The geotechnical investigations were carried out using core drilling coupled pressuremeter testing for each zone. The coring was realized by rotation using a 90 mm diameter double core barrel on a drilling machine. According to the boreholes drilled, the water table varied between 3.0 and 10.0 m during the investigation periods. There is a sandy-clay layer at an average depth of between 0.0 m and 5.0 m, underlain by blocks of basanites with olivines. These basanites have a micro-grained to grainy texture, sometimes healthy and altered by the presence of vesicles ( Figure 3 ). The rock quality designation (RQD) values of the rock vary between 45 and 80 %, which corresponds to poor and good quality, according to D. Deere. The pressuremeter test carried out only in the clay layers and in the soft, weathered rock has been made in accordance with Standard NF 94 110, 2000 using a Menard pressuremeter ( Figure 4 ). The average limit pressure varies from 0.270 to 1.33 MPa and from 2.20 to 19.20 MPa for the Menard modulus (EM) for the sand clay layers. This means that the materials have a firm consistency [6] . As for the basanites, the Menard modulus values vary between 23.50 and 297 MPa and between 1.28 and 7.01 MPa for the limit pressure. The lithology of the three zones is characterised by the presence of recent sandy-clay formations overlying basaltic volcanic formations. At zones 1 and 2, the rock layer is sub-surface. In zone 3, however, it is interbedded between two layers of soil. The lithological sections and results of the pressuremeter parameters for the different zones are shown in Figures 5(a)-(c) .

The most widely known rock mass systems are D. Deere’s RQD [7] , Bieniawski’s RMR [8] , Q-system of Barton [9] and Geological Strength Index (GSI) [10] . In this study, only the RMR and GSI will be used to characterize the rock and determine the Hoek and Brown parameters. The RMR was first introduced by Bieniawski (1973) and later modified over the years by the author until its latest version in 1989. Six parameters characterizing the intact rock and joints are taken into account to express the RMR: (01) strength of intact rock, (02) the value of the RQD, (03) mean spacing of discontinuities, (04) condition of discontinuities, (04) groundwater, (05) conditions and (06) the orientation of the discontinuities. The value of the RMR varies from 0 to 100. The sum of the six parameters is used to estimate the RMR value.

$RMR=R_1+R_2+R_3+R_4+R_5+R{}_6$(1)

The Geological Strength Index (GSI) is a recent classification system for hard and soft rock masses. It was introduced by Hoek (1994), Hoek et al. (1995) and improved by Hoek and Brown (1997). It was introduced specifically for estimating rock properties. Relations have been proposed by Hoek and Brown (1997) to estimate the GSI [11] from the RMR. These relationships are as follows:

$GSI=RM{R}^{\prime }-5\text{if}RM{R}^{\prime }>23$(2)

$RM{R}^{\prime }$: Modified Bieniawski rock mass rating, calculated using a value of 15 for the coefficient relating to water (R₅ = 15) and a zero value for the correction coefficient relating to the orientation of discontinuities (R₆ = 0). Outcrops, rock faces and core holes are the most widely used sources of information for estimating RMR and GSI values for rock massifs [12] ( Figure 6 ).

For the numerical calculation of bearing capacity, the finite element method with the Plaxis 2D code is chosen. The behaviour of the soil is governed by an elastic-perfectly plastic law and the modified Hoek-Brown failure criterion for rock mass. A rigid spread footing was modeled with a width of 1.0 m and subjected to a vertical load on the surface of the homogeneous rock mass. During the generation of the mesh, the 15-node triangular elements with a fine mesh were used. As for boundary conditions, horizontal and vertical displacements are fixed on the extremities. The load-displacement curve was used to estimate the bearing capacity. The progressive displacement of the footing is accompanied by an increase in stress in the massif. This stress under the footing stabilizes at a value that indicates a yield point, which corresponds to the load-bearing capacity. Other approaches to determining the bearing capacity of rock foundations are empirical and analytical methods. Empirical methods are based on observations, tests and the parameters of the Hoek-Brown failure criterion. Analytical approaches, on the other hand, are based on limit equilibrium theorems, the method of characteristics or slip lines, and the limit analysis method with its two approaches, kinematic and static. As with ultimate bearing capacity, calculating foundation settlement is an important design parameter. Settlement is given by the expression of Schleicher (1926), pressuremeter tests and numerical modelling. Table 1 and Table 2 give some expressions for calculating bearing capacity and settlement respectively.

q_ult: ultimate bearing capacity; q_a: allowable bearing capacity; q_u: unconfined compressive strength; RQD: rock quality designation; q_c: uniaxial compression strength of intact rock; m and s: material constants in the Hoek and Brown failure criterion; K_p: bearing capacity factor; K_s: empirical coefficient depending on the spacing of discontinuities; C: cohesion; ϕ: internal friction angle; ζ_n and β_n: constants of rock mass; N_σ and N_β: bearing capacity factor; Pl_e: limit pressure; q₀: overburden pressure after construction.

