3.1.1 Description, identification and classification

The chemical and mineralogical composition categorized most of the rock samples as pure limestone, with only 30 % of them classified as argillaceous limestones and marls (Arab C and D breccias, Hith, and lower Sulaiy). Magnesium-rich limestones are restricted to Arab D limestone and upper Jubaila. The petrographic analysis showed that most of the units corresponded to calcarenitic, bioclastic, and lithoclastic limestones with heterogeneous texture; from mud-rich mudstone and wackstone to grain-supported lithoclastic or peloidal packstone fabric (Fig. 2). Some samples presented brecciated textures made up of polymictic rock fragments (<1 cm), quite likely due to the complete interbedded gypsum and anhydrite dissolution and the subsequent brecciation under lithostatic load, as mainly observed in Hith.

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Fig. 2

Core photographs examples: a) Jubaila calcarenite; b) Arab D calcarenite with burrows; c) Arab D clay breccia; d) Arab C carbonate breccia; e) Arab ABC aphanitic limestone with geodic porosity; f) Hith carbonate and clay breccia; g) brecciated aphanitic-calcarenitic Sulaiy.

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3.1.2 Physical properties

The unit weight at the natural water content values typically ranged from 22 to 27 kN/m³, with an average of 24.6 kN/m³. Only slight differences were found comparing the results of the well layered units (Jubaila and Arab D limestone) with the brecciated formations (Arab D and C breccias, Arab ABC, Hith and Sulaiy) as shown in Fig. 3a. The natural water content typically oscillated from 0.1 to 1.1%. The porosity varied from 0.1 to 8.1% with an average of 2.5%, which is in the range of the typical values for limestone (5–20 %) suggested by Serrano (2002). These values matched quite well with the average unit weight of 22.75 kN/m³ and porosity of 2 to 12% for Sulaiy limestone reported in the city by Abd El Aal (2015).

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Fig. 3

Boxplots for each geotechnical unit: a) unit weight at the natural water content (γ); b) unconfined compressive strength (σ_ci); c) point load index (Is₅₀).

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3.1.3 Mechanical and elasticity properties

The unconfined compressive strength over 718 rock samples ranged from 2.2 to 133.2 MPa, with an average of 37.8 MPa and median value of 32.7 MPa. Strength results on rock samples showed higher values for the bedded limestone rock layers (Jubaila and Arab D limestone) with an average of 51 MPa, than for the brecciated units (Arab D and C breccias, Arab ABC, Hith and Sulaiy) with 25 MPa (Fig. 3b). These values matched relatively well with the average dry strength previously evaluated by ADA (1990): 39.9 and 26.5 MPa for Jubaila aphanitic and calcarenitc limestone respectively; 19.8, 23.1, and 25.3 MPa for Arab aphanitic, breccia, and calcarenite correspondingly; and 25.6, 17.9, and 21.3 MPa for Sulaiy aphanitic, breccia and calcarenite respectively. In addition, their findings trend towards weakness with increasing moisture content (23 to 73% reduction).

The strength results were also indirectly obtained from point load test determinations (Fig. 3c) which presented high scatter of the variation coefficient (V_x of 0.58). The Is₅₀ index varied from 0.3 to 8.3 MPa, which are typical values for limestone. Comparing the strength results obtained from unconfined compressive strength test with the ones directly obtained from point load (Fig. 3c), there is fairly the same trend towards strength per geotechnical unit. These values are slightly lower than the ones obtained by Abdlmutalib et al. (2015) in an outcrop 60 km south of Riyadh for Upper Jubaila and Arab-D Member. They ranged from 1.5 MPa for the laminated mudstone to 14 MPa for the grainstone lithofacies. On the other hand, triaxial laboratory tests on rock resulted in an average Hoek-Brown parameter “m_i” of 12 for the bedded limestone and 15 for the brecciated units.

Rock units show a modulus of elasticity typically ranging from 10 to 55 GPa, meanwhile, the Poisson ratio is generally between 0.2 and 0.3. The stiffness results obtained from the triaxial tests are higher (average and median modulus of 41 GPa) than the ones gained from the uniaxial strength tests with bands (33 GPa), probably due to the effect of the confining pressure in weak rocks, which increase the friction in micro fissures (Mingqing, 2003). In this regard, Alnuaim et al. (2019) obtained from nine rock core specimens of Jubaila and Arab Formation in two sites of Riyadh city, an average value of Poisson’s ratio of 0.25 and Young’s modulus ranging from 45 to 59 GPa. These average values are greater than the ones obtained along Line 3, probably due to the number of test results and different specimens’ geometry.

