Geoth. Energ. Sci., 2, 21–37, 2014 www.geoth-energ-sci.net/2/21/2014/ doi:10.5194/gtes-2-21-2014 © Author(s) 2014. CC Attribution 3.0 License. Empirical relations of rock properties of outcrop and core samples from the Northwest German Basin for geothermal drilling D. Reyer1,* and S. L. Philipp1 1Georg August University of Göttingen, Geoscience Centre, Department of Structural Geology and Geodynamics, Germany *now at: State Authority of Mining, Energy and Geology – Zentrum für TiefenGeothermie, Celle, Germany Correspondence to: D. Reyer (dorothea.reyer@geo.uni-goettingen.de) Received: 26 March 2013 – Revised: 12 August 2014 – Accepted: 15 August 2014 – Published: 8 September 2014 Abstract. Information about geomechanical and physical rock properties, particularly uniaxial compressive strength (UCS), are needed for geomechanical model development and updating with logging-while-drilling methods to minimise costs and risks of the drilling process. The following parameters with importance at dif- ferent stages of geothermal exploitation and drilling are presented for typical sedimentary and volcanic rocks of the Northwest German Basin (NWGB): physical (P wave velocities, porosity, and bulk and grain density) and geomechanical parameters (UCS, static Young’s modulus, destruction work and indirect tensile strength both perpendicular and parallel to bedding) for 35 rock samples from quarries and 14 core samples of sandstones and carbonate rocks. With regression analyses (linear- and non-linear) empirical relations are developed to predict UCS values from all other parameters. Analyses focus on sedimentary rocks and were repeated separately for clastic rock samples or carbonate rock samples as well as for outcrop samples or core samples. Empirical relations have high statistical significance for Young’s modulus, tensile strength and destruction work; for physical properties, there is a wider scatter of data and prediction of UCS is less precise. For most relations, properties of core samples plot within the scatter of outcrop samples and lie within the 90 % prediction bands of developed regression functions. The results indicate the applicability of empirical relations that are based on outcrop data on questions related to drilling operations when the database contains a sufficient number of samples with varying rock properties. The presented equations may help to predict UCS values for sedimentary rocks at depth, and thus develop suitable geomechanical models for the adaptation of the drilling strategy on rock mechanical conditions in the NWGB. 1 Introduction In Germany, the North German Basin (NGB) is one re- gion with considerable geothermal low-enthalpy potential (Paschen et al., 2003). To utilise this potential, deep well- bores have to be drilled to reach prospective geothermal reservoir rocks at depths of 3000–6000 m. Well construction is therefore the main expense factor of geothermal projects in this region. In sedimentary successions such as the NGB, one of the major problems and expenditures may be related to wellbore stability issues (e.g. Dusseault, 2011; Zeynali, 2012). Such wellbore instabilities are recognised as a drilling challenge that may considerably increase drilling costs and safety risks (Proehl, 2002; York et al., 2009; Li et al., 2012). The profit margin of geothermal projects, however, is rather small compared with hydrocarbon projects. Therefore, a sub- stantial reduction of costs for well construction and comple- tion is desirable (cf. www.gebo-nds.de). Evaluation of in situ rock mechanical behaviour requires different information. Important input data include estimates of mechanical conditions, pore pressures, and stress state. According to Zeynali (2012), two of the most important me- chanical factors affecting wellbore stability are the mechani- cal properties of rock – including anisotropy of strengths and Published by Copernicus Publications on behalf of the GtV Service GmbH and the IGA Service GmbH. 22 D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samples elastic moduli (e.g. Heap et al., 2010) – and in situ stresses existing in different layers of rock. Development of a ge- omechanical model before starting the drilling operation is a powerful tool to prevent wellbore instabilities and minimise drilling costs of geothermal wells (Khaksar et al., 2009). For drilling through a rock mass, such model captures the initial equilibrium state that describes the stresses, pore pressure, and geomechanical properties. With logging-while-drilling data the initially computed geomechanical model can be con- tinuously adapted to the conditions at depth. For such geomechanical modelling, the uniaxial compres- sive strength (UCS) is the most important geomechanical input parameter (Chang et al., 2006; Nabaei and Shahbazi, 2012; Vogt et al., 2012). There already exist several software approaches for building and updating geomechanical mod- els (Settari and Walters, 2001; geomechanics software, e.g. GMI – http://www.baker-hughes.com). Generally, such ge- omechanical modelling software uses empirical relationships that were developed for hydrocarbon reservoirs. To date there do not exist such relationships for geothermal reservoirs of the NGB. Here, the geological setting may be completely different leading to other rock mechanical conditions. There- fore, existing methods for geomechanical modelling have to be reviewed carefully and adapted where needed. There are several relevant parameters with importance given to different stages of geothermal exploitation and drilling. Physical properties such as density, ρ, and P and S wave velocities, vp and vs (compressional and shear wave velocities), are parameters that can be measured directly in wellbores; the porosity, 8, is derivable from such well logs (Edlmann et al., 1998). The dynamic Young modulus is de- rived from velocity and density logs (Fricke and Schön, 1999; Zoback, 2007; Rider and Kennedy, 2011). Geome- chanical parameters are important for reservoir exploitation and drilling operations. The static Young modulus, Es, is interesting in terms of predictions of fracture propagation (Jaeger et al., 2007; Gudmundsson, 2011). The indirect ten- sile strength, T0, gives information about the rock’s resis- tance to tensile fractures. These parameters are of interest in terms of dimensioning of hydraulic fracturing operations, wellbore stability and drilling mud selection (e.g. Zoback, 2007). The destruction work, W , is one parameter provid- ing information on the amount of energy needed to destroy the rock while drilling. It is known to correlate with the drilling efficiency which is a term used to describe the ef- fects of a number of geological and machine parameters on the drilling velocity (Thuro, 1997). Therefore, it is desir- able to make reasonable assumptions about