Lab1 Rock Young's modulus E and unconfined compression strength UCS

Summary

The video explains how to calculate unconfined compressive strength (UCS) and Young's modulus using cylindrical rock samples. The process involves applying axial loads to the sample and measuring the resulting stress and strain. The workflow consists of four steps: measuring the sample, setting up the loading frame, fracturing the rock, and analyzing the data. Key aspects include ensuring sample quality, controlling the loading process, and calculating parameters from force and displacement data. The results yield Young's modulus from loading/unloading cycles and the UCS as the peak stress the rock can withstand.

Takeaways

• 🧱 UCS and junk modulus are calculated using axial load applied to cylindrical cores.
• 📏 Strain is calculated by comparing the change in length (delta L) to the initial length of the sample.
• 📊 Stress is calculated as the applied force divided by the area of the cylindrical sample.
• ⚖️ Junk modulus is determined from the differential stress and differential strain during loading.
• 📈 UCS (unconfined compressive strength) is calculated by finding the peak force the sample can withstand divided by its area.
• 🔍 Step 1 involves measuring and checking the sample’s quality, including verifying if the sample is straight and ensuring the end faces are parallel.
• ⚙️ Step 2 includes setting up the loading frame and confirming that the stress applied is parallel to the sample’s axis.
• 🪨 Step 3 involves fracturing the rock by increasing force and then analyzing the load-displacement data.
• 📑 Step 4 is data analysis, converting force and displacement into stress and strain to calculate the junk modulus and UCS.
• 🔬 The final parameters obtained are junk modulus during loading and unloading and UCS from the peak stress point.

Q & A

What are UCS and Young's modulus, and how are they determined?

UCS (Uniaxial Compressive Strength) and Young's modulus are determined using cylindrical rock samples. UCS is the maximum stress the sample can withstand before breaking, while Young's modulus measures the stiffness of the rock. Both are determined by applying an axial load to a cylindrical core and calculating stress and strain.

What are the four steps involved in calculating UCS and Young's modulus?

The four steps are: 1) measuring the sample, 2) setting up the loading frame, 3) fracturing the rock, and 4) analyzing the data.

Why is it important to check the quality of the rock sample before testing?

It is important to check the quality to ensure the sample is suitable for testing, as samples need to be as close to perfectly cylindrical as possible. Measurements such as the diameter and length are taken to verify uniformity and parallelism of the end faces.

How is stress calculated during the experiment?

Stress is calculated as the force applied over the cross-sectional area of the cylindrical sample.

How do you determine whether a sample is straight?

A sample is considered straight if the diameter measurements taken at different parts of the sample are nearly the same. The average of these measurements is used to represent the diameter.

What role does the loading frame play in the experiment?

The loading frame is used to apply a controlled force to the cylindrical sample. It ensures that the applied stress is parallel to the axis of the sample, and allows the measurement of load and displacement.

What are channels 1 and 3 used for during the experiment?

Channel 1 is used to measure the load (force) applied to the sample, while Channel 3 measures the vertical displacement of the sample.

What is the purpose of using a protective plastic around the sample?

The protective plastic is used to prevent injury or damage if the sample fractures and fragments are ejected during the experiment.

How is the Young's modulus calculated during the experiment?

Young's modulus is calculated as the slope of the stress-strain curve, either during loading or unloading. It is the differential stress divided by the differential strain.

What is the significance of the peak stress in the experiment?

The peak stress represents the maximum force the sample can withstand before fracturing, which is used to determine the UCS of the rock.

Outlines

00:00

🧪 Introduction to UCS and Young’s Modulus Testing Using Cylindrical Samples

In this section, the process of calculating Unconfined Compressive Strength (UCS) and Young’s modulus using cylindrical cores is introduced. The core is placed between two surfaces, and an axial load is applied. As the force compresses the sample, its length shortens, producing strain. Stress is calculated as the force divided by the sample’s area. Young’s modulus is derived from the relationship between stress and strain, while UCS is determined from the peak force the sample can withstand. The process involves four main steps: measuring the sample, setting up the loading frame, fracturing the rock, and analyzing the data.

05:01

📏 Measuring and Preparing the Sample

This section details the first step of the process, which involves measuring the sample and conducting quality checks to ensure accuracy. Measurements focus on the diameter to confirm the sample’s straightness and consistency across different points. The length is measured at various angles to ensure parallelism of the sample's end faces, which is critical for applying even force. Additionally, the weight of the sample is recorded. These checks are essential to ensure that force is applied evenly along the axis of the cylindrical sample during testing.

10:02

🔧 Setting Up the Loading Frame

In this phase, the setup of the loading frame is explained. The frame's end faces must be aligned to ensure that stress is applied evenly along the sample's axis. Two key parameters are measured: channel 1, which tracks the applied force, and channel 3, which records vertical displacement. The seating speed is used to slowly move the lower part of the frame until the sample is in light contact with the upper frame. Displacement and strain measurements confirm that the sample is correctly positioned for testing. Protective plastic is placed around the sample to ensure safety during fracture.

