Journal of Engineering Geology

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The choice of a suitable bearing capacity of soil becomes the most important issue to be considered in any project. This paper describes analytical investigation conducted to evaluate the ultimate bearing capacity of adjacent footings in various spacings of footings. Bearing capacity of adjacent footings is determined based on virtual retaining wall method by applying equilibrium between active and passive forces. Results indicate the ultimate bearing capacity of each foundation changes due to the interference effect of the failure surface in the soil and it depends on footings spacing. In the present study, effect of soil type, depth of adjacent footings and reinforced soil is investigated on bearing capacity of adjacent footings. Results indicate closely spaced footings, can decrease or increase bearing capacity of adjacent footings with respect to single footings. Also, reinforced soil increases bearing capacity of closely spaced footings with respect to single footings on unreinforced soil, it depends on footings spacing. Finally, the predicted results are compared with those reported from experiments, analytical and numerical results performed by others, indicating an acceptable agreement.
 

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The studied region in this research (Alborz province) is structurally located in Alborz poly_orogenic system of northern Iran. The purpose of this research is combining the remote sensing and geology sciences to show fault lineaments by analyzing satellite data in a vast region and also comparison between lineaments layer and recognized faults in geology maps. Firstly, two scenes of Landsat ETM+ satellite images with 164-35 and 165-35 numbers were mosaicked and also according to coordinates of research area (46^◦ 30´ to 48^◦ east longitude and 34^◦ to 35^◦ north latitude degree) have been crop. Then with remote sensing methods such as combination of bands, filtering, NDVI index to reconstruction the vegetation, principal components analysis (PCA) and band relativity in gray scale and color images  have been analyzed the satellite images. Finally, by using the above mentioned methods, the map of fault lineaments and map of lineaments density for Alborz province have been prepared and compared with recognized faults.

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Introduction
Earth is a dynamic system. Change is one of its features. At its surface, there is almost no region that over the past few thousand years has not affected its neotectonic activities. In fact, it can be said that active neotectonic is changing the surface of the earth. Among geological methods for analyzing active tectonic movements, deciphering the geomorphology and morphotectonic nature play a very important role, because many geomorphic complications are sensitive to active tectonic movements and the geometric analysis of these complications provides evidence of the type, rate, and configuration of active tectonic deformations. Moreover, these geomorphic indices at a regional scale provide basic reconnaissance tool to identify tectonically active regions, their susceptibility to tectonic deformation, and level of tectonic activity.
In the presented study, tectonic activities and geological structural features of the Vark basin in Lorestan province, such as the discontinuities that may be detected on satellite imagery as lineaments, and in many cases control landslide occurrences, have been analyzed using the GIS and remote sensing.
Material and methods
Neotectonic investigation in the area: in order to analyze and to evaluate the tectonic movements in the Vark basin, considering the validity of geomorphic indices, longitudinal gradient (SL), river meanders (S), basin hypsometric curves (HC) and asymmetry factor (AF) have been used.  After calculating the desired indices, the tectonic activity of the area has been evaluated using the index of active tectonic (IAT).
Vark basin lineaments map derived from satellite images with proper resolution: using remote sensing techniques and visual interpretation of the OLI Landsat 8 satellite imagery, all fractures and lineaments of the region were identified and then by preparing the rose diagram, the trend of the lineaments of the area analyzed.
Landslide hazard zonation in the Vark basin: In this study, in addition to plotting landslide occurrence Points, eight other factors were also investigated. In order to provide a map of the factors affecting slip, the digital elevation model (DEM) in ENVI 4.8 and ArcGIS soft wares were used and the maps of slope, slope aspects, altitude classes, area geology, land use, topography and precipitation were prepared. Then, in order to zoning the landslide hazard, fuzzy logic method has been used. Fuzzy logic is based on the fuzzy layers and the fuzzy inference process.
Results and discussion
Analyzing the Neotectonic of the Area: as stated above, the relative active-Neotectonic (IRAT) index is derived from the interpolation of the morphotectonic indexes. In this case, after reviewing the morphotectonic indices of the study area and determining the activity rate of each indicator, the classification or prioritization of these activities were done. The results obtained from calculating the active tectonic index indicate that the study area with IAT is equal to one, has an active neotectonic.
Preparing the Lineation Maps of the Area: in this research, the aim of the data processing including satellite imagery and digital elevation model is identification and extraction of fractures and faults in the Vark basin. To this end, we can use the integration of the information layers derived from the above processes. In this step, all layers of information are logged into the ArcGIS software so that their overlap can provide a map of fractures and faults. On each information layer processed there is a series of lineaments recognizable that can be visually distinguished. After extraction of lineaments by comparing them with bundle compounds and maps derived from digital elevation model and geological map of the region, the lineaments of fractures and faults were separated from other lineaments and their shape file map has been prepared. In order to plot the rose diagram of fractures and faults, the Polar Plots ArcGIS Extension was used. The results obtained from this rose diagram showed that the dominant trend is the northwest southeast followed the trend in the region.
Preparing a map of landslide hazards zoning in the region and investigating its relationship with the lineaments: In order to overlap layers affecting the area's landslide hazard, Gamma fuzzy operator (λ= 0.9) has been used and landslides hazard mapping prepared. Based on the results, 12.40, 8.25, 37, 32.61 and 9.73 percent of the area are located in the very low, moderate, high and very high-risk classes, respectively.
In order to investigate the relationship between the lineaments and the landslide hazard maps as parameters that are affected by the tectonic activities of the area, the lineaments map was integrated with the map of landslide hazard. The results show that the most of lineaments identified in the study area have a northwest-southeast trend that are similar to the main faults of the region and Zagros. It can therefore be said that the lineaments are influenced by the faults and folds mechanism of the region. According to the lineament density in areas in places that are exposed to landslides, one can understand the close relationship between the lineaments and the landslide.
Conclusion
Based on the results obtained from relative active tectonics index, the Vark basin has an active neotectonic, which leads to an uplift in parts of the basin, as well as tilting in the southern part of the area.
In this research, the tectonic of the area, and then the relationship between the lineaments and the map of the landslide risk, as two phenomena affected by active neotectonic were reviewed. Investigating the lineaments of the region shows that the dominant trend is fractures north-west-south-east and following the trend in the region. In addition, analyzing the relationship between the lineaments with the map of the landslide hazard of the area shows that there is a close relationship between the lineaments and the zones with high risk of slipping.