these parameters for drilling through the rock units. To do so, we need em- pirical relations between UCS and parameters which are ei- ther knowable before drilling or determinable with logging- while-drilling tools. With well logs from existing adjacent boreholes, a geomechanical model can be built using empir- ical relations between rock-strength values and physical pa- rameters. Empirical relations can then be used for validation of the geomechanical model while- and after-drilling by up- dating the model continuously with logging data. Determining geomechanical and physical parameters di- rectly from core material, however, is expensive and time- consuming because a large number of core samples are needed, and core material is rare (e.g. Khaksar et al., 2009). Therefore, in this study we aim to improve predictions of me- chanical properties for rocks at depth. First, we present data on geomechanical and physical properties of representative rock types of the NGB. We sampled 35 mainly sedimentary rocks of the western sub-basin of the NGB, the Northwest German Basin (NWGB), from Lower Permian to Upper Cre- taceous, exposed in outcrop analogues, i.e. quarries. In addi- tion to these outcrop samples, we analysed 14 core samples from two wellbores with the same stratigraphic units, com- parable lithologies and facies as equivalent samples to anal- yse mechanical property changes due to uplift and alteration. Secondly, we used the data of sedimentary rocks to perform regression analyses, together with calculation of coefficients of determination (R2), between UCS and the described pa- rameters, separately for outcrop samples only and including core samples. To analyse the statistical significance of the developed regression functions, 90 % confidence and predic- tion bands are added. The rock properties of core samples are compared with the results of outcrop samples from the devel- oped equations of outcrop samples to examine the relevance of outcrop samples for predicting rock properties at depths. The regression functions may help predict UCS values for sedimentary rocks at depth, and thus develop a suitable ge- omechanical model for the adaptation of the drilling strategy on rock mechanical conditions. 2 Geologic setting and sample locations The study area is part of the NWGB, the western part of the NGB, located in northwestern Germany (Walter, 2007). The NGB initiated in the Late Carboniferous–Permian due to rift- ing processes subsequent to the Variscan orogenesis (Betz et al., 1987; Ziegler, 1990). From marine to continental condi- tions, the sedimentary succession is characterised by chang- ing sedimentation environments. Therefore, the NWGB is comprised of mainly carbonate and clastic rocks with some intercalated evaporates leading to very heterogeneous rock mechanical conditions. The study area is located at the southern and western margins of the western region of the North German Basin (Fig. 1; cf. Reyer et al., 2012). Sedimentary rocks that oc- cur at geothermally relevant depths in the centre and north of the NWGB crop out at the basin margins and can be sam- pled in quarries. In such outcrop analogues, listed in Table 1, we took samples of two main rock types: carbonate rocks (Triassic, Jurassic, and Cretaceous age) and sandstones (Per- mian, Triassic, Jurassic, and Cretaceous age; Table 1). Three Rotliegend volcanic rock (Permian) samples are included to Geoth. Energ. Sci., 2, 21–37, 2014 www.geoth-energ-sci.net/2/21/2014/ D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samples 23 30 1 2 Figure 1. North German Basin (modified after www.geotis.de) with the locations of sampled 3 wellbores and quarries and the exposed rock types (see key) in the NWGB (rough location 4 marked). 5 6 Figure 1. North German Basin (modified after http://www.geotis. de) with the locations of sampled wellbores and quarries and the ex- posed rock types (see key) in the NWGB (rough location marked). obtain rock property data over a wide range of lithologies present in the NWGB (Fig. 1). For four carbonate rock units and three sandstone units, the equivalent core samples were identified and sampled from two wellbores: Groß Buchholz (Gt1) and Eulenflucht 1 (EF1; Table 1). 3 Methods 3.1 Density and porosity The bulk density, ρd [g cm−3], was determined from dry cylindrical specimens with a GeoPyc 1360 (Micromeritics), setting measured volume and mass in relation. For the same specimens, we measured the grain density, ρ0 [g cm−3], with an Ultrapycnometer 1000 (Quantachrome) at room tempera- ture using 99.9 % helium, previously measured ρd and spec- imen’s mass. The total porosity, 8, given in [%], was calculated from ρ0 and ρd. Samples are separated in low- (0–10 %), medium- (10–20 %), and high-porosity (> 20 %) rocks for further in- terpretation of rock properties. 3.2 Rock testing Uniaxial compression tests were performed stress-controlled at a constant rate of 0.5 MPa s−1 on specimens with length– diameter ratios of 2–2.5 to determine UCS and Es (ISRM, 2007). For each outcrop sample, six specimens with diame- ters of 40 mm were measured, both parallel and perpendic- ular to sedimentary bedding or, for volcanic rocks, with re- spect to surface orientation. Core samples were tested only perpendicular to bedding due to limited core material. vp is measured (Tektronix TDS 5034B; 1 MHz rectangular pulse) to eliminate defective specimens. Es is determined at the linear–elastic deformation path of the stress–strain curve. For rock samples showing brittle failure, we calculated W (Thuro, 1997) as the area below the stress-strain curve given in kilojoules per cubic metre. T0 is measured both parallel and perpendicular to sed- imentary bedding on specimens with diameters of 40 mm and lengths of 15–20 mm with Brazilian tests (ISRM, 2007). Both parallel and perpendicular to bedding, a minimum of nine (outcrop samples) and four specimens (core samples), respectively, were tested. 3.3 Statistical analyses For each sample, both parallel and perpendicular to bed- ding, mean values and standard deviations of the tested spec- imens were calculated for geomechanical parameters and vp. We performed regression analyses (linear and non-linear) of mean values for UCS with 8, ρd, vp, and Es and for W and T0 with UCS, respectively. Different regression analy- ses were made for each pair of parameters: (1) all samples to obtain a good overview, (2) sandstone samples only, and (3) carbonate samples only. In each case, regressions were made both for outcrop samples only and for all samples in- cluding core samples. For outcrop sample equations, 90 % confidence and prediction bands are included. Confidence bands represent the 90 % certainty of regression curve es- timation based on limited sample data (Wooldridge, 2009; Brink, 2010). Prediction bands cover the range in which the values of future measurements of associated samples lie with a probability of 90 %. Based on these bands core sample re- sults are compared with outcrop results. 