🚀 Fracturing the Sample

Here, the process of fracturing the rock sample is described. After the initial setup, the displacement speed is used to gradually increase the load until the sample fractures. This process involves cycling the load multiple times to observe the sample’s behavior under both loading and unloading conditions. Once the sample fractures, the test ends, and data collection is stopped. The fracture process provides critical data on how the material responds to stress and when it reaches its breaking point.

📊 Data Analysis and Calculation of Young’s Modulus and UCS

The final step focuses on data analysis. Key measurements include force and vertical displacement, which are used to calculate Young’s modulus and UCS. The initial dimensions of the sample (length and diameter) are used to convert force into stress and displacement into strain. The analysis produces a stress-strain curve, which allows for the calculation of Young’s modulus (during both loading and unloading) as the slope of the curve. The peak stress point, which occurs just before the rock breaks, is used to determine the UCS.

🔍 Conclusion: Calculating Key Parameters

This section concludes the process, summarizing how the three key parameters—Young’s modulus during both loading and unloading, and UCS—are derived from the testing procedure. These parameters provide insight into the material's mechanical properties and its ability to withstand stress before fracturing.

Keywords

💡UCS (Uniaxial Compressive Strength)

UCS refers to the maximum axial load a cylindrical sample can withstand before failure. It is a critical measure of a material's strength under compressive forces, and in the video, it is calculated as the peak force over the area of the cylindrical rock sample. This parameter is fundamental for understanding the material's resistance to fracturing under pressure.

💡Young's Modulus

Young's Modulus is a measure of the stiffness of a material and is defined as the ratio of stress to strain within the elastic region of the stress-strain curve. The video explains how Young's Modulus is derived from the differential stress and strain applied to the rock sample during the loading process, allowing for the calculation of the material’s ability to deform elastically.

💡Axial Load

Axial load is the force applied along the axis of a cylindrical rock sample during testing. This load causes the sample to compress, and the change in its length is used to determine strain. The video shows how applying axial load allows for the calculation of stress, strain, and eventually the material properties such as UCS and Young's Modulus.

💡Strain

Strain is the measure of deformation experienced by the material when a force is applied, expressed as the change in length divided by the original length. In the video, strain is calculated as the sample gets shorter under axial load, and it is a key component in determining both Young's Modulus and UCS.

💡Stress

Stress is the force applied per unit area on a material, calculated as the axial load divided by the cross-sectional area of the cylindrical sample. The video explains how stress, combined with strain, is used to derive material properties like Young's Modulus and UCS, giving insight into the sample's mechanical behavior.

💡Loading Frame

The loading frame is the device used to apply the axial load to the rock sample during testing. The video outlines how the loading frame ensures that force is applied parallel to the axis of the sample, allowing for accurate measurements of stress and strain. It also controls the speed at which the sample is loaded and unloaded.

💡Fracture

Fracture refers to the breaking of the rock sample when it can no longer withstand the applied load. The video demonstrates how increasing the axial load leads to a peak stress point, after which the sample fractures, providing the UCS. The fractured rock is analyzed further to understand its mechanical properties.

💡Displacement

Displacement in the context of the video refers to the vertical movement of the loading frame as force is applied to the sample. This displacement is recorded to measure how much the sample deforms (shortens) under load, which is essential for calculating strain. The video emphasizes the importance of monitoring displacement to ensure accurate measurements.

💡Cylindrical Core Sample

A cylindrical core sample is the rock specimen used in testing, which is shaped as a cylinder. In the video, proper preparation and measurement of this sample, including its diameter and length, are crucial for accurate calculations of stress, strain, UCS, and Young's Modulus. Ensuring the sample is straight and its ends are parallel is also important for consistent results.

💡Data Analysis

Data analysis involves processing the force and displacement data collected during the testing procedure. In the video, this includes filtering the relevant data channels, transforming raw force and displacement measurements into stress and strain, and using these values to calculate Young's Modulus and UCS. The analysis of this data helps in understanding the material’s mechanical properties.

Highlights

Explanation of how to calculate UCS and junk modulus using cylindrical core samples.

Introduction of axial load application over the cylindrical sample to measure strain and stress.

Process of calculating junk modulus by combining differential stress and differential strain.

UCS calculation method as the peak force a sample holds over the area of the cylindrical sample.

Step-by-step workflow: 1) Measure the sample, 2) Set up the loading frame, 3) Fracture the rock, 4) Analyze the data.

Importance of checking the sample for quality control to ensure it's a good cylindrical sample.

Method of measuring diameter at different points of the sample to determine the average diameter.

Ensuring the parallel alignment of the sample's ends to guarantee proper force application.

Detailed instructions on setting up the loading frame, ensuring alignment with levels and bubble indicators.

Explanation of the seating speed and displacement speed during the experiment.

Repetitive loading and unloading to observe how the junk modulus changes.

Observation of force-displacement cycles leading up to the rock's fracture.

Post-experiment analysis of force and displacement data to calculate stress and strain.

Visual observation and data extraction after the rock fractures, including capturing images of the fractured sample.

