where (N1)60 is the SPT-N normalised to an overburden pressure of 101 kPa (i.e., atmospheric pressure) with a hammer efficiency of 60%. N is the measured SPT blow count. CN is the correction factor for overburden stress. CB is the correction factor for borehole diameter. CE is the correction factor for the hammer energy ratio. CR is the correction factor for rod length. CS is the correction factor for samplers with and without liners.
where amax is the peak horizontal ground acceleration (PGA) at the ground surface, g is the gravitational acceleration, σvc and \(\sigma_vc^\prime \) are the total overburden stress and effective overburden stress, respectively, and rd is the stress reduction factor as given in Eq. 10.
Homework 1 Calculating Overburden Stress
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where \(N_\textm =\) SPT-N value, \(C_\textN = N_\textm\) normalization factor regarding overburden stress, \(C_\textE = 60/100 =\) corrected hammer energy ratio, \(C_\textB =\) borehole diameter correction factor, \(C_\textR =\) correction factor for rod length, and \(C_\texts =\) sampler correction.
Because equivalent depth models base all calculations on a relationship with the overburden gradient, the Overburden Gradient is the core element of the pore pressure model. If the overburden gradient is not representative of the actual vertical stress, all calculations of pore pressure and fracture gradient will be erroneous. Thus, a representative overburden gradient is critical to the applicability and confidence of the pore pressure model.
The calculated overburden stress at any depth is a function of the combined effect of the force of gravity on the total mass above and tectonic stresses. In the Oil and Gas Industry, the overburden stress has never been measured. The stress has been measured in other industries such as mining. They utilize strain gauges to measure the actual stress in the formation. Placing a strain gauge in an open borehole has not been practical, thus the overburden stress has never been measured in a well.
In pore pressure modelling, the overburden stress at any depth is assumed to consist of the combined effect of the force of gravity on the total mass above that depth without including the effect of tectonic stresses.
The calculated overburden stress at any depth is the sum of the force applied by the total mass above that particular depth. As depth increases, the density of the formation is not constant. The overburden stress is calculated by dividing the strata into a continuous series of discrete elements from the surface or mud line to a specified depth, then adding incrementally the force due to gravity of each element, beginning at the model reference height. At any specified depth, the calculated overburden stress will be the force due to gravity applied by the total mass above that depth.
The calculated overburden gradient is equal to the equivalent density of a fluid of a column height equal to the distance from the specified depth to the reference height (such as a drill floor or mean sea level) necessary to generate a force equal to the calculated overburden stress.
The densities used to calculate the overburden stress are from density logs, density transforms using sonic travel time and interval velocity, and an assumed shallow density profile. Very seldom is there density log measurements for the shallowest portion of the subsurface. The shallow density profile begins at the surface for onshore locations, and at the mud line for offshore locations. Determining the shallow density for a surface location is relatively easy. Go to the location, collect a sample of the surface strata, and measure the density. For offshore locations the mud line density is almost always not a data element collected when surface coring is conducted, and is not known.
Local rate of deposition is affected by shallow geologic structures. Time, in addition to the overburden stress, is a factor influencing the degree of compaction. At the apex of a structure, the depositional sequence being deposited today will be thinner than away from the crest of the structure. For a given depth, the deposits at the crest of the structure will have been subjected to compaction for a longer period of time than away from the crest of the structure. Therefore, mud line density of clay is greater at the apex of the structure than away from the crest of the structure.
The overburden gradient is calculated using the total mass above the depth of the calculation. For different water depths, the percentage of density attributed to water varies at a specific total depth will be different for each different water depth. Water has a density of 1.0 to 1.05 g/cc, and rock densities normally range from 2.2 to 2.5 g/cc below the depth of shallow density. Given the same rock density below the mud line, the total overburden stress at 30,000 feet and a water depth of 3,000 feet will be greater than the total overburden stress at 30,000 feet true vertical depth and a water depth of 9,000 feet.
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Homework has been identified in numerous studies and articles as a dominant or significant source of stress and anxiety for students.[13] Studies on the relation between homework and health are few compared to studies on academic performance.[14][15]
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Figure 1. A stress polygon assuming a pore pressure of 4400 psi, an overburden stress of 11000 psi, a coefficient of sliding friction of 0.6, a mud pressure of 5900 psi, a tensile strength of 0 psi, a breakout width of 0, and an unconfined compressive strength of 14000 psi. A Co line represents a breakout, and a To line represents a drilling induced tensile fracture.
where the subscripts n and log refer to the normal and measured values of density, resistivity, or sonic delta-t; Pp is the actual pore pressure, and Phyd is the normal hydrostatic pore pressure. Calibration of this method requires knowing the appropriate normal value of each parameter. It is important to realize that, in contrast to trend-line methods, the ratio method does not use overburden or effective stress explicitly and thus is not an effective stress method. This can lead to unphysical situations, such as calculated pore pressures that are higher than the overburden. The ratio method is also applied to analyses of pore pressure from the drilling exponent (Fig. 2).[1]
In general, effective stress methods must be calibrated, preferably using log data. However, they can also be calibrated empirically using approaches similar to those used to select trend lines, and they account explicitly for local changes in overburden and other stresses. The equation plotted in Fig. 4 is an example of relationships of the form
The classical centroid effect occurs when an initially flat reservoir surrounded by and in equilibrium with overpressured shale is loaded asymmetrically and tilted, leading to a hydrostatic gradient in the sand that is in equilibrium with the original pore pressure at the depth of the sand prior to tilting. At the same time, pore pressure in the shale, which has extremely low permeability after it has been compacted, changes in such a way as to maintain a constant effective stress equal to the original effective stress at the depth of the sand prior to tilting. At the depth of the centroid (usually taken to be the mean elevation of the sand), the shale and sand pore pressures are equal. This effect is shown diagrammatically in Fig. 8.[7] Because the pressure in the shale decreases upward at the same rate as the overburden (that is, proportional to the density of the shale itself), it is much lower at the top of the reservoir than is the pore pressure within the reservoir, which decreases at a slower rate that is proportional to the fluid density in the reservoir. Below the centroid, pore pressure in the sand is less than that in the adjacent shale. 2ff7e9595c
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