4 Experimental results 4.1 Physical properties In Tables 2 and 3, mean values of dry bulk density, grain density, calculated porosities, and P wave velocities of all rock samples are listed. The approximate lithology is given to better appraise the following data analyses. For sandstones and carbonates, we have sample data over a wide range of porosities; the lowest porosities occur in core samples. Accordingly, the dry bulk density values show a wide range. Grain densities of carbonates are highest due to a higher mineral density of the carbonates’ main component calcite as compared with quartz. The grain densities strongly depend on the amount of heavy minerals: (1) hematite-rich Triassic sandstones have high ρ0 values (> 2.7 g cm−3); (2) carbonate samples with increased grain densities contain large amounts of ferrous carbonates. vp values clearly depend on lithology. Carbonate samples show mean values of vp from 3277 m s−1 (porous chalk marl: www.geoth-energ-sci.net/2/21/2014/ Geoth. Energ. Sci., 2, 21–37, 2014 24 D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samples Table 1. All samples from outcrops and wellbores with sample ID, local name, lithology, stratigraphical units, and total vertical depths of core samples. Sample ID Lithology System Local name KrCa Chalk marl Kreidemergel GoSa Sandstone Sudmerberg F. HoT Marl Rotpläner BrCe Limestone Cretaceous Cenoman-Kalk OLH Sandstone Hils Sst. GiUK Sandstone Gildehaus Sst. FrUK Sandstone Bentheimer Sst. OK Sandstone Wealden Sst. ThüJ Limestone Serpulit GVa Limestone Gigas Schichten OKDa Limestone Jurassic Oberer Kimmeridge ShJk Limestone Korallenoolith HSDi, HSDi2 Limestones Heersumer Schichten AlWo Sandstone Aalen Sst. koQ Sandstone Rhät Sst. koVe Sandstone Rhät Sst. kuWe Siltstone Lettenkohlen Sst. EM Limestone Trochitenkalk H Limestone Schaumkalk EL1, EL2, EL3 Limestones Triassic Wellenkalk soWa Shale-Gypsum Röt 1 smHN Sandstone Hardegsen-Folge smD Sandstone Detfurth-Folge smVG, smVG2 Sandstones Volpriehausen-Folge suHe Limestone Rogenstein BiSu Sandstone Bernburg-Folge BeRo, BeRoK Sandstones Rotliegend Sst. DöRo Andesite Permian Rotliegend-Vulkanit FL2, FL6 Rhyolites Rotliegend-Vulkanit Wellbore 1: Eulenflucht 1 (EF1) Wellbore 2: Groß Buchholz (Gt1) TVD [m] Gt1WS1 Sandstone Wealden Sst. 1.221 Gt1WS2 Sandstone Cretaceous Wealden Sst. 1.211 EF1WS Sandstone Wealden Sst. 135 EF1GS Limestone Gigas Schichten 210 EF1OK Limestone Oberer Kimmeridge 243 EF1UKK Limestone Jurassic Korallenoolith 282 EF1KO Limestone Korallenoolith 286 EF1HS Limestone Heersumer Schichten 325 Gt1DU1 Sandstone Detfurth-Folge ∼ 3535.8 Gt1DU2 Sandstone Detfurth-Folge ∼ 3534.3 Gt1DU3 Sandstone Triassic Detfurth-Folge ∼ 3534.7 Gt1DW Siltstone Detfurth-Folge ∼ 3537.2 Gt1VS1 Sandstone Volpriehausen-Folge ∼ 3655.6 Gt1VS2 Sandstone Volpriehausen-Folge ∼ 3657.8 Sst.: sandstone, F.: formation; TVD: total vertical depth Geoth. Energ. Sci., 2, 21–37, 2014 www.geoth-energ-sci.net/2/21/2014/ D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samples 25 Table 2. Lithology, dry bulk density, grain density, porosity and P wave velocity for outcrop samples. Sample ID Specified lithology ρd [g cm−3] ρ0 [g cm−3] 8 [%] vp [m s−1]+SD KrCa Porous chalk marl 2.18 2.86 23.9 3277± 84 GoSa Medium-grained sandstone 2.53 2.69 6 3772± 70 HoT Marl 2.59 2.73 5.2 5116± 199 BrCe Bioclast-bearing matrix LS 2.66 2.77 3.8 4674± 258 OLH Medium-grained sandstone 2.09 2.77 24.6 2291± 63 GiUK Medium-grained sandstone 2.11 2.68 21.6 2576± 130 FrUK Fine-grained sandstone 2.36 2.68 12.1 2172± 87 OK Medium-grained sandstone 2.29 2.80 18.3 2942± 120 ThüJ Bioclast-rich matrix LS 2.07 2.83 26.7 4262± 215 GVa Porous sparry LS 2.29 2.96 22.8 3967± 106 OKDa Bioclast-rich matrix LS 2.63 2.83 7.2 5134± 100 ShJk Bioclast-bearing oolite 2.61 2.74 4.6 5171± 154 HSDi Micro-sparry LS 2.53 2.78 9.1 5084± 350 HSDi2 Bioclast-rich sparry LS 2.40 2.78 13.7 4787± 236 AlWo Medium-grained sandstone 2.09 2.69 22.5 3000± 184 koQ Medium-grained sandstone 2.27 2.84 20.1 3222± 36 koVe Fine-grained sandstone 2.34 2.77 15.6 2980± 38 kuWe Siltstone 2.59 2.68 3.4 3951± 126 EM Bioclast-rich sparry LS 2.71 2.79 2.9 5607± 164 H Porous sparry LS 2.40 2.77 13.2 4888± 73 EL1 Dolomitic LS 2.53 2.98 15.1 4683± 133 EL2 Massy matrix LS 2.74 2.75 0.3 6158± 8 EL3 Dolomitic LS 2.66 2.94 9.4 4526± 23 soWa Shale-gypsum alternation 2.33 2.39 2.5 3690± 120 smHN Medium-grained sandstone 2.26 2.71 16.6 2574± 64 smD Medium-grained sandstone 2.38 2.76 13.7 2986± 22 smVG Medium-grained sandstone 2.32 2.72 14.4 2948± 78 smVG2 Medium-grained sandstone 2.17 2.74 20.6 2074± 89 suHe Sparry oolite 2.71 2.75 1.5 5368± 136 BiSu Medium-grained sandstone 2.15 2.79 22.9 2110± 6 BeRoK Conglomeratic sandstone 2.58 2.67 3.2 3564± 78 BeRo Medium-grained sandstone 2.52 2.69 6.6 3426± 29 DöRo Andesite 2.72 2.72 0.1 5449± 23 FL2 Rhyolite 2.63 2.64 0.1 5260± 44 FL6 Rhyolite 2.69 2.69 0.1 5342± 64 LS, limestone; ρd, dry bulk density; ρ0, grain density; 8, porosity; vp, P wave velocity; SD, standard deviation KrCa) to 6158 m s−1 (massy matrix limestone: EL2). Mostly, the standard deviations of carbonate samples are high. This is pronounced in carbonates with either a high presence of lithoclasts or due to rock heterogeneities. vp in sandstones are considerably slower than in carbonate rocks. The lowest values relate to high porosities. In volcanic rock samples, vp is rather high (about 5300 m s−1) with small variation and standard deviations. 4.2 Rock mechanical properties In Table 4, mean values of the geomechanical parameters of all samples are listed. The standard deviations of all measure- ments for every sample are given. Measured parameter val- ues of the eight clastic core samples are higher than those of the 14 outcrop samples. The differences between outcrop and core samples of carbonate rocks are, in contrast, rather small. Parameter values of the three volcanic rock samples are con- siderably higher than of sedimentary outcrop samples. 