavement materials in Nigeria [35].

Teme et al. (1994) studied samples to evaluate the suitability of rocks for application as building construction aggregates. The analyzed properties included UCS, tensile strength, porosity, water absorption, and dynamic fragmentation [36]. For ten locations in the Assuit Governorate (Mamdouh, 1997), the physical and mechanical properties of various building construction aggregates were evaluated, and were the primary factors that helped determine the best use of limestone in each location. The evaluation was based on the quality index, which incorporates the different properties and their weights [37]. Mahrous et al. (2010, 2019) evaluated Egyptian limestones, based on index properties, strength, chemical and petrographic factors, and abrasion resistance by collecting samples from different locations. The experimental results revealed that certain Egyptian limestones were adequate for use as highway pavement construction materials and recommendations were made based on those results [38]. Shohda et al. (2016) conducted numerous geotechnical analyses on selected rock samples from seven locations in Egypt to assess the suitability of these rocks for ornamental use. The analyzed properties included UCS, porosity, water absorption, hardness (SiO₂ content), resistance to abrasion, and durability. An evaluation of these stones based on a quality index scheme showed that granite is an ideal ornamental stone for use outdoors and indoors, marble is suitable primarily for enclosed spaces, and serpentine permits both interior and exterior applications [39].

7. Results and Discussion

TOPSIS was implemented to manage the use of natural rock as a sustainable approach to canal lining. The TOPSIS technique was employed as a multi-criteria decision-making method for sustainable selection among different natural building materials considering the mechanical and physical properties and cost considerations.

According to the weight values that we estimated based on questionnaires and interviews of experts, we determined the weights for the material properties that impact the canal lining performance. This study modified the UBC method by considering various economic, technical, socio-cultural, and environmental factors. Each of these factors was weighted according to its impact on the application and purposes of the project.

Table 5. Criteria for conversion to new approach based on weight and rate.

Weights/Rates	0.4	0.4	0.6	0.8	0.6	0.8	0.8	0.6
	CS	TS	DIS	W. ab.	D.	Abr.	PWV	Cost
L1	0.2	0.2	0.8	0.2	0.4	0.2	0.6	0.2
L2	0.2	0.2	0.8	0.2	0.4	0.2	0.4	0.2
L3	0.2	0.2	0.8	0.2	0.8	0.2	0.4	0.2
L4	0.2	0.2	0.8	0.2	0.8	0.2	0.4	0.2
D1	0.2	0.4	0.8	0.2	0.8	1	0.8	0.4
D2	0.2	0.4	0.8	0.2	0.8	1	0.8	0.4
D3	0.2	0.4	0.8	0.2	0.8	1	1	0.4
B1	0.2	0.4	0.8	0.6	0.8	0.8	1	0.6
B2	0.2	0.4	0.8	0.6	0.8	0.8	0.8	0.6
B3	0.2	0.4	0.8	0.6	0.8	0.8	1	0.6

presents the criteria for conversion of the UBC criteria to the new approach, whereby all properties were weighted to approximately 1.

Table 6. Normalized matrix.

	CS	TS	DIS	W. ab.	D.	Abr.	PWV	Cost
L1	0.3162	0.1890	0.3162	0.1715	0.1715	0.0887	0.2500	0.1525
L2	0.3162	0.1890	0.3162	0.1715	0.1715	0.0887	0.1667	0.1525
L3	0.3162	0.1890	0.3162	0.1715	0.3430	0.0887	0.1667	0.1525
L4	0.3162	0.1890	0.3162	0.1715	0.3430	0.0887	0.1667	0.1525
D1	0.3162	0.3780	0.3162	0.1715	0.3430	0.4437	0.3333	0.305
D2	0.3162	0.3780	0.3162	0.1715	0.3430	0.4437	0.3333	0.305
D3	0.3536	0.3922	0.3536	0.1768	0.3536	0.4472	0.4369	0.305
B1	0.3162	0.3780	0.3162	0.5145	0.3430	0.3549	0.4167	0.463
B2	0.3162	0.3780	0.3162	0.5145	0.3430	0.3549	0.3333	0.458
B3	0.3162	0.3780	0.3162	0.5145	0.3430	0.3549	0.4167	0.458

presents the normalized matrix, which was calculated using Equation (1).

Table 7. Normalized matrix multiplied by rate for every property.

	CS	TS	DIS	W. ab.	D.	Abr.	PWV	Cost, LE
L1	1.2649	0.0756	0.1897	0.1372	0.1029	0.0710	0.2000	0.0915
L2	1.2649	0.0756	0.1897	0.1372	0.1029	0.0710	0.1333	0.0915
L3	1.2649	0.0756	0.1897	0.1372	0.2058	0.0710	0.1333	0.0915
L4	1.2649	0.0756	0.1897	0.1372	0.2058	0.0710	0.1333	0.0915
D1	1.2649	0.1512	0.1897	0.1372	0.2058	0.3549	0.2667	0.183
D2	1.2649	0.1512	0.1897	0.1372	0.2058	0.3549	0.2667	0.183
D3	1.4142	0.1569	0.2121	0.1414	0.2121	0.3578	0.3495	0.183
B1	1.2649	0.1512	0.1897	0.4116	0.2058	0.2840	0.3333	0.2777
B2	1.2649	0.1512	0.1897	0.4116	0.2058	0.2840	0.2667	0.2745
B3	1.2649	0.1512	0.1897	0.4116	0.2058	0.2840	0.3333	0.2745

summarizes the normalized matrix multiplied by the rate for each property.

Table 8. Positive ideal and negative ideal solutions.

V+	1.2649	0.0756	0.1897	0.1372	0.1029	0.0710	0.1333
V−	1.4142	0.1569	0.2121	0.4116	0.2121	0.3578	0.3495

illustrates the positive and negative ideal solutions, and

Table 9. Euclidean distance from the ideal worst and ranking.

Si+	Si−	Pi	Rank
0.0667	0.5059	0.88	1	L1
0.5294	0.5294	0.50	6	L2
0.5181	0.5181	0.50	6	L3
0.5181	0.5181	0.50	6	L4
0.3376	0.3241	0.49	7	D1
0.3376	0.3738	0.53	5	D2
0.2863	0.3282	0.53	5	D3
0.1690	0.4824	0.74	2	B1
0.1876	0.2643	0.58	4	B2
0.1691	0.2515	0.60	3	B3

presents the final results according to the Euclidean distance from the ideal worst and ranking [27,28,29].

8. Conclusions

The UBC method was adjusted in this study to be more efficient for TOPSIS. Hence, this study employed TOPSIS to select the best rock according to technical and economic determinants among different types of rocks. This application will assist authorities in making sustainable decisions for canal linings, which is a national project.

Employing TOPSIS after improving the UBC in watercourse linings is a novel application, but many studies have used TOPSIS in various applications. As shown in Section 1, the high creditability of TOPSIS as a scientific method due to its flexibility and concise data were the motivations behind its application in this study.

The results show that selecting a suitable stone for a canal lining depends on its specifications, which are associated with mechanical and economic considerations. In this study, TOPSIS was modified by linking all criteria-related parameters in a simple manner to obtain accurate results. The final results provide indicators for decision makers to select a suitable rock type based on the total points assigned to all rock properties. We found limestone L1 to be the best rock type, followed by B1, etc., according to the final results summarized in Table 8. Practically, limestone has been employed on the sides of canal linings in Egypt based on experience, but this study proves it theoretically for the first time.