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Introduction
One of the most sensitive and important issues in some civil engineering projects is slope design and application. The process of slope design always involve many uncertainties. Hence, it is impossible to accurately comment on its stability or instability. Most of the uncertainties in the slope stability analysis are related to the nature of materials, geometry, environmental conditions, model errors, and measuring errors as well. Therefore, the slope stability analysis with a deterministic approach which uses the concept of safety factor would often not result satisfactory. Consequently, the use of probabilistic methods is more advised. Accordingly, in recent years, the probability analysis has been used to slope stability analysis. In these analyses, the effective quantities of slope stability are considered as statistical distributions, and the reliability coefficient would then be a statistical distribution. Likewise, one of the approaches to simulate uncertainties in the probabilistic analysis is to use the variation coefficient. If the variation coefficient changes, the probability of failure will change accordingly. When the variation coefficient becomes a larger number, costly solutions are required to reduce the probability of failure. If the variation coefficient becomes low, the reliability will be increased and the required costs to reduce the probability of failure will be decreased. Therefore, determining the amount of variation coefficient in these analyses is very important. Furthermore, the correlation coefficient between the quantities is another effective parameter in computing the probability of failure.
Material and methods
In this research, the stability analysis of the slope facing the spillway of the Shiraz Kavar dam has been done in two probabilistic and deterministic methods. Since circular slip probability is more likely than other types of failure, in the analysis of the stability of this slope, the problem of circular failure is very important, and an appropriate equilibrium program should be used for circular failure analysis. Therefore, SLIDE software was used to slope stability analysis. For material behavior, the Hook-Brown failure criterion was applied. In order to determine the strength parameters of the criterion, Geological Strength Index (GSI), uniaxial compressive strength (UCS) and rock constant parameter m_i were used. For crushed rock with a moderate quality of crushing, the GSI quality of the rock mass was about 23 to 38, which the average value of that for the rock mass of the overflow was assumed 35. Also, the uniaxial compressive strength of the rock was evaluated about 50 to 100 MPa with an average value of 75 MPa. In addition, the value of m_i was 10, and due to mechanized drilling, the disturbance factor was considered to be 1. The amount of unit weight was assumed to be 22 kN/m³. The initial model used for deterministic and probabilistic analyses, is the Morgenstern-Price model. To conduct probabilistic analyses, Monte Carlo simulation was performed using random sampling method (RS-MC) and 200,000 sampling were used to converge the simulation results. To determine the coefficient of variation and the probability distribution of UCS, GSI and m_i, the proposed values ​​of Hook (1998) were applied and for unit weight (γ) James Rodriguez and Sitar (2007) studies were used. Also, the minimum and maximum values ​​of UCS and GSI are determined based on the results of experiments, and Third Sigma rule was utilized for m_i and γ quantities. Since the earthquake phenomenon is rarely of great intensity and the number of small earthquakes is higher, therefore the truncated exponential distribution function can be in good agreement with the results of the earthquake. Usually, the maximum magnitude of the earthquake acceleration coefficient is twice that of the average.
Results and discussion
In the presented paper evaluation denotes that the safety factor computed by probabilistic analysis is given as a distribution function. The function provides a clearer view of failure condition. However, a deterministic analysis only illustrates a certain value for the failure. In addition, the results of the probabilistic analysis show that it is possible to optimize the dip of the slope; such that it remains completely stable and the volume of earthwork is also minimized. Therefore, by using probabilistic analysis, the optimal dip of the slope was determined. In these circumstances, the amount of earthwork was decreased by 28,000 cubic meters. Also, the sensitivity analysis of the variation coefficient and correlation coefficient between parameters are analyzed. The results of the sensitivity analysis of the failure probability versus the variation coefficient of the quantities showed that the quantities of sensitivity factor for static conditions is greater than the corresponding pseudo-static, and the GSI amount is the highest, while the specific gravity has the least effect on the probability value. In addition, the analysis indicated that if the GSI coefficient of over 21% is selected, the probability of a static failure is higher than the permissible limit. Also, increasing the variation coefficient of quantities by as much as 50% exhibits that the probability of static failure is still below the permissible limit. Also, the correlation coefficient between UCS and GSI shows that the higher variation coefficient of the quantities is chosen, the more variations of failure probability compared to . In the case of pseudo-static conditions, variations in the failure probability are linear in relation to , while in static conditions, these changes are exponential for an increase of 50% in the variation coefficient. Also, to reduce the coefficient of variation by 50%, the probability of static failure for different values of  is approximately zero.