5 Empirical relations of rock properties with UCS The rock property data, presented in Tables 2, 3, and 4, may be used directly to calibrate an existing geomechanical model by attaching UCS values to log profiles and deducing equiv- alent values of tensile strength and destruction work using empirical relations. In situ rocks and core samples, how- ever, may have completely different rock properties. Thus, we compare properties of core samples and outcrop samples to analyse if properties of in situ rocks can be predicted based on data from outcrop samples from the same geologic setting. www.geoth-energ-sci.net/2/21/2014/ Geoth. Energ. Sci., 2, 21–37, 2014 26 D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samples Table 3. Lithology, dry bulk density, grain density, porosity and P wave velocity for core samples. Core samples: Sample ID Specified lithology ρd [g cm−3] ρ0 [g cm−3] 8 [%] vp [m s−1]+SD Gt1WS1 Coarse-grained sandstone 2.40 2.84 15.5 4854± 38 Gt1WS2 Medium-grained sandstone 2.58 2.79 7.6 2950± 267 EF1WS Medium-grained sandstone 2.25 2.79 19.4 2638± 28 EF1MM Shale gypsum 2.88 2.95 2.4 5808± 110 EF1GS Sparry LS 2.48 2.78 10.8 5832± 65 EF1OK Bioclast-rich matrix LS 2.72 2.78 2.1 5732± 50 EF1UKK Bioclast-rich sparry LS 2.76 2.77 0.2 5412± 53 EF1KO Sparry oolite 2.72 2.79 2.6 6053± 59 EF1HS Bioclast-rich sparry LS 2.18 2.82 22.8 3831± 87 Gt1DU1 Medium-grained sandstone 2.69 2.70 0.4 4981± 33 Gt1DU2 Coarse-grained sandstone 2.73 2.75 1.0 3410± 78 Gt1DU3 Medium-grained sandstone 2.67 2.77 3.6 4906± 96 Gt1DW Siltstone 2.83 2.87 1.1 5166± 123 Gt1VS1 Medium-grained sandstone 2.71 2.72 0.1 4745± 62 Gt1VS2 Coarse-grained sandstone 2.69 2.77 2.8 4539± 54 LS, limestone; ρd, dry bulk density; ρ0, grain density; 8, porosity; vp, P wave velocity; SD, standard deviationFigure 2        0 50 100 150 200 250 300 0 5 10 15 20 25 30 Φ [%] U C S [ M P a ] a b 2 2.2 2.4 2.6 2.8 3 ρd [g/cm ] 3 0 50 100 150 200 250 300 U C S [ M P a ] all samples - perpendicular 0 5 10 15 20 25 Φ [%] clastic rocks only 2 2.2 2.4 2.6 2.8 3 ρd [g/cm ] 3 0 5 10 15 20 25 Φ [%] carbonates only 2 2.2 2.4 2.6 2.8 3 ρd [g/cm ] 3 c e f g 30 30 1b) 1a) 9b) 9a) 13b) 13a) 3b) 3a) 10b) 10a) 14b) 14a) 0 5 10 15 20 25 Φ [%] 30 d 2) Outcrop samples parallel to layering 2 2.2 2.4 2.6 2.8 3 ρd [g/cm ] 3 h 4) all samples - parallel Outcrop samples Core samples Regression curve: Outcrop samples Regression curve: Outcrop+core samples Figure 2. UCS measured perpendicular to bedding vs. (a–c) 8 and (e–g) ρd, respectively, separately for all samples (a, e; n= 49), only clastic rock samples (b, f; n= 24) and only carbonate samples (c, g; n= 20) for outcrop and core samples; regression curves shown for both outcrop and core samples and outcrop samples only. UCS measured parallel to bedding vs. (d) 8 and (h) ρd (n= 33); for regression equations see Table 5. For UCS, error bars stand for standard deviations of all measurements of every sample (Table 4). For density and porosity, error bars represent measuring accurancies of 1 % and 5 %, respectively. In Table 5, the results of regression analyses for the different parameters, presented in following sections, are summarised. 5.1 Empirical relations for UCS prediction 5.1.1 Density and porosity Porosity and bulk density are two parameters that can be determined with geophysical logs. Many previous studies showed that there are strong correlations between UCS and both parameters (e.g. Lama and Vutukuri, 1978; Jizba, 1991; Wong et al., 1997; Palchik, 1999). In Fig. 2, both porosity and bulk density are plotted against UCS measured perpendicular and parallel to bedding. It is obvious that there is a wide scatter of data resulting in rather poor statistical significance of the empirical relations (Ta- ble 5). However, the prediction of in situ properties based on outcrop sample results is one of the main questions of this study. It is conspicuous that in all cases, and especially for carbonates, outcrop and core samples show a similar range Geoth. Energ. Sci., 2, 21–37, 2014 www.geoth-energ-sci.net/2/21/2014/ D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samples 27 Table 4. Mean values of the geomechanical parameters UCS, Young’s modulus, destruction work, and indirect tensile strength, measured perpendicular and parallel to bedding, for all samples including standard deviations. Sample UCS±SD [MPa] Es±SD [GPa] W ±SD [kJ m−3] T0±SD [MPa] ID par. perp. par. perp. par. perp. par. perp. KrCa 36± 7 31± 4 12.7± 1.2 13.5± 1.1 106± 20 133± 30 2.0± 0.6 2.7± 0.8 GoSa 35± 2 75± 11 7.9± 0.5 30.3± 11.1 215± 26 213± 41 2.6± 0.4 5.9± 0.3 HoT 81± 7 112± 15 40.6± 4.2 34.1± 6.8 263± 60 332± 67 5.2± 1.0 8.0± 1.7 BrCe 126± 5 91± 29 44.1± 4.0 26.8± 6.1 282± 17 301± 15 6.7± 0.9 7.6± 0.6 OLH 37± 7 23± 10 15.1± 5.5 10.9± 6.5 118± 19 50± 6 3.1± 0.3 3.1± 0.3 GiUK 56± 2 47± 4 19.7± 4.6 15.7± 2.1 175± 25 198± 41 4.1± 0.4 3.1± 0.2 FrUK 45± 7 55± 4 12.0± 3.5 13.7± 4.5 245± 21 248± 38 2.4± 0.3 2.8± 0.4 OK 82± 6 73± 7 19.3± 1.5 18.0± 2.6 394± 34 404± 17 3.8± 0.9 4.2± 0.8 ThüJ 23± 5 26± 5 14.7± 1.3 13.3± 3.9 69± 10 77± 9 2.3± 0.4 2.7± 0.4 GVa 48± 1 53± 11 14.5± 2.4 14.9± 4.7 151± 13 174± 36 3.5± 0.6 4.8± 0.4 OKDa 79± 1 71± 24 35.6± 6.8 30.2± 1.8 207± 24 137± 20 6.3± 0.6 4.5± 0.6 ShJk 97± 3 109± 3 46.4± 3.3 43.4± 8.0 499± 67 558± 91 5.2± 1.1 6.5± 1.0 HSDi 58± 12 74± 13 37.3± 6.6 27.7± 0.9 203± 31 317± 21 5.5± 1.5 6.9± 0.7 HSDi2 – 48± 4 – 36.5± 3.8 – 215± 78 4.3± 1.7 6.6± 1.0 AlWo 21± 3 48± 9 6.1± 0.9 15.8± 2.5 90± 11 154± 17 1.3± 0.2 4.1± 0.6 koQ 64± 8 85± 12 16.1± 1.5 20.1± 1.2 395± 36 378± 60 2.9± 0.5 3.6± 0.7 koVe 86± 5 112± 6 20.6± 2.4 24.1± 2.3 638± 53 699± 91 4.4± 0.7 4.9± 1.0 kuWe 41± 4 63± 19 17.3± 1.7 20.7± 2.0 202± 5 142± 13 5.9± 1.0 6.0± 0.7 EM 82± 10 75± 7 47.0± 4.2 36.9± 4.1 299± 64 339± 54 7.0± 1.8 6.1± 1.2 H 46± 4 38± 1 16.5± 2.6 24.5± 6.5 154± 43 89± 18 4.2± 0.8 4.0± 1.1 EL1 96± 12 159± 20 30.8± 2.5 31.3± 1.2 410± 68 542± 76 5.5± 1.2 10.2± 2.6 EL2 162± 19 179± 19 81.6± 6.5 49.2± 1.4 546± 43 479± 37 7.5± 1.3 9.0± 2.2 EL3 – 104± 11 – 28.6± 2.3 – 424± 53 6.2± 1.5 10.3± 1.9 soWa 32± 5 – 20.6± 5.6 – 66± 10 – 2.2± 0.4 4.2± 1.1 smHN 32± 4 43± 11 13.4± 2.2 12.5± 4.9 141± 8 181± 26 1.8± 0.5 2.6± 0.7 smD 137± 8 133± 7 27.5± 2.4 27.9± 2.5 521± 86 561± 57 5.5± 0.9 7.7± 0.9 smVG 61± 1 64± 4 13.4± 2.4 12.4± 0.7 282± 2 366± 22 2.4± 0.7 2.8± 0.4 smVG2 29± 3 31± 4 6.1± 0.7 6.8± 1.2 111± 28 245± 21 2.3± 0.3 2.6± 0.3 suHe 65± 6 99± 10 71.5± 6.8 41.8± 4.6 426± 45 476± 100 6.0± 1.4 7.7± 2.3 BiSu 44± 2 46± 1 8.9± 2.3 10.3± 1.8 186± 24 228± 14 2.0± 0.3 2.2± 0.3 BeRo 66± 7 81± 2 17.0± 4.0 19.5± 2.5 281± 42 333± 73 3.1± 1.0 4.0± 0.7 DöRo 236± 19 223± 25 41.8± 5.8 41.1± 4.3 873± 75 1052± 116 13.9± 2.0 18.8± 2.9 FL2 124± 18 186± 18 44.1± 4.6 39.0± 5.2 738± 85 744± 68 9.8± 2.3 10.6± 1.8 FL6 173± 21 243± 24 46.0± 4.8 46.2± 4.6 1004± 96 986± 29 12.9± 2.5 15.7± 2.0 Gt1WS1 – 152± 15 – 43.6± 4.4 – 677± 34 3.6± 1.0 7.2± 0.2 Gt1WS2 – 65± 7 – 19.8± 2.0 – 636± 32 1.3± 0.1 2.8± 1.0 EF1WS – 88± 15 – 28.2± 5.4 – 333± 5 3.9± 0.5 4.1± 0.5 EF1MM – 16± 4 – 51.5± 5.3 – 28± 1 2.7± 1.4 5.0± 1.3 EF1GS – 172± 18 – 41.3± 4.2 – 549± 27 8.2± 1.4 8.7± 2.6 EF1OK – 149± 15 – 35.2± 4.0 – 334± 17 6.0± 1.7 7.7± 2.0 EF1UKK – 132± 19 – 49.7± 1.4 – 320± 16 6.2± 2.1 7.4± 1.8 EF1KO – 160± 19 – 55.8± 1.8 – 584± 65 7.0± 1.6 7.4± 1.9 EF1HS – 122± 11 – 30.2± 3.1 – 235± 12 7.3± 1.5 6.3± 1.7 Gt1DU1 – 147± 23 – 33.0± 0.3 – 635± 19 4.5± 1.6 12.1± 3.4 Gt1DU2 – 107± 4 – 25.4± 3.2 – 541± 27 5.7± 0.4 6.5± 1.5 Gt1DU3 – 164± 20 – 37.0± 5.9 – 907± 45 9.3± 2.7 10.2± 0.7 Gt1DW – 141± 12 – 35.9± 3.5 – 304± 49 6.1± 2.1 11.2± 3.0 Gt1VS1 – 128± 28 – 