Introduction - Importance of Hardened Cement...

This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved.

Mechanical Behavoir of Cement

Version 6 – June 26, 2013

CHARGE

Develop a technical report on the characterization of mechanical behavior of cement and test methods to measure

the mechanical parameters of cement in the laboratory.

EXECUTIVE SUMMARY

This document outlines the testing procedures often used to determine the mechanical behavior of cement.

Understanding cement mechanical behavior allows oil and gas wells to be better designed for long term integrity.

Testing protocals were compiled from several labs. Cooperative testing was used to identify how repeatable the

methods currently are. Testing was also partially used to guide specifics within the procedures. Test methods

analyzed and contained within the document:

Cement Sample Preperation

Unconfined Compression (static)

o Ultimate Compressive Strength

o Elastic Modulus

o Poisson’s Ratio

o Cyclic Testing

Direct and Indirect Tension

o Tensile Strength

Confined Testing

o Shear Failure Envolope

Accoustic Methods (dynamic)

o Elastic Modulus

o Poisson’s Ratio

o Bulk Modulus

TR on Mechanical Testing of Cement 1 of 48


ContentsPage

CHARGE........................................................................................................................................................................1Develop a technical report on the characterization of mechanical behavior of cement and test methods to measure the mechanical parameters of cement in the laboratory..................................................................................................1ABSTRACT....................................................................................................................................................................11. Introduction - Importance of Hardened Cement Properties......................................................................................32. Terms and Definitions...............................................................................................................................................3

2.1 Stress.................................................................................................................................................................32.2 Strain.................................................................................................................................................................3

2.2.1 Axial strain.............................................................................................................................................42.2.2 Transverse strain....................................................................................................................................4

2.3 Elastic constants...............................................................................................................................................42.3.1 Young’s modulus...................................................................................................................................42.3.2 Poisson’s ratio........................................................................................................................................5

2.4 Unconfined Compressive Strength (UCS)........................................................................................................53. Mechanical Testing Specimen Preparation...............................................................................................................5

3.1 Cement Slurry Preparation...............................................................................................................................53.2 Casting Cement Specimens..............................................................................................................................63.3 Cement Curing Procedure................................................................................................................................83.4 Cylinder Preparation.........................................................................................................................................93.5 Quality Control Check for Specimen Integrity..............................................................................................10

4. Testing Equipment and Common Uniaxial Compression Test Setup.....................................................................114.1 Tesing Equipment...........................................................................................................................................114.2 Common Test Setup.......................................................................................................................................11

5. Unconfined Compression Testing...........................................................................................................................125.1 Test Procedures..............................................................................................................................................13

5.1.1 Loading specimen monotonically........................................................................................................135.1.2 Loading specimen cyclically...............................................................................................................14

5.2 Test Result Interpretation...............................................................................................................................145.3 Typical Test Result.........................................................................................................................................16

6. Tensile Testing........................................................................................................................................................186.1 Test procedures of direct tension test (using briquette specimens)................................................................186.2 Test procedures of splitting tension test (Brazilian test)................................................................................186.3 Test Result Interpretation...............................................................................................................................20

7. Triaxial Testing.......................................................................................................................................................207.1 Confined Compressive Strength.....................................................................................................................21

7.1.1 Typical triaxial test results...................................................................................................................217.2 Triaxial test interpretation..............................................................................................................................227.3 Friction Angle (Φ) and Cohesion (c).............................................................................................................24

8. Acoustic measurements...........................................................................................................................................249. Reporting.................................................................................................................................................................26References.....................................................................................................................................................................2710.Appendix 1 – Cooperative Testing Results.............................................................................................................28

10.1Slurry stability................................................................................................................................................2810.2Monotonic uniaxial compression tests...........................................................................................................2910.3Cyclic uniaxial compression tests..................................................................................................................3410.4Mechanical property test results.....................................................................................................................39

11.Appendix 2 - TASK GROUP PARTICIPANTS.....................................................................................................