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Introduction
The dispersivity phenomenon occurs due to the dissolution of some of the ions in clay soils or against the shear stress of normal water flow in cohesion-less soils. Water surface flows in low slopes cause surface erosion of dispersive soils. Dispersivity in the soil starts from a point and gradually expands; the starting point can be the holes from the activity of the animals, the existing cracks or the growth path of the roots of the plants. There is a lot of field evidence to recognize the dispersivity of the loess soils. In field investigations, soil dispersivity can be detected according to the following parameters: geological origin of the loess soil, mineralogical composition, gradation, drainage pattern, slaking of agglomerates, specific morphology, high permeability, geographical area (length and width relative to origin), soil color, relationship between slope and soil erosion, precipitation, erosion of column cracks, heeling, mud flowing runoff and the presence of salt crystals in loess soils. In terms of sedimentological characteristics and engineering geological properties, Golestan loesses have been dispersed in three areas 1, 2 and 3, which are consistent with the loesses of clay, silt, and sand types, respectively.
Material and methods
Loess soils in three regions of east and northeast of Golestan province were sampled. Sampling was conducted in two forms of wax-coated agglomerates and metallic cylindrical tubes. Depth of sampling follows the foundation of the buildings located on the Mehr Housing site and the Cheshme Lee village, varying from 0.5 to 2 meters. On the path of the Beqqeje Bala village, sampling was carried out from the path trench. After transferring to the laboratory, samples were subjected to gradation testing, Atterberg limits test to determine the unit weight of the volume and density.
The pinhole test was done on samples with the unit weight of normal volume (g_n) and maximum volume (g_dmax) and its rate of dispersion was determined. The research background, field evidence and the results of laboratory experiments indicate the dispersion of soil sampling areas. The results show that soil compaction reduces the severity of dispersion and decreases the flow rate, so that the flow rate has decreased in the Maravehtapeh sample by 38%, in the Cheshmeli sample by 13% and in the Beqqeje Bala sample by 43%. Compaction cannot eliminate the dispersion of soil. Adding nanoclay decreases the severity of soil dispersion and eliminates its dispersion properties in most cases.
In order to evaluate the effect of nanoclay on severity and to decrease the dispersion property of soil with ratios of 0.5, 1, 2, 3, 4 and 5 wt%, of Montmorillonite Nanoclay was added.
The nanoclay used in the present research was selected from the Sigma-Aldrich America Company called montmorillonite nanoclay and was purchased from its domestic representative, i.e. Iranian Nanomaterials Pioneers Company. The product has a density of 300 to 370 kilograms per cubic meter and a particle size of between 1 and 2 nm. The specific surface area of the nanoparticle is about 250 square meters per gram. Its color in normal light and in 1 to 2% moisture is yellow to yellowish buff.
Results and discussion
The rate of dispersion of samples with nanoclay was measured in Pinhole Test Apparatus. Also, the method of mixing nanoclay with dispersive soil shows different behaviors in severity of dispersion and its reduction. Given that the specific surface of nanoclay is high and this property can include the whole surface of soil grains as a sticky coating and increase soil cohesion, the mixing method is practically one of the most important steps in examining the effect of nanoclay on soil stabilization. At ratios of 0.5, 1, 2, 3, 4 and 5 wt% of nanoclay, nanoclay was mixed with soils of sampling regions by four methods:
In the method A, they were completely mixed with the preparation of a homogeneous mud from soil and nanoclay via an electric mixer.
In the method B, mixing of loess soil with nanoclay was performed in optimum water content.
In the method C, mixing of loess soil with nanoclay was conducted in the form of dough by hand mixer. In the method D, mixing of loess soil with nanoclay was carried out in the form of vibration dry by grading sieve shaker.
After mixing with nanoclay in the desired method (four methods A, B, C, D), the samples were first stored in sealed plastic containers for 24 hours. Then, the samples containing nanoclay were reconstructed in cylindrical mold of the pinhole device with the unit weight of maximum dry volume and moisture of two percent higher than the optimum moisture content and a hole was created in the middle of it. The samples remained in this position for 24 hours, and then the test was performed. Testing was carried out on each sample according to the standard D4647-93, and flow rate reading was done over a period of two minutes to 18 minutes.
Conclusion
The conclusion of this study shows that the three loess samples taken have a dispersivity potential and the flow rate is low in the unit weight of maximum volume, but the dispersivity potential does not eliminate. Adding nanoclay with any weight ratio reduces the flow rate and eliminates the soil dispersivity potential.
The results of this survey showed that 1% nanoclay weight ratio is technically and economically the most appropriate mixing ratio. With this weight ratio, the method of preparing homogeneous mud with an electric mixer (method A) produces the lowest flow rate, so that the flow rate from 1.3 ml per second in pure soil to 0.3 ml per second in the soil containing nanoclay is reduced by 50 mm. Therefore, it can be said that this method is more suitable, but it is not operationally efficient and the method B is more appropriate. In the method B, the flow rate reaches from 1.3 to 0.55 ml per second.