37.2± 9.6 – 342± 32 3.6± 1.5 7.9± 1.6 Gt1VS2 – 187± 15 – 35.1± 2.8 – 707± 35 7.0± 1.7 8.3± 1.2 SD, Standard deviation; UCS, uniaxial compressive strength; Es, static Young’s modulus; W , destruction work; T0, indirect tensile strength. www.geoth-energ-sci.net/2/21/2014/ Geoth. Energ. Sci., 2, 21–37, 2014 28 D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samplesFigure 3        2000 3000 4000 5000 6000 7000 all samples clastic rocks only carbonates onlya b c 0 50 100 150 200 250 300 U C S [ M P a ] 0 v [m/s]p e f Φ < 10% 10% < 2Φ < 0% 20% < Φ 1000 2000 3000 4000 5000 6000 7000 v [m/s]p 1000 2000 3000 4000 5000 6000 70000 v [m/s]p 1000 2000 3000 4000 5000 6000 7000 v [m/s]p 1000 2000 3000 4000 5000 6000 7000 v [m/s]p 1000 5b) 5a) 11b) 11a) 15b) 15a) d 0 50 100 150 200 250 300 U C S [ M P a ] 2000 3000 4000 5000 6000 70000 v [m/s]p 1000 parallel to layering Outcrop samples 6) Outcrop samples Core samples Regression curve: outcrop samples Regression curve: outcrop+core samples Figure 3. vp vs. UCS for specimens taken perpendicular to bedding for outcrop and core samples separately for (a) all samples (n= 49), (b) only clastic rock samples (n= 24) and (c) only carbonate samples (n= 20); (d) vp vs. UCS for all specimens taken parallel to bedding (n= 33); regression curves shown for both outcrop and core samples and outcrop samples only; for regression equations see Table 5. Error bars stand for standard deviations of all measurements of every sample (Tables 2–4). (e–f) vp vs. UCS for low-, medium- and high-porosity samples of clastic rocks (e) and carbonates (f). of both 8 and ρ values. Though clastic core samples plot far above the regression curve of UCS–8 of outcrop samples this is mainly based on the lack of outcrop samples with low porosities (Fig. 2b). For UCS–ρ, however, core samples plot along an extension of the regression curve for outcrop data (Fig. 2f). Data therefore show that, if core samples are in- cluded, the best fit regression curve is similar to the one with outcrop data only. 5.1.2 P wave velocity Many studies show that UCS correlates positively with vp and travel time, respectively (Freyburg, 1972; McNally, 1987; Kahraman, 2001; Sharma and Singh, 2008). vp is one parameter determined easily with borehole acoustic logs (e.g. Fricke and Schön, 1999; Rider and Kennedy, 2011) and it may be relevant for the geomechanical model validation and logging-while-drilling. UCS–vp data show a wide scatter for all samples both perpendicular and parallel to bedding (Fig. 3a, d). The co- efficients of determination are rather poor for both outcrop samples only and core samples included (Table 5). However, there are only small differences between best fit curves for outcrop samples only and core samples included. Especially for carbonates, the regression curve differs only slightly when core samples are included (Fig. 3c). There is some de- viation for clastic rocks due to lacking low-porosity outcrop samples (Fig. 3b). The coefficient of determination is yet considerably higher if core samples are included (Eq. 11b). There are conspicuous interdependencies between UCS, vp and porosity for both clastic rocks and carbonates. High- porosity clastic and carbonate rocks have the lowest UCS and vp values, and low-porosity samples have the highest values (Fig. 3e, f). If porosities are plotted vs. P wave velocities (Fig. 4) there is a clear linear relationship for carbonates at higher vp values. The mineralogical composition of clastic rock samples is more heterogeneous compared with carbon- ate samples reflected in a wider scatter of vp values at lower UCS values. vp values strongly depend on mineral composi- tion due to the minerals’ different elastic wave velocities (e.g. Gebrande et al., 1982). Sandstones’ main component quartz has a considerably lower vp than calcite, the main component of carbonates. vp of dolomite is lower, too. Consequently, two samples with dolomitic composition (EL1, EL3) plot above the regression curve of carbonates (Fig. 3c). 5.1.3 Young’s modulus Former studies showed that, in most cases, there is a strong correlation between Es and UCS (Sachpazis, 1990; Ag- gistalis et al., 1996; Palchik, 1999; Dinçer et al., 2004). Our data, shown in Fig. 5, are in good agreement with Geoth. Energ. Sci., 2, 21–37, 2014 www.geoth-energ-sci.net/2/21/2014/ D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samples 29 Table 5. Summarised results of statistical analyses for the correlation of UCS with different parameters of both outcrop and core samples and outcrop samples only with coefficients of determination R2. Outcrop samples only Outcrop and core samples Eq. UCS [MPa] R2 Eq. UCS [MPa] R2 All samples (1a) −28.6 ln(8)+ 144.2 0.675 (1b) 151.95 e−0.0518 0.526 (2)* −22.2 ln(8)+ 115.9 0.558 (3a) 0.775 ρ5.16 0.571 (3b) 1.285 ρ4.66 0.520 (4)* 0.568 e1.943ρ 0.498 (5a) 23.763 e0.0003vp 0.314 (5b) 0.029 vp – 19.09 0.405 (6)* 0.019 vp 0.269 (7a) 2.474E1.102s 0.590 (7b) 3.335E1.008s 0.686 (8)* 7.538E0.698s 0.639 Sandstones (9a) 110.73 e−0.0378 0.206 (9b) 152.6 e−0.0538 0.608 (10a) 3.453ρ3.427 0.266 (10b) 2.245ρ4.0132 0.493 (11a) 0.025 v0.980p 0.185 (11b) 4× 10−6 v2p+ 0.009 vp+ 11.5 0.651 (12a) 4.319E0.944s 0.682 (12b) 3.364E1.035s 0.822 Carbonates (13a) 129.95 e−0.0518 0.517 (13b) 137.08 e−0.0438 0.390 (14a) 0.319 ρ5.953 0.708 (14b) 1.116 ρ4.741 0.476 (15a) 2× 10−7 v2.351p 0.351 (15b) 8.535 e0.0005vp 0.360 (16a) 1.928E1.098s 0.576 (16b) 1.783E1.138s 0.616 Outcrop samples only Outcrop and core samples Eq. Regression function R2 Eq. Regression function R2 All samples (17a) W = 3.953 UCS 0.824 (17b) W = 5.954 UCS0.9023 0.678 (18)* W = 3.026 UCS1.07 0.816 (19a) T0 = 0.0002UCS2+ 0.023 UCS+ 2.30 0.861 (19b) T0 = 0.0002 UCS2+ 0.02 UCS+ 2.35 0.787 (20)* T0 = 3× 10−5 UCS2+ 0.047 UCS+ 1.01 0.797 Sandstones (21a) W = 2.867 UCS1.102 0.729 (21b) W = 7.164 UCS0.889 0.611 (22a) T0 = 0.0002 UCS2+ 0.0065 UCS+ 2.46 0.581 (22b) T0 = 1.9125e0.01UCS 0.758 Carbonates (23a) W = 3.714 UCS0.98 0.804 (23b) W = 4.851 UCS0.906 0.769 (24a) T0 = 3.79 ln(UCS)− 9.997 0.862 (24b) T0 = 0.407 UCS0.609 0.817 * Parallel to bedding. Figure 4        0 1000 2000 3000 4000 5000 6000 7000 0 5 10 15 20 25 30 Porosity [%] v [k m /s ] p Carbonates Clastic rocks Figure 4. Porosity vs. vp for carbonates and clastic rocks (see key) with linear regression lines. these studies, especially for the lithologically separated plots (Fig. 5b, c). Coefficients of determination are in most cases high. To better analyse the statistical significance of the de- veloped regression functions for outcrop samples, 90 % con- fidence and prediction bands are added. If all lithologies are plotted together, there is a certain scat- ter of data both perpendicular and parallel to bedding re- flected in wide 90 % prediction bands (Fig. 5a, d). Parallel to bedding the Es values tend to be slightly higher than