Final data analysis steps to calculate the junk modulus and UCS from force, displacement, and sample dimensions.

Transcripts

hello everybody

now we are going to

see how we calculate the ucs and

junk modulus using cylindrical cores

so the way that we calculate these two

parameters

are is using uh

an axial load we are going to place

the sample in between

this two sides and we are going to

apply a force over the

cylindrical sample

this sample as we apply the force is

going to get

shorter to

by an amount than tile and that amount

delta l compared to the initial length

that we have is going to give us

the strain that we have this

is going to be combined with the stress

which is calculated as a force over

the area of the cylindrical sample

when we combine strain with stress

we can calculate the junk modulus as a

differential stress

with respect with respect to the

differential

strain that we are applying for the rock

then we can calculate

the ucs as the peak force

that the sample is able to hold over the

area of the

cylinder the workflow that we use to

calculate this

is through four steps

the step one is just to measure the

sample

step two is the setting up

the loading frame the step three is

fracturing the rock

and the step four is the data analysis

and we see that in our first step

we have to not only to measure the

sample but we have to quality check it

to see if actually is a good sample

to perform the measurements

this is because samples are not

perfectly cylindrical

so we have to do some measurements

before

uh using the sample then

first we are going to control the

diameter of the sample

so our first question in here is is the

sample straight

if the sample is straight what we see is

that

measurements are different

parts of the sample

are going to give nearly the same

diameter

and then the diameter of the sample is

going to be the average of them

then we are going to measure the length

with the length we are going to control

as well

if the n faces are parallel

or not this is to ensure that the

force that we are applying is actually

alone is parallel to the axis

of the of the plug that we are using

again we are going to measure at

different angles

and we are going to address the

measurement to obtain an

average length finally

we are going to measure the weight of

the

sample then we are going to

setting up the loading frame so first

we are going to control as well that our

end faces in the loading frame

are parallel one respect to the other

which means

this bottom with this lower part

and then we are going to use a level

just and we have to be sure that the

bubble

on top and at the bottom are having the

same direction

so we ensure that our strain

stress applied is along

is parallel to the axis of the sample

then we are going to

sit the sample to see the sample we have

to

check the parameters that we have to

handle

and the the frame so

when we operate the frame what we are

moving is the

lower part of the frame based on that

we are going to measure two main

parameters

channel one which is the load that we

are

applying in terms of

force and channel 3

which is the displacement which is this

indicates the vertical displacement that

we have with the sample

and then we can choose whether to move

the lower part

either up or down

to increase or decrease the force that

we are

applying over the sample to control the

speed

at which we are moving this

a lower section of the frame we are

going to use the bottom speed

once we click on speed we can see that

we can

change the

speed so f2 is going to be used

just to choose the digit and f3 and f4

are going to use to either

increase or decrease by one

the value of the rate

in these experiments we are going to use

only

two values one value for sitting speed

and one slower value for displacement

speed

so when we want to see the sample we are

going to use the

seating speed the sitting speed

we are going to put in contact

the upper part of the frame with our

sample

without making the actual strain

and contact the

lower part which means that we are going

to move

up until we see that the force

slightly increases this is an indicator

that actually the sample is in contact

with the frames

then we are going to place and hold the

string goes

gauge actually here we are going to see

that the

displacement 2 is going to slightly

increase as well

indicating that we are having

measurements

in both of these channels finally

we are going to place just a protective

plastic around the sample just in case

that it fracture

and explodes we we are

safe from this issue

so the final picture before fracturing

the rock

is this we are going to have the

sampling contact

the string is placed and the protected

plastic

around the sample so once we have

these three aspects example we can start

fracturing the rock

now we are going to follow the same

procedure but

instead of using the set sitting speed

we are going to use the displacement

speed

now we can repeat loading and

uh loading forces to see how junk

modulus

works for during this loading and

unloading process so first we are going

to

increase the force moving up

the bottom and then moving down to see

the unloading

and we are going to repeat this this

cycle a couple of times

and then increase until we fracture the

rock

once we factor the row what we observe

is that we have a

great fourth stroke and then

we can stop our measurement since we are

going to observe that the

rock is tracked once we stop

we can take a picture of the fracture

and we can extract the data file

the fractal rock will look like this

so after we extracted the data and we

clean

all the laboratory we move into the

data analysis what we see is that we are

going to have

many measurements with our respect

to time and where

we have only two channels that are going

to be useful for us

which are force and the displacement two

from these two parameters we are going

to calculate the jam modulus and the ucs

so what we doing here is actually we are

going to filter

only the force and the change in length

and we are going to include now the

initial longitude of the sample and the

diameter of the sample to calculate the

area

based on that we can transform our force

and our vertical displacement into

stress

and vertical strength from this we are

going to see

a plot with this shape

and we can choose

an interval to calculate the gel modes

during either during loading or either

during

unloading as the slope of

the line that we are measuring

finally we can choose the peak stress

which is the point that the rock is

broken as

uh as our ecs

and now that

now we have our three parameters which

is

giant modulus both loading and unloading

and finally the ucs