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Introduction
The standard penetration test (SPT) is one of the most common tests in geotechnical investigations. The results of this test are known as a simple, inexpensive, and tangible criterion in geological and geotechnical engineering. Many computational methods and engineering judgments depend on the results of this test. In this research, estimation of physical and engineering properties of clay soils was carried out using statistical methods based on standard penetration test results. The scope of this case study is related to a variety of clayey soils in Tabriz (the northwest of Iran). The existing relationships were confirmed based on database of this study. After statistical analysis of the database, eight relationships including single and two-variable associations have been proposed to estimate the physical and engineering properties with better performance using nonlinear regression.
Material and Methods
Different types of clayey silt and marl layers spread in Tabriz were included for the purpose of this study. The geological age of these layers dates back to the Miocene and Pliocene era. This research was conducted in two sections of the field and analysis. Two machine boreholes were drilled, and, based on ASTM, a standard penetration test with other laboratory tests were performed on the soil specimens in order to determine the physical and plasticity properties. According to the results of this study and the existing data, a total of 107 series were prepared. Based on the soil properties, 11 variables were selected including the fine grain percentage (FGP), liquid limit (LL), plastic limit (PL), percentage of clay particles (C), plastic index (PI), consistency index (CI), activity (A), dry unit weight (γ_d), natural moisture content (w_n), initial void ratio (e_o), and effective vertical stress (σ'_v). The standard penetration tests were run for each meter in drilled boreholes. The results of this test were corrected according to NCEER method. The correlation between the variables and corrected standardized penetration test results (N₆₀) were studied by Spearman ranking coefficient. Verifications of the existing eight experimental relationships between  standard penetration and other soil properties, proposed by Kayabasi (2015) and Hoshmand et al., (2012), were checked out using the findings and data of the present study. The linear, exponential, logarithmic, and exponential regressions between each variable and N₆₀ were investigated using SPSS software, version 16. The best regression with the highest R² for each variable was selected. Eight new relationships were proposed. Performance of the suggested relationships was compared with the existing relationships.
Results and Discussion
The findings of the current study could be summarized as:
1. The clay soils of the studied area in Tabriz were classified into four categories including CH, MH, CL, and ML according to USCS classification. The range of changes in plastic index and liquid limits of the samples were 9.19 ~ 45% and 29 ~ 77%, respectively. The corrected standard penetration test results (N₆₀) changed from 9 to 28 showing that soil compression was low to high.
2. The highest positive and negative Spearman correlation coefficients were related to the consistency index (+0.772) and moisture content (-0.759), respectively.
3. The existing empirical relationships, based on the database of this study, were found to have better statistical coefficients in terms of consistency index, activity, moisture percentage, and fine grained percentage. In term of sample depth, the experimental relationship, showed the lowest statistical coefficient.
4. Four single-variable and two-variable relationships were proposed by nonlinear regression analysis. Using these relationships, clay soil properties including activity, moisture content, fine grain percentage, and consistency index were estimated based on N_60. In addition, two relations were proposed between sample depth (D) and vertical effective stress (σ'_v) with N₆₀. The statistical coefficients of the suggested relationships were better than the existing empirical relationships. The proposed relationship of estimating the consistency index with coefficient (R²) of 0.673 and regression line slope of about 1 had the best performance.
Conclusion
In general, the main objective of this study was to investigate the correlation between physical and plasticity properties of clay soils and N₆₀ on Tabriz clayey soils. Clay soils of the present study included various silty and marl layers. Sufficient correlation was observed between the physical and engineering properties of clay soils and N₆₀. The validation of the existing experimental relationships based on A, w_n, FGP, and D resulted in weak statistical coefficients (R² <5) employing the database of the current study. Six new experimental relationships were proposed to estimate A, FGP, w_n, and CI as well as two correlations of N₆₀ with effective stress and sample depth. Generally, the results have been revealed that the statistical coefficients of the proposed relationships were improved compared with the existing relationships. The most suitable relationship was the estimation of soil consistency index (R²~70) and root mean square error (RMSE=129). Finally, due to the novelty of this research topic, verification and development of the proposed relationships for the soils has been recommended in other areas.