Rock units were categorized as “low strength” and “high modulus ratio” (E_i/σ_ci > 500) according to Deere and Miller (1966) as shown in Fig. 4. This high modulus ratio is typical in other limestones in Arabia (Al-Shayea, 2004), with extreme values higher than 1200.

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Fig. 4

Engineering Classification for intact rock.

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3.1.4 Physico-mechanical correlations

Regarding correlation between density and strength tests, better correlation was found between the thinly bedded limestone rocks (Jubaila and Arab D limestone) than the brecciated carbonate rocks (Arab brecciated rock units, Hith and Sulaiy), however, both had a low Determination Coefficient (R² < 0.4). On the other hand, a good linear correlation (R² > 0.9) was found between the maximum axial stress and strain (Fig. 5).

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Fig. 5

Stress–strain ratio of the unconfined compression strength test.

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According to Bieniawski (1974) an average correction factor for all types of rock is feasible (σ_ci≈24·Is₅₀). Contrastingly, Romana (1999) presented variable factor depending on the type of rock, ranging from 18 to 24 for well cemented limestone and 12 to 18 for poor cemented limestones. The point load data resulted in a wide range of results and a linear regression among point load and uniaxial strength of 17.7, in place of the most common value of 22–24. Such a result was associated with the brecciated nature of most of the rocks and the fact that the point load results are not very effective in the range of 0 to 2 MPa. The average σ_ci /Is₅₀ ratio of these rock units was 19 for the bedded limestone units (Jubaila and Arab D limestone), and approximately 16 for the brecciated and slumped rock layers (Arab D and C breccias, Arab ABC, Hith and Sulaiy). Moreover, higher average coefficients and more consistent results were obtained through point load testing of axial specimens (Is₅₀ of 3.6 MPa and V_x of 0.03) than diametral ones (2.2 MPa and 0.58) as previously assessed testing weak rocks by Bowden et al. (1998).

3.1.5 Characteristic values of intact rock parameters

Based on the statistical analysis carried out, the lower or inferior characteristic value (X_k,inf) and the higher or superior characteristic value (X_k,sup) as a 95 % confidence limit for the mean were calculated (Table 1). Considering the size and distribution of the available data, a Percentile of 33 % was in general satisfactorily adopted in Line 3. Tighter rules were not justified regarding this kind of ground, where brecciated and well-bedded rocks may coexist.

3.2.1 Geomechanical classification

In addition to the bedding (S0), four joint sets (due to lithification under lithostatic load) of subvertical joints have been recognized in geomechanical surveys (J1 to J4), for both the undisturbed limestone and the brecciated units (Fig. 6a). This fact is coherent with the sedimentary wedge context, evidence of the absence of tectonic deformation. The bedding is of close spacing (Fig. 6b), partially open (Fig. 6c), of very high persistence (Fig. 6d), and with weathering rock infilling (Fig. 6e) according to ISRM (1981). The joint sets (J1 to J4) show patent differences between the unaltered bedded limestones and the brecciated formations, the latter showing, closer spacing, lower persistence, and higher weathering infilling.

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Fig. 6

Joint set data from geomechanical surveys in open outcrops: a) orientation; b) spacing (mm); c) opening (mm) d) persistence or continuity (m); e) infilling (mm).

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Starting from the 46 Schmidt rebound number measured in the geomechanical surveys (between 44 and 59 in Jubaila and 20 to 54 in Sulaiy) and a basic angle of friction (Ø_b) of 25°, a residual angle of friction (Ø_r) of 15° was calculated. The Schmidt rebound hammer was also used to evaluate the Joint Compressive Strength (JCS) of the walls as proposed by Deere and Miller (1966) resulting in 10 to 30 MPa. The Joint Roughness Coefficient (JRC) was estimated as 10 “smooth undulating” by comparing the appearance of the surface of the rock joints with the standard profiles published by Barton and Choubey (1977). The RQD measured in borehole cores (Table 2) describes most of the rock units as “fair” (Jubaila, Arab D limestone, Arab C breccia, Arab ABC and Sulaiy), classifying the rest of the geotechnical units as “poor” (Arab D breccia and Hith). The unaltered bedded limestone units are classified as good rock (65 > RMR > 62) and the fractured and brecciated, as fair rocks (57 > RMR > 42) as shown in Table 2. Most of the values are within the range of GSI = RMR–2 (bedded limestone) and GSI = RMR–4 (carbonate breccias).

