Practical exercises

Some structural geological exercises performed by geologists are presented in this chapter. Many of the practical problems are related to the orientation of planes, lines or principal stress directions. We have chosen to pay particular attention to the Mohr circle, used for analysing stress as well as strain, and to the use of orientation diagrams that allow the geologist to visualize structural data in 3D. Fractured outcrops and seismological data are presented under the form of exercises that help the geologist to document the state of stress associated with past or present geodynamic processes. The chapter ends with a very classic exercise based on the principle of Archimedes.

Determination of Mohr-Coulomb Parameters for Modelling of Concrete

Cohesion is defined as the shear strength of material when compressive stress is zero. This article presents a new method for the experimental determination of cohesion at pre-set angles of shear deformation. Specially designed moulds are created to force deformation (close to τ-axis) at fixed pre-set values of angle with respect to normal stress σ. Testing is performed on series of concrete blocks of different strengths. From the compressive side, cohesion is determined from the extrapolation of the linear Mohr–Coulomb (MC) model, as the intercept on the shear stress axis. From the tensile stress side (from the left), cohesion is obtained using the Brazilian test results: first, indirect tensile strength of material σtBT is measured, then Mohr circle diagram values are calculated and cohesion is determined as the value of shear stress τBT on the Mohr circle where normal stress (σ)t = 0. A hypothesis is made that cohesion is the common point between two tests. In the numerical part, a theory of ultimate load is applied to model Brazilian test using the angle of shear friction from the MC model. Matching experimental and numerical results confirm that the proposed procedure is applicable in numerical analysis.

Estimation of paleostress from pore fluid pressure of the quartz veins and its significance in the Cu-Pb-Zn mineralization (Ambaji, Aravalli-Delhi mobile belt, NW India)

<p>Quartz veins are produced from the crystallization of the last silica enriched hydrothermal phase from granitic magma circulating along the pre-existing fracture of rock. In many instances, these hydrothermal fluid act as a carrier for the ore minerals. The intrusion of quartz veins along fractures depends upon the tectonic stress conditions in the area. Fluid pressure (P<sub>f</sub>) of these ascending liquids should be higher than the normal compressive stress (σ<sub>n</sub>) to dilate the fractures. We are studying the quartz vein intrusion in the Cu‒Pb‒Zn mineralization belt of Ambaji, South Delhi terrane, Aravalli- Delhi mobile belt, NW India. The host rocks include mica schist, amphibolite, calc schist, talc tremolite schist, and four phases of granite intrusion (G<sub>0</sub>‒G<sub>3</sub>). The age of G<sub>0</sub>, G<sub>1</sub>, G<sub>2</sub> and G<sub>3</sub> granite are 960, 860, 800, and 750 Ma respectively. The rocks underwent three phases of folding (F<sub>1</sub>‒F<sub>3</sub>) and show greenschist to amphibolite facies metamorphism. The quartz vein intrusion is related to syn to post F<sub>3</sub> folding and G<sub>3</sub> granite magmatism. This final phase hydrothermal fluid extremely altered host rock and formed biotite-tourmaline-quartz and tremolite-actinolite-talc-chlorite greisen along the contact. The greisen host chalcopyrite-pyrite-galena-sphalerite mineralization suggesting the ore minerals were transported by the quartz vein. Vein orientation, stress condition, fluid pressure fluctuation, and fluid temperature can decide the fracture dilation and mineralization processes. Therefore, this work concentrates on the geometrical distribution of the vein orientation data. From this we deduced (i) girdle distribution pattern of vein data  (ii) σ<sub>1</sub> = 120º/75º, σ<sub>2</sub> = 052º/07º, σ<sub>3</sub> = 323º/07º indicate maximum extension was NW-SE and σ<sub>1</sub>σ<sub>2</sub> plane strikes was N52ºE, (iii) θ<sub>2</sub> =12º, θ<sub>3</sub> = 40º  and (iv) R'(driving pressure ratio) = 0.95, ϕ (tectonic stress ratio) = 0.90 indicates high value for R' leading to dilation of wide range of fractures. Further, the high ϕ value suggests uniaxial extension. Microscopic petrography of fluid inclusions shows three generations of inclusion like primary inclusion, secondary inclusion, and pseudosecondary inclusion. Most of the inclusion has aqueous and vapour phase and some inclusions show solid halite phase. We observed different types of trail bound of inclusion like intragranular inclusion, intergranular inclusion and transgranular inclusion, which suggest deformation and recrystallization in the rock. We are studying microthermometry analysis of fluid inclusion present in the quartz vein and trying to estimate the fluid pressure. With the help of fluid pressure, the 3D Mohr circle will be constructed and paleostress will be quantified. That will help in understanding the stress condition and mineralization in the rock.</p><p>Keywords: Veins, Fractures, Paleostress, 3D Mohr Circle, Mineralisation, Fluid Inclusion, Microthermometry</p>

Correlation between shear and normal strength for brittle reinforced concrete member considering internal stress condition of concrete

Formulas used to predict shear strength of reinforced concrete in different standards do not always correspond to each other due to the complexity of the shear transfer mechanism. Currently there is no generally accepted method of shear strength pridiction, however, traditionally, shear strength anticipation of a structural concrete elements is performed differently on members with or without shear reinforcement. These empirical approches tend to predict the shear strength too conservatively; alternatively, shear strength of concrete can be easily predicted by Mohr-Coulomb theory. In case of high-axial load and low shear reinforcement, the strength is likely to be determined by the concrete's shear crack. Therefore, a method to predict the strength of concrete with Mohr-circle has been proposed but the circles crossed the boundary and could not evaluate the strength correctly. Mohr circle can be used for prediction of diagonal tension failure strength but the circle cannot be evaluated. In this paper, Mohr circles were investigated considering all steps of cyclic loading until shear crack occurred. It also investigates a correlation between shear strength and normal strength through recognition of the Mohr-Coulomb failure criteria for each specimen.