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Introduction
One-dimensional site response analysis is widely performed to account for local site effects during an earthquake. Most of these approaches assume that dynamic soil properties are frequency independent. Laboratory test results as well as in-situ testing show that shear modulus and damping ratio are dependent on the frequency of loading. Although the amplification factor at ground surface with respect to frequency dependent dynamic properties of mixed alluvium materials under different near-fault motions with various velocity period is recognized, it is not well characterized and quantified.
Material and analysis methods
In this study, the tests results of samples which obtained from the drilling borehole (BH14) form Pardis city in Iran, are used. The soil is classified as clayey of high plasticity/clayey sand (CH/SC) and almost uniform and similar in the whole log profile.
Shear modulus and damping ratios versus shear strain curves (ASTM D3999) of CH/SC natural materials at effective confining pressures of 1, 2 and 5 kg/cm² with frequency of 0.5, 2, 5, and 10 Hz were used in one dimension response analyses using EERA Code.
Generally the damping ratio versus shear strain of the studied materials under low loading frequency (i.e. 0.5 Hz) almost falls in the range identified in literature. However, at higher loading frequencies (5 and 10 Hz) the damping ratios completely fall above the known upper bound trend. It is observed that, in general, the G and D values increase as loading frequency increases. Moreover, at certain strain G/G_max ratio decreases as loading frequency is increased.
Different dynamics behaviour curves were used in analyses, in isotropic consolidation conditions. In order to assess the amplification, acceleration spectra, acceleration spectra ratio, coefficient of B, at ground surface under eight well-known near-fault ground motions, 1728 one dimensional analyses were carried out with EERA code. The analyses have been performed for three base acceleration levels, namely, 0.1 g, 0.35 g and 1 g, using the simple time history scaling method. Field and laboratory test results of shear wave velocity were used in the analyses.
In this study, several well-known near-fault motion records are utilized for ground response analyses. Near-fault earthquakes records were selected from the strong motion database of the Pacific Earthquake Engineering Research Center (PEER) and Iran Strong Motion Network (ISMN) for specific reasons of location of the near faults sites.
In current building codes, the upper 30 m soil deposits overlying the higher impedance earth crust are regarded as the most relevant and significant in characterizing the seismic behavior of a site. Therefore, it is useful to accomplish investigations for obtaining their amplification and spectral acceleration for 30 m and even thicker (e.g. 60 m, for usual deep excavation in Iran), in order to have economical and safe designs and constructions.
Results and discussion
Figure 1 presents a comparison of normalized spectral acceleration (B factor) versus period for 30 m and 60 m thick profiles and Vs testing for frequencies dependent and independent analyses under input base acceleration of 0.35g for longitudinal component of used earthquakes. B factor of Iranian Standard 2800 and UBC97 also has been presented in the figure. The spectral acceleration at short period for frequency dependent analysis is higher than that of the frequency independent analysis. The  increases in frequency dependent analysis and higher thick profile (i.e. 60 m).
Conclusion
Results show that the effect of loading frequency has a considerable influence on the acceleration response at the ground surface. For both 30 m and 60 m soil columns, the increase of the loading frequency, decreases the amplification factor especially in the short period zone of the spectra. Based on the acceleration response spectra of near field strong motions derived for soils types of I and IV in this study, the period corresponding to  in the design spectrum of Iranian Standard 2800 should increase to 0.5 and 1.4, respectively. Therefore, selection of the appropriate G and D curves measured at frequency similar to those of the anticipated cyclic loading (e.g. seismic) has a paramount importance../files/site1/files/134/1.pdf