if perpendicular. For small UCS and Es values the relationship between the parameters is excellent, and with higher values the scatter increases considerably. The core samples comply with the data of outcrop samples. When core results are in- cluded, the quality of regression analysis fit is even improved and is demonstrated by a higher coefficient of determination (Fig. 5a; Table 5). If sandstone samples are plotted separately, the coeffi- cient of determination is high and confidence and predic- tion bands, respectively, are narrow (Table 5; Fig. 5b). It has www.geoth-energ-sci.net/2/21/2014/ Geoth. Energ. Sci., 2, 21–37, 2014 30 D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samplesFigure 5        all samples E [GPa]s clastic rocks only E [GPa]s carbonates only a b c 0 50 100 150 200 250 300 0 E [GPa]s U C S [ M P a ] 10 20 30 40 50 60 70 10 20 30 40 50 60 70 10 20 30 40 50 60 70 E [GPa]s 0 10 20 30 40 50 60 70 0 50 100 150 200 250 300 U C S [ M P a ] E [GPa]s 10 20 30 40 50 60 70 e f 7b) 7a) 12b) 12a) 16b) 16a) d 0 20 40 60 80 100 E [GPa]s 8) Outcrop samples Core samples Φ < 10% 10% < 2Φ < 0% 20% < Φ parallel to layering Outcrop samples Regression curve: outcrop samples Regression curve: outcrop+core samples 90% prediction bands 90% confidence bands Figure 5. Es vs. UCS for specimens taken perpendicular to bedding for outcrop and core samples separately for (a) all samples (n= 49), (b) only clastic rock samples (n= 24) and (c) only carbonate samples (n= 19); (d) Es vs. UCS for all specimens taken parallel to bedding (n= 33). Regression curves shown for both outcrop and core samples and outcrop samples only; 90 % prediction and confidence bands are included; for regression equations see Table 5. Error bars stand for standard deviations of all measurements of every sample (Table 4). (e, f) Es vs. UCS for low-, medium- and high-porosity samples of clastic rocks (e) and carbonates (f). to be considered that the sampled carbonates are both ma- trix and sparry limestones with varying amount of bioclasts (cf. Tables 2, 3). These more-heterogeneous compositions of carbonate samples are reflected in statistically less satisfac- tory results (R2 = 0.576; Table 5) with wider prediction and confidence bands (Fig. 5c). The increase of the regression curve is lower than for sandstone samples; that is, a carbon- ate sample is expected to have a higher Es value than a sand- stone sample of similar UCS. For both, sandstones and car- bonates, equivalent core samples match the scatter of outcrop data well and lie within the 90 % prediction bands. There are only minor changes of regression curves if core samples are included (Fig. 5b, c). There is a known relationship between porosity and Young’s modulus of rocks (e.g. Rajabzadeh et al., 2012). Therefore, we redraw the UCS–Es data of sandstones and carbonates with different marks for low-, medium- and high- porosity rocks (Fig. 5e, f). Sandstones and carbonates with high porosities have the lowest UCS and Es values; the dif- ferences between medium- and low-porosity rocks are less pronounced. Both porosity classes include medium UCS and Es values as well as high values. 5.2 Deriving rock properties from UCS 5.2.1 Destruction work The destruction work is an important parameter for dimen- sioning and planning of drilling projects and correlates with drilling efficiency (Thuro, 1997). Rocks which strongly de- form while loading have high destruction-work values be- cause for specimen failure more energy is needed. The de- struction work, calculated as the area below the stress–strain curve of the uniaxial compression test, is plotted against UCS of the different samples (Fig. 6). Regression analyses show that power-law functions fit best in most cases, and coefficients of determination are rather high in all cases. To analyse the statistical significance, 90 % confidence and prediction bands are added. For outcrop samples parallel and perpendicular to bed- ding, the fit is excellent with narrow bands (Fig. 6a, d; Ta- ble 5). There are, however, clear lithological differences of the destruction-work values. For carbonates, core samples show a considerable deviation from the regression function of outcrop data more to lower W values for similar UCS (Fig. 6c). For sandstones, core samples show a wider scat- ter, in some cases even beyond the 90 % prediction bands of outcrop samples (Fig. 6b). The slope for clastic rock samples is considerably steeper than that of carbonate rocks (Fig. 6c). That is, more energy is needed to destruct a sandstone sample Geoth. Energ. Sci., 2, 21–37, 2014 www.geoth-energ-sci.net/2/21/2014/ D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samples 31Figure 6        0 200 400 600 800 1000 1200 0 50 200 250 300 UCS [MPa] all samples 150100 clastic rocks only a b carbonates onlyc e f 17b) 17a) 21b) 21a) 23b) 23a) UCS [MPa] d 18)parallel to layering Outcrop samples Φ < 10% 10% < 2Φ < 0% 20% < Φ 0 50 200 250 UCS [MPa] 150100 0 50 200 250 300150100 0 50 200 250150100 0 50 200 250150100 0 50 200 250150100 UCS [MPa] UCS [MPa] UCS [MPa] 0 200 400 600 800 1000 1200 W [ k J/ m ] 3 W [ k J/ m ] 3 Regression curve: outcrop samples Regression curve: outcrop+core samples 90% prediction bands 90% confidence bands Outcrop samples Core samples Figure 6. UCS vs. W for specimens taken perpendicular to bedding for outcrop and core samples separately for (a) all samples (n= 49), (b) only clastic rock samples (n= 24) and (c) only carbonate samples (n= 18); (d) UCS vs. W for all specimens taken parallel to bedding (n= 33). Regression curves shown for both outcrop and core samples and outcrop samples only; 90 % prediction and confidence bands are included; for regression equations see Table 5. Error bars stand for standard deviations of all measurements of every sample (Table 4). (e–f) UCS vs. W for low-, medium- and high-porosity samples of clastic rocks (e) and carbonates (f). than a carbonate sample of the same UCS value. From that we infer that sandstone samples receive more deformation at the same applied stress than carbonate samples. In the same way as we did for UCS–Es values (Fig. 5e, f), UCS–W data of sandstones and carbonates with low-, medium- and high-porosity rocks are plotted separately (Fig. 6e, f). Also in this case, sandstones and carbonates with high porosities have the lowest UCS and W values; the differences between medium- and low-porosity rocks are less clear. For carbonate samples, however, we recognise that low-porosity samples tend to have higher UCS and W values than high-porosity samples (Fig. 6f). 