Study area
The study was carried out on the flanks of Chipinque Mountain, located in the northern portion of the Sierra Madre Oriental (Northeast of Mexico, Fig. 1). The climate in the mountain changes drastically depending on the elevation and location. The altitude varies from 750 to 2,200 m.a.s.l., being located between the geographical coordinates 100 ° 18´ and 100 ° 24´ W and 25 ° 33´ and 25 ° 35´ N. According to the Köppen classification (1936) modified by García (1973), the study area has a climate type of BS1 (h ’) hw (e)’ ’w’ ’, (semiarid, with marked rains in summer). The average annual temperature is 20.5º C and an annual average rainfall of 595 mm, dominating lithosol and rendzine soils (INEGI, 1986).
The vegetation consists of a mixed forest of Pinus and Quercus species, among which are Pinus pseudostrobus (Lindl.), P. teocote (Schiede. Ex Schltdl. & Cham.) and the Quercus genus: Q. rysophylla (Weath), Q. laeta (Liemb), Q. polymorpha (Schltdl. & Cham.), Q. laceyi (Small) and Q. canbyi (Trel.) (Alanís et al. 2008).
Sampling and root procedures
Four native tree species were selected for root characterization and tensile strength test. The root sampling of each plant species, was carried out manually and then 5 individuals per species were randomly selected (Zavala et al. 2019). The roots were extracted from exposed root systems with the purpose of minimum disturbance in the area (Sanchez et al. 2017b) and one complete root system for future procedures. The samples were cut, carefully packed and stored in paper bags. In order to preserve their moisture content, they were stored in a cooler container at the moment of extraction. The root morphological properties were determined in situ prior taking photographs and sampling the roots. Sampling was done at five depths: 0 to 10 cm, 10 to 20 cm, 20 to 30 cm, 30 to 40 cm and 40 to 50 cm. The collected samples were transferred to the corresponding laboratories at the Facultad de Ciencias Forestales, Universidad Autónoma de Nuevo León. The species selection was made taking into account their native characteristics: natural distribution, abundance and presence in hillside areas. In this way, the species considered were: Cercis Canadensis L. (Fabaceae), Celtis laevigata Willd. (Cannabaceae), Quercus rysophylla Weath. (Fabaceae) and Ligustrum lucidum W.T.Aiton (Oleaceae) (Fig. 2).
Tensile strength test. At the laboratory, the test was well conducted with a total of 120 segments (0.01 to 0.99 mm): 30 per species. The methodology used (Sánchez et al 2017) was carried out using a Universal Testing Machine SHIMADZU type SLFL-100Kn. Root samples were clamped and pulled at a constant speed of 10 mm/min. After each test, the root sample diameter (mm) was measured. Data was visualized using the material testing operation software Trapezium. The applied force (N) required to break the root was taken as a measurement of root breakage to calculate tensile strength (Ts, N/mm2).
Ts = Fmax/π (D/2)2 (1)
Where: Fmax is the maximum force to root breakage (N) and D is the average root diameter (mm) (Mattia et al. 2005, Bischetti et al. 2005, De Baets et al. 2008, Genet et al. 2005).
Root area ratio determination
On the field, pictures were taken to calculate the root area ratio (RAR), which is defined as the fraction of the soil cross–sectional area occupied by roots per unit area (Gray and Leiser 1982). On the other hand the method of root counting by image analysis described by Vogt and Persson (1991) was used to calculate root area ratio, which consists on the mapping and counting of the exposed roots on a trench from images in order to calculate the cross–sectional area and recreate the root system. This method emulates the traditional profile wall method proposed by Bohm (1979) (Sánchez et al. 2017a). This root trait is a function of depth, so it was taken in the field at five depths 0 to 10 cm, 10 to 20 cm, 20 to 30 cm, 30 to 40 cm and 40 to 50 cm. This was done by counting the number and thickness of roots in the soil block.
Soil-root cohesion estimation
The influence of roots on soil (fixation) can be expressed as a cohesion term (O’Loughlin 1974; Wu 1976; Waldron 1977) in the Morh–Coulomb failure criteria were the soil–root composite shear strength (Sr) is calculated as follows:
Sr = c′ + (σ – u)tanφ′ + ∆S (2)
where c′ is the effective cohesion of the soil, σ is the normal stress due the weight of the water and soil of sliding mass, u is the soil pore–water pressure, φ′ is the effective friction angle of the soil and ∆S is the apparent cohesion provided by the presence of roots.
The theoretical model developed by Wu (1976), Waldron (1977) and Wu et al. (1979) to estimate the shear strength increase due to presence of roots, assumes that roots are flexible, elastic and perpendicularly oriented to the slip surface when the soil layer is moving. This can be translated into tangential and normal components, specifying how the roots are oriented (normal component) and the magnitude of the force that is provided (tangential component). Assuming that the soil friction angle is not affected (O’Loughlin 1974), the additional cohesion (∆S) provided by roots can be calculated as:
∆S = tr (sinβ + cosβtanφ′) (3)
where tr is the average mobilized tensile strength of roots per unit area of the soil and β is the angle of root distortion in the shear zone. Sensitivity analyses show that the values of (sinβ + cosβtanφ′) can be approximated as 1.2 for 30° < φ′ < 40° and 48° < β < 72° (Wu et al. 1979; Wu 1995). Thus, the equation can be simplified as:
∆S = 1.2tr (4)
and tr can be calculated as:
where Tri is the tensile strength of an individual root (i) and (Ari|A) is the root area ratio or proportion of root cross sectional area to soil cross sectional area A.
Statistical analysis
Data were analyzed using the Statistical Package for Social Sciences (SPSS) standard version 13.0 for Windows (SPSS Inc., Chicago, IL.). Root tensile strength (Ts) showed supposition of normal distribution and was analyzed using a two-way ANOVA. Since root area ratio (RAR) and root cohesion (Cr) data did not show the assumptions of normal distribution, these variables were analyzed using the non-parametric Kruskal-Wallis test (Steel and Torrie 1980). In order to analyze root area ratio (RAR) and root cohesion (Cr) values for each species for soil depth, the Mann-Whitney U nonparametric test without correction at a p = 0.05 was applied. Power regression models were generated for the correlation species with root tensile strength (p < 0.01).