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Introduction
Rock masses have an enormous geometrical discontinuities such as void, notch, crack and flaw. These geometrical discontinuities which play as stress concentrator, cause to reduce the load bearing capacity of rock masses. In rock masses, the crack is the most important geometrical discontinuity assessed frequently by civil, mechanical and mining engineers and researcher. The fracture mechanics which is a branch of mechanical engineering science, has been often used for investigating the cracked rock samples. The fracture toughness is one of the important parameters in the fracture mechanics which describes the resistance of materials against the crack growth. On the other hand, since orientation of cracks relative to the loading directions can be arbitrary, brittle fracture in rocks may happen due to a combination of two major fracture modes, i.e. crack opening mode (mode I) and crack sliding mode without any opening or closing the crack flanks (mode II). In order to obtain the fracture toughness of rocks, several test configurations under pure mode I have been proposed. One of the parameters that has the influence on the fracture toughness of rocks and other materials is the thickness of test sample. Previous experimental results showed that the fracture toughness of rocks increases by increasing the specimen thickness until a specific thickness. After that, the fracture toughness decreases for thicker samples until plane strain condition occurs. Then, the fracture toughness becomes a fixed value when the thickness of sample varies.
The all preceding studies have been dealt with considering the effect of specimen thickness on fracture toughness focusing only the mode I fracture toughness and there is few research concerning the thickness effect on the mode II fracture toughness of rocks. Therefore, the aim of this paper is to investigate experimentally the effect of specimen thickness on the mode II fracture toughness.
Material and methods
To investigate the thickness effect on the mode II fracture toughness of rocks, several fracture tests were conducted on the semi-circular bend (SCB) specimens. The SCB specimen is a semi-disk of radius R and thickness t including an edge crack of length a loaded under three-point bending. When the crack is along the applied load and the bottom supports are symmetric relative to vertical crack, the SCB sample is under pure mode I loading. One of the methods for achieving the mixed mode loading in SCB sample is the asymmetry distances of bottom supports from the vertical crack located at the middle of bottom edge (see Figure 1). The pure mode II in this type of SCB sample is attained at a specific distances, i.e. at specific values of S₁ and S₂. These values of supporting distance can be obtained from finite element analysis.

