1. Introduction
The erosion of sandy beaches and the scarcity of natural material for artificial beach nourishment is a serious problem worldwide [
1]. The sedimentary budget and the capacity to maintain coastal morphology is based on the balance between the generation, destruction and transport of sediments [
2]. Determining the influence of the diverse factors involved in sediment erosion is important to minimize coastal erosion [
3]. Erosion begins with the transport of sediment particles by waves and currents (near-shore rip or long-shore) [
4,
5,
6]. Transport can result in the loss of beach sediment over short to medium time frames due to passing the depth of closure (in reference to the active zone of sediment transport according to Hallermeier [
7]) where particles will not be returned to the beach even in storm events [
7], or to the wear and consequent loss of size of the particles, by breakage, rounding or dissolution [
8]. The results of various studies show that the different components that form the sediment exert significant control over its durability [
9,
10].
The concept of sediment durability can be associated with material fatigue, i.e., material breakage produced by long-lasting dynamic stresses [
11]. Although there are many studies on the fatigue of materials such as steel and concrete, the study on sediment, and specifically on beach sand is much more limited [
12]. Even so, the few studies conducted show that the defects of these particles, like micro cracks, pores, grain boundaries, etc. [
13], are the beginning of cracking and brittle breakage of the material [
14].
To know the behavior of the material for intervening on the coasts with the least possible impact, the accelerated particle wear test (APW) enables the study of the wear behavior suffered by the sand particles in the swash zone of the beach [
8]. In addition, the mineralogical composition and morphology of the particles play an important role in their durability [
15,
16], and consequently in the retreat of the shoreline.
The number of factors involved in both shoreline erosion (with continuous temporal and spatial changes) and sediment wear complicate attempts to accurately model this complex system. The projected actions on the coast must be developed sustainably with criteria of the circular economy. Thus, knowing the useful life period (durability or period prior to complete sediment weathering) of the material to be used in coastal nourishment helps to optimize resources, reducing the number and cost of nourishments and the effects on ecosystems due to the reduction in negative effects caused during the fills (water turbidity, possible partial burying of vegetation species, etc.). This implies lowering the impact of these actions on the environment, making the coastal recovery process more sustainable.
In this work, a classification of sediment quality is established based on an index generated from the physical characteristics of the sediment and the results of the APW test. Principal component analysis, discriminant analysis and ANOVAs were conducted to establish three groups of sediment quality (good, regular and poor). This offers the coastal engineer a tool to determine the most sustainable sediment (most economical and durable material of those available) to be used in beach nourishment projects.
3. Sediment Quality Classification Index (SQCI)
The PCA showed only one component in its result, i.e., that the four variables originally introduced became one. The coefficients needed for the calculation of the main component scores are shown in
Table 3.
Converting to values of 0 and 1, the value obtained using the PCA (named Sediment Quality Classification Index) in each one of the study samples is shown in
Figure 2. A priori, it can be seen that the samples with a longer duration in the APW test present a higher value of the index. From the observation of the values, the following three classification ranges are established:
Poor quality—SQCI < 0.48;
Regular quality—SQCI between 0.48 and 0.70;
Good quality—SQCI > 0.70.
This proposed classification was used to perform the discriminant analysis, which provided two canonical functions (
Table 4). The eigenvalues of the two functions that constitute the model are very unequal. The first function explains 79.2% of the variability available in the data, while the second function only explains 20.8%. Similarly, the canonical correlation of the first function is very strong (0.879), while that of the second function is strong (0.686) according to the scale of Evans [
17].
Wilks’ Lambda contrasts hierarchically the significance of the two obtained functions (
Table 5), that is, it contrasts the hypothesis of equality of the centroids. As can be observed, the value of Wilks’ Lambda statistic decreases with each step of the model, which indicates that, as variables are incorporated into the model, the groups are less and less overlapping. The first line (1 through 2) contrasts the null hypothesis that the complete model (both discriminant functions taken together) does not enable the means of the groups to be distinguished. Since the value of Wilks’ Lambda has a critical level (Sig. = 0.000) lower than 0.05, it is possible to conclude that the model can distinguish significantly between the groups. In the second line (2) it is contrasted if the means of the groups are equal in the second discriminant function. Wilks’ Lambda takes a value very close to 1, but the critical level (Sig. = 0.000) is less than 0.05, so it can be concluded that the second function discriminates between at least two of the groups.
The matrix of standardized coefficients (
Table 6) contains two discriminant functions, the first one being the one with the highest discriminative capacity. This first function discriminates, fundamentally, by the number of cycles. The second function attributes the highest weighting to
mn.
Table 7 shows the location of the centroids in each of the discriminant functions. Both functions distinguish with great precision between the different sediment qualities since only 3% of the samples studied do not match the defined classification (
Figure 3). The first canonical function allows effective differentiation between the poor- and good-quality sediment since both centroids are strongly separated from each other (negative and positive zone of the axis, respectively). Additionally, it allows the regular quality to be distinguished, although if only one canonical function was used there could be confusion between it and the poor and good qualities since the regular quality centroid is close to the other two. The second canonical function mainly distinguishes the regular quality from the other two classifications, since the centroid of the regular quality is in the positive zone of the axis, while the centroids of the other two qualities are in the negative zone.
Figure 3 shows the territorial map (space corresponding to each of the groups in the plane defined by the two discriminant functions: the first function on the abscissa axis and the second function on the ordinate axis). The centroids of each group are represented by squares. Observing the location of the centroids in the figure, it can be seen that the first function has greater discriminant capacity than the second since the centroids are dispersed or moved further away in the horizontal direction compared to the vertical. Since the discriminant provides the same values as those proposed for the classification of the sediment, except for 22 (Los Locos beach, Torrevieja), 43 (Levante beach, Salou) and 9 (Cristo beach, Estepona), which are within the limits of the territorial map, it can be concluded that the established ranges are valid for classifying the quality of the sediment.
Through the ANOVA, the differences between the four variables are studied according to quality classification of the sediment. The main difference between groups is shown in the number of cycles in the APW test (
Figure 4b). The poor-quality sediment has an average of 2.5 cycles, while the regular-quality sediment has an average of 6.16, and the good-quality sediment has an average of 18.8 cycles. The rest of the variables present differences between two groups; the median size shows significant differences between good, poor and regular quality (
Figure 4a). The weight loss in the first cycle (
W1), and the relationship between the accumulated weight lost between the first and next-to-last cycles and the number of cycles elapsed (
mn) also show differences between sediment quality classes (
Figure 4c,d, respectively).
Finally, using both the index (SQCI) obtained from the PCA and the discriminant functions, 28 new samples from quarry material are classified.
Figure 5 and
Figure 6 show that the results of both analyses are in complete agreement. Analyzing the results in detail, 68% of the samples are classified as poor quality, which is mainly due to the number of cycles in the APW test; according to the canonical function 1 of the discriminant analysis (
Table 6) the
Cycles are the variable that most influences the classification with a value of 0.69. To discover, in more depth, why these quarry samples present such poor quality, it will be necessary to undertake detailed analysis of the mineralogical composition and morphology of the particles, as suggested by different authors [
14,
18]; if only the median size of these samples is considered (0.304 mm) their classification should be between regular and good, and not poor as obtained (
Figure 5 and
Figure 6).
Therefore, the final equation of the Sediment Quality Classification Index to employ the four variables (without standardizing) will be Equation (2), using the ranges of poor quality SQCI < 0.48, regular quality 0.48 < SQCI < 0.70, and good quality SQCI > 0.70.