5.2.2 Indirect tensile strength For rocks, there is a known correlation between compres- sive and tensile strength with a factor of approximately 10 between these two parameters (e.g. Hobbs, 1964; Lockner, 1995). Our results are in good accordance; coefficients of de- termination are high in all cases with very narrow confidence and prediction bands. Overall, the values of core samples are similar to the values of outcrop samples and plot within the 90 % prediction bands. Both regression functions, devel- oped for clastic rocks, are very similar, and core results fit well within the scatter that is quite similar to outcrop results (Fig. 7b; Eqs. 22a, b). For carbonates, the equivalent core samples also plot within the 90 % prediction bands (Fig. 7c). However, there are clear lithological differences in the in- direct tensile strength values of the outcrop samples (Fig. 7b, c). For low UCS, T0 values of clastic rock samples are lower than those of carbonates; for high UCS, however, the increase of T0 values is less for carbonates, leading to higher values of clastic rock samples. We plot UCS–T0 data of sandstones and carbonates with low-, medium- and high-porosity rocks (Fig. 7e, f; see key). This empirical relation also shows that high-porosity sam- ples of clastic rocks and carbonates have the lowest UCS and T0 values; the differences between medium and low- porosity rocks are less clear. In contrast to the UCS–W re- lation (Fig. 6) where carbonates tend to have higher values, we recognise that in this case low-porosity sandstone sam- ples tend to have higher UCS and T0 values. 6 Discussion 6.1 Applicability of empirical relations to predict in situ rock properties A comparison of empirical relations, determined from out- crop samples only, with properties of core samples gives in- formation on parameter changes due to load removal and www.geoth-energ-sci.net/2/21/2014/ Geoth. Energ. Sci., 2, 21–37, 2014 32 D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samplesFigure 7        all samples clastic rocks onlya carbonates only 0 50 100 150 250 300 UCS [MPa] 0 5 10 15 20 25 T [M P a ] 0 UCS [MPa] T [M P a ] 0 e f 19b) 19a) 22b) 24b) 24a) d 20) Outcrop samples Core samples Φ < 10% 10% < 2Φ < 0% 20% < Φ parallel to layering Outcrop samples 200 0 50 100 150 250200 0 5 10 15 20 0 50 100 150 250 300 UCS [MPa] 200 0 50 100 150 250200 0 50 100 150 250200 0 50 100 150 250200 UCS [MPa] UCS [MPa] UCS [MPa] 22a) Regression curve: outcrop samples Regression curve: outcrop+core samples 90% prediction bands 90% confidence bands Figure 7. UCS vs. T0 for specimens taken perpendicular to bedding for outcrop and core samples separately for (a) all samples (n= 49), (b) only clastic rock samples (n= 24) and (c) only carbonate samples (n= 18); (d) UCS vs. T0 for all specimens taken parallel to bedding (n= 33). Regression curves shown for both outcrop and core samples and outcrop samples only; 90 % prediction and confidence bands are included; for regression equations see Table 5. Error bars stand for standard deviations of all measurements of every sample (Table 4). (e–f) UCS vs. T0 for low-, medium- and high-porosity samples of clastic rocks (e) and carbonates (f). beginning of alteration. We found that the developed empir- ical relations with or without core samples are quite simi- lar for all analysed parameters (cf. Sect. 5, Table 5). Sim- ply, core samples have similar or only slightly higher values than outcrop samples. That is, the ratios of UCS with the considered parameters do not change considerably. Based on these findings it is assumed that these parameter–UCS ratios remain unaffected by unloading. Only the destruction work shows some divergence between outcrop and core samples. For carbonates with high UCS, destruction-work values of core samples tend to be lower than those of outcrop sam- ples with comparable UCS resulting in a steeper regression function for outcrop samples only (Fig. 6c). That is, for the destruction of core samples less energy is needed than for outcrop samples. This may be caused by higher porosities of outcrop samples where more energy can be absorbed by pore-space destruction before brittle failure occurs. The de- struction work, measured in laboratory, correlates with the in situ drillability of rocks (Thuro, 1997). Therefore, the de- struction work, measured in laboratory, is strongly related to field-work efforts. The UCS–Es relationship indicates that clastic and car- bonate rocks including their core equivalents show different behaviour. A carbonate rock is expected to have a higher Es compared with a clastic rock of the same UCS (Fig. 5). The intensity of deformation depends on the rock strength, the stresses applied and the time over which the stresses are acting and accumulating. It is known that carbonate rocks react differently to stresses than clastic rocks (e.g. Lock- ner, 1995; Jaeger et al., 2007). On long-term-stress applica- tions clastic rocks may receive more brittle deformation than carbonate rocks due to pressure-solution and slip-folding processes which are typical phenomena in carbonates (Fos- sen, 2010). These are deformation processes which act on a longer timescale. At drilling operations, however, there is only a short-term-stress application on the rock mass simi- larly to laboratory experiments. That is, the UCS–E relation- ship is developed for a similar timescale as the goal of this study, namely drilling applications, and not for long-term- deformation processes. All data in this study were determined in laboratory mea- surements of dry rock specimens. Applying the results to in situ conditions is non-trivial for some parameters because rocks at depth are loaded by overburden and confining pres- sures and are commonly saturated with fluids. Saturation and pressures have strong effects on some of the described pa- rameters. The compressional wave velocity is one parameter which can be determined easily by using a borehole acoustic log. It has to be taken into account that vp measurements in bore- holes comprise a larger volume which may include fractures and are obtained with different frequencies than laboratory Geoth. Energ. Sci., 2, 21–37, 2014 www.geoth-energ-sci.net/2/21/2014/ D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samples 33 measurements. Therefore, in most cases, saturated samples, measured in laboratory, give higher vp values than in situ rocks determined from well logs (e.g. Popp and Kern, 1994; Zamora et al., 1994). Laboratory measurements of dry spec- imens will give lower velocities than those of fully satu- rated samples (Nur and Simmons, 1969). Kahraman (2007) showed that for sedimentary rocks there is a strong linear correlation between P wave velocities of dry vdp and satu- rated rocks vwp . Most rocks show significant trends of UCS reduction with increasing degree of saturation (Shakoor and Barefield, 2009; Karakul and Ulusay, 2013). For Miocene limestones, there is a reduction of UCS and T0 values with increasing saturation (Vásárhelyi, 2005). Similarly, Baud et al. (2000) showed that there is a weakening effect of wa- ter on