3.2.2 Rock mass properties

The Generalized Hoek-Brown rock mass parameters were calculated (Fig. 7) based on the intact rock parameters (Table 2). The correlation between the intact rock properties calculated from laboratory tests (σ_ci, E_i and m_i) and the rock mass parameters calculated with RocData (σ_cm and E_rm) using the GSI, correspond well between geotechnical units, reflecting a geotechnical quality reduction from the bedded limestone units to the brecciated formations. Consequently, a geotechnical quality decrease from the western section (bedded limestone outcrops) to the eastern section of Line 3 (brecciated rocks formations) is revealed (Fig. 1b).

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Fig. 7

Rock mass strength parameters: a) major (σ₁) versus minor principal stress (σ₃); b) shear (τ) versus normal (σ) stress space. Legend: σ_t, uniaxial tensile strength; σ_c, uniaxial compressive strength; σ_cm, compressive strength of rock mass and E_rm, deformation modulus of the rock mass.

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3.2.3 Geophysical investigation

Crosshole and downhole seismic testing resulted in P-wave and S-wave velocities increase with depth, reflecting a subsurface geomechanical quality improvement. Good results were obtained for P-waves; contrastingly, S-waves signal showed poorer results and quality, mainly due to the high background noise. The undisturbed limestone units (Jubaila and Arab D limestone) generally resulted in the highest P-wave velocities (2000–3000 m/s). On the other hand, the brecciated layers (Arab C and D breccias, Arab ABC limestone, Hith and Sulaiy) usually showed lower velocities with P-wave values ranging from 1500 to 2500 m/s.

The seismic refraction tomography has resulted in P-wave velocities of 3000 to 4500 m/s for the competent calcareous bedrock composed of the Jubaila and Arab D limestone. Lower P-wave velocities (2000 to 3000 m/s) are associated with the brecciated terms of the Arab formations, Hith and Sulaiy. Comparing the P-wave velocity from seismic refraction tomography with P-wave velocity from downhole and crosshole tests, it was found that the velocities from the latter are lower. This is explained by the horizontally integrating effect of seismic refraction compared with point-based sampling of the seismic tests inside boreholes (Cueto et al., 2018b).

Finally, the electrical resistivity tomography has mainly given information about the weathering and jointing state of the rocks, with low resistivity values usually indicating more weathered or fractured zones (<200 Ωm), while the high resistivity values correspond to the solid carbonate bedrock (200–700 Ωm). The limitations of this method prevented noticeable contrast of resistivity between different geological formations, due to the similar lithological features.

3.2.4 Rock mass stiffness

The results of the 48 pressuremeter tests carried out (76 mm diameter OYO dilatometer) presented an average pressuremeter modulus of 3.7 GPa. There is a clear difference between the massive limestone unit with an average pressuremeter modulus of 7.6 GPa, and the brecciated rocks which reached an average value of 2.8 GPa (Fig. 8). An increase of pressuremeter modulus and shear modulus was observed related to the quality of the rock in terms of RQD, RMR and GSI. Comparing the elasticity modulus directly obtained from pressuremeter tests with the modulus calculated based on different geomechanical correlation equations (Fig. 8), it is evident that the latter overestimates the rock mass modulus. This overestimation is more pronounced as the value of RMR increases.

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Fig. 8

Comparison between the average rock mass modulus (E_rm) estimated with empirical relationships (Serafim and Pereira 1983; Hoek et al. 2002, Galera et al. 2005, Hoek and Diederichs 2006) against average in-situ pressuremeter test results based on the calculated RMR and GSI.

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The dynamic elasticity modulus obtained from the downhole and crosshole tests presented values ranging from 2 to 10 GPa, while the dynamic shear modulus varied from 1 to 4.5 GPa and the Poisson ratio resulted in values differing from 0.20 to 0.35. The average values of elasticity dynamic modulus determined along Line 3 with the seismic wave velocities for each geotechnical unit are in the range of 5 to 8 GPa, which is approximately 1 to 4 times higher than the static ones measured with pressuremeter tests. This is explained because the static moduli refer to a portion of the mass rather than the whole rock mass, and this difference is wider when the rock mass conditions are poorer (Martínez-Martínez et al., 2012). Although a trend like this is to be expected due to the different range of strains involved in a seismic excitation and in a static loading, the gap appears to be wide indeed and is presumably related to local effects of the borehole walls.