δ, S: settlement in mm; E: Young’s modulus; ν: Poisson’s ratio; C_d: Shape factor of foundation; B: footing width; λ_c, λ_d: Shape coefficients depending on the footing dimensions; E_d, E_c: Pressuremeter equivalent modulus; α: rheological coefficient of the soil or rock; q: vertical stress applied by the foundation; σ_v0: Total vertical stress.

Tables 3-5 summarize the physical and mechanical properties and geomechanical classification of the sandy clay and basanite strata. Laboratory tests on soil samples taken from clayey sand strata showed a unit weight ranging from 13.83 to 19.06 kN/m³, with a plasticity index varying between 15.78 and 20.40, confirming the clay’s low plasticity. The results of the shear test illustrate soil with friction angle and cohesion values confirming the clayey tendency. The basanite facies in the study areas were geomechanically classified using the RMR and GSI systems. The rock matrix has an average compressive strength of between 24.27 and 34 MPa, corresponding to a grade ranging from 2 to 4. The RQD varies between 58.20% and 72.96%, corresponding to a grade of 13. The average spacing of the discontinuities ranges from 150 to 390 mm, giving a score of 8 to 10. The discontinuities have slightly rough shoulders with slightly too heavily weathered surfaces. A score of 10 is awarded for wet rock (presence of water table) and 15 for dry rock. Finally, the RMR of our rock mass ranges from 60 to 62, with a GSI of 55 ± 5, which corresponds to medium to good quality basanites overall.

The results of the bearing capacity according to the different approaches are presented in Table 6 and Table 7 . A comparison was made by means of a histogram, which gave the allowable bearing capacity ( Figure 7 ). There is a scattering of results between the different methods. The range of bearing capacity values is between 1.92 and 11.39 MPa for the empirical approaches and from 7.13 to 25.50 MPa for the analytical approaches. For the empirical approaches, the results obtained with the Canadian code, Eurocode 7 [22] and the pressuremeter test give very similar bearing capacity values. The advantage of the Canadian and Eurocode 7 approaches is that they take into account both the joint spacing and the compressive strength of the rock. With the pressuremeter test in our case study, the value of the capacity is underestimated, due to the fact that the limiting pressure of the rock is much lower than its breaking pressure. The pressuremeter

method, derived from soil mechanics, assumes a continuous, homogeneous soil and does not take discontinuities into account when estimating bearing capacity, so it is less suitable for fractured or only slightly fractured rock masses. With Peck’s approach, the bearing capacity increases with the RQD and not with the compressive strength. This means that two rock formations with different strengths [23] , for example, healthy basanite and weathered vesicular basanite having the same RQD, will have the same bearing capacity, even if they have different compressive strengths. The limitations of determining bearing capacity using RQD quickly show. The American code gives very pessimistic and conservative capacity estimates and does not take into account the joints of the rock mass. As far as analytical approaches are concerned, Merifield’s method gives the highest bearing capacity values. This overestimation of the bearing capacity with the Merrified approach is explained by its bearing factor, which is significantly higher than those proposed by Serrano-Ollala, Wyllie Duncan and Terzaghi. The Finite Element Method (FEM) using load-displacement curves was used to estimate the ultimate bearing capacity ( Figures 8(a)-(c) ). The material parameters are mi = 25, GSI = 60 and 55 and Rc = 28; 24.27 and 34 MPa. The results obtained using the Finite Element Method give values between 13.98 and 19.77 MPa.

Foundation displacements were obtained from pressuremeter tests, the Schleicher method and numerical modelling. The results show very low displacements ( Table 8 ). In the case of a thin clay sand layer resting on the bedrock at a shallow depth ( Figure 9(a) , Figure 9(b) ), the rigidity of the bedrock reduces the settlement of the foundation, compared with the case where the bedrock is at a great depth ( Figure 9(c) ). The difference in rigidity between the clay layer and the rock layer leads to differential settlement when footings are laid at different levels, especially for spread footings. In addition, settlement calculations based on the results of the finite element method in a compressible layer on a rigid base are more suitable than pressuremeter tests and the Schleicher method. These results confirm those of [2] .