Figure 1. The schematic of SCB sample.
The fracture tests were done both on pure mode I and pure mode II, for the sake of comprehensiveness. Therefore, 32 SCB samples with 4 different thicknesses and 4 repetition for each specimen size were tested for both pure mode I and pure mode II. The specimens were cut from Ghorveh marble sheets with different thicknesses by water jet machine. Then, the specimens were cracked artificially by a high speed rotary diamond saw blade. The specimen dimensions and loading conditions are presented in Table 1. Finally, the cracked SCB samples were tested by using a 300 kN ball-screw universal test machine. Table 1 also gives the average of four fracture loads (P_f) obtained for each thickness of specimen.
Table 1. The specimen dimensions and loading conditions.

	S.D.  (N)	Pf  (N)	S2 (mm)	S1 (mm)	a (mm)	t (mm)	R (mm)
Pure mode I	150	3220	57	57	28.5	15	95
Pure mode II	350	4726	11	57
Pure mode I	360	6711	57	57	28.5	25	95
Pure mode II	882	9445	11	57
Pure mode I	1450	20285	57	57	28.5	50	95
Pure mode II	4179	25441	11	57
Pure mode I	4672	31810	57	57	28.5	80	95
Pure mode II	4686	36848	11	57

Results and discussion
The mode I and mode II fracture toughness (K_Ic and K_IIc) can be calculated for SCB samples from following equations:
(1)
(2)
where P_f is fracture load, R and t are the radius and thickness of SCB sample, respectively K_I^* and K_II^* are geometry factors which depend on geometrical ratios a/R, S₁/R and S₂/R and independent of specimen dimensions and magnitude of applied load. These dimensionless parameters are often obtained from finite element analysis. For tested SCB samples, the values of K_I^* and K_II^* were extracted from previous studies as shown in Table 2. Substituting the fracture loads and specimen dimensions from Table 1 and the values of K_I^* and K_II^* given in Table 2 into Eqs. (1) and (2), the mode I and mode II fracture toughness were calculated as listed in Table 2. Figure 2 also shows the variations of mode I and mode II fracture toughness with respect to specimen thickness. As seen from this figure, the fracture toughness for both pure modes increases for thicker samples until a specific thickness. After that, the values of K_Ic and K_IIc decrease by increasing the specimen thickness. For plane strain condition in which the thickness of specimen is relatively large, the values of K_Ic and K_IIc are nearly constant.
 
 
Table 2. The dimensionless parameters K_I^* and K_II^* for tested SCB samples and their corresponding fracture toughness.

	KIIc (MPa.√m)	KIc (MPa.√m)	KII*	KI*	t	R
Pure mode I	0.0	1.125	0.0	0.644	15	95
Pure mode II	0.897	0.0	0.35	0.0
Pure mode I	0.0	1.411	0.0	0.644	25	95
Pure mode II	1.075	0.0	0.35	0.0
Pure mode I	0.0	2.126	0.0	0.644	50	95
Pure mode II	1.448	0.0	0.35	0.0
Pure mode I	0.0	2.083	0.0	0.644	80	95
Pure mode II	1.311	0.0	0.35	0.0

The other point assessed in the present study is the dependency of fracture path on specimen thickness in mode II loading. It was shown that the fracture trajectory becomes more curvilinearly when the thickness of specimen increases.

Figure 2. The variations of K_Ic and K_IIc versus the specimen thickness.
Conclusion
The effect of specimen thickness on the mode I and mode II fracture toughness of rock was investigated experimentally using the SCB specimens. The experimental results showed that the fracture toughness for both pure modes increases when the thickness of specimen increases until a specific thickness. After that, the values of K_Ic and K_IIc decrease by increasing the specimen thickness. For plane strain condition in which the thickness of specimen is relatively large, the values of K_Ic and K_IIc are nearly constant. Also, it is shown the crack grows more curvilinearly for thicker SCB samples../files/site1/files/142/1.pdf
 

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