sandstone. Triaxial tests have shown that compres- sive strength and Young’s modulus of rocks positively corre- late with confining pressure (Nur and Simmons, 1969; You, 2003; Zoback, 2007). All laboratory measurements have been carried out on high-quality samples where discontinuities such as fractures are absent. In situ rocks, in contrast, typically include frac- tures. That is, UCS and Es values measured with labora- tory tests tend to be higher than those measured in situ (Priest, 1993; Huang et al., 1995). The presented data of Young’s modulus were determined with uniaxial compres- sive tests, which give static Young’s modulus values referring to fracture propagation (cf., Section 1; Jaeger et al., 2007). In boreholes, from acoustic logs, dynamic Young’s moduli are obtained (Zoback, 2007; Rider and Kennedy, 2011). The comparison of dynamic and static Young’s moduli is compli- cated. Discontinuities such as fractures have different effects on static measurements of Young’s modulus and P wave propagation. Martínez-Martínez et al. (2012), for example, showed that, for carbonate rocks, there is only a poor linear relationship which can be corrected by using vp and Pois- son’s ratio. This shows that transfer to in situ conditions has to be con- sidered carefully for each parameter individually. For validation purposes, it is advisable to apply the devel- oped equations on logging data of wellbores in the NWGB for UCS calculation. It would then be possible to compare the calculated UCS values with the actual UCS values mea- sured with cores of the same wellbore (cf., Vogt et al., 2012). The estimation of rock strength is not only possible with em- pirical relations as presented in this study but also with mi- cromechanical methods (e.g, Sammis and Ashby, 1986; Zhu et al., 2011), which are powerful tools to understand failure processes in rock. To build a geomechanical model before starting the drilling operation, such micromechanical meth- ods may be a good supplemental option when using data from adjacent wellbores. 6.2 Comparison with previous studies Many empirical relations between UCS and other parameters were developed. In Table 6, selected equations are presented. None of these relations, however, refer to the NWGB. These functions fit best for the geological situation the analysed samples belong to and are only valid for the defined range of parameter values (cf. Fig. 8). In most cases, the functions relate to a specific lithology. The presented regression analyses show that coefficients of determination of the regression curves for carbonates have, in most cases, smaller values compared with sand- stone samples. Carbonate samples from the NWGB include sparry and matrix limestones, bioclast-rich limestones, oo- lites, marls, and dense and porous limestones (cf. Tables 2, 3). This means that the lithology of sampled carbonates is much more variable than that of sandstones. This may be one reason for the wider range of mechanical and physical data and the poorer relations of UCS–Es (Eqs. 12b, 16b), UCS– vp (Eqs. 11b, 15b), and UCS–8 (Eqs. 9b, 13b). In former studies on limestones (e.g. McNally, 1987; Sachpazis, 1990; Bradford et al., 1998; Chang et al., 2006) the lithology, for which the empirical relation was developed, is specified. Ac- cordingly, the presented relationships are more trustworthy if they refer to a specific lithology (cf. Eqs. 9–16, 21–24). If only general assumptions of UCS values are needed (e.g. from well logs of heterogeneous stratifications) or the lithol- ogy of the respective wellbore section cannot be defined pre- cisely, it appears to be better to apply the empirical relations generated for all samples (Eqs. 1–8, 17–20). To compare the regression functions, developed in this study, with the relations of previous studies we use a graphic representation considering the range of parameter values for which the relations were developed (Table 6; Fig. 8). Differences between the functions are depicted. For clas- tic rocks, there are significant variations for small porosities (Fig. 8a.1). Vernik et al. (1993; Eq. 25) predict much higher UCS for low-porosity sandstones (8< 15 %) and lower UCS for high-porosity sandstones (8> 25 %) than Eqs. (9a) and (9b). They, however, determined UCS values from triaxial testing, which gives higher UCS values than uniaxial com- pressive strength measurements (cf. Zoback, 2007). The ef- fects of small discontinuities on rock strength are smaller when confining pressure is applied. For carbonate rock samples, however, the calculated re- gression functions (Eqs. 13a, b) fit perfectly well with pre- vious studies (Fig. 8a.2). Only for high-porosity carbonate rocks (8> 15 %) are the smallest variations from Eq. (30) in the range of 10 MPa for UCS. The errors of the empirical relations between UCS–vp and UCS–1t , respectively, are high for all studies (cf. Table 5). The determined regression functions of previous studies are, however, quite similar to Eq. (11b) for clastic rocks (Fig. 8b). The UCS–vp relation of Freyburg (1972; Eq. 34) is in good accordance with our results. The data relate to sandstones www.geoth-energ-sci.net/2/21/2014/ Geoth. Energ. Sci., 2, 21–37, 2014 34 D. Reyer and S. L. Philipp: Empirical relations of rock properties of outcrop and core samplesFigure 8    Φ [%] a.1 U C S [ M P a ] 250 200 150 100 50 0 0 5 10 15 20 25 Φ [%] a.2 0 5 10 15 20 25 9a 9b 25 26 13a 13b 27 28 E [GPa]s b.1 b.2 U C S [ M P a ] 250 200 150 100 50 0 0 10 20 30 40 50 60 E [GPa]s 0 10 20 30 40 50 60 16a 16b 35 38 12a 12b 36 37 v [m/s]p 1000 2000 3000 4000 5000 6000 15a 15b 31 33 v [m/s]p 1000 2000 3000 4000 5000 6000 c.1 U C S [ M P a ] 200 150 100 50 0 c.3 Δt μs/ft[ ] 0 50 100 150 200 11a 11b 2930 00 11a 11b 32 34 c.2 Figure 8. Correlations between UCS and the parameters (a) porosity, (b) Es and (c) vp separately for clastic rocks and carbonates; correla- tions from this study and those published by other authors (equation numbers shown) consider the range of parameter values for which the functions are valid. Table 6. Correlations between UCS and the parameters porosity, P wave velocity, travel time and Young’s modulus reported by other authors. Eq. Parameter UCS2 : 1 [MPa] Rock type Reference (25) 8 254 (1–0.0278) [8 in %] Clastic rocks Vernik et al. (1993) (26) 277 e−0.18 [8 in %] Sandstones (0.2 <8< 33 %) Chang et al. (2006) (27) 143.8 e−0.06958 [8 in %] High UCS limestones (5 <8< 20 %) Chang et al. (2006) (28) 135.9 e−488 [8 in %] High UCS limestones (0 <8< 20 %) Chang et al. (2006) (29) vp /1t 1277 e−0.0361t [1t in µs ft−1] Sandstones McNally (1987) (30) 1174 e−0.03581t [1t in µs ft−1] Clastic rocks McNally (1987) (31) 56.71 vp–192.93 [vp in km s−1] Limestones, clastic rocks (3.9 < vp < 5.2 km s−1) Çobanog˘lu and Çelik (2008) (32) 0.0642 vp–117.99 [vp in m s−1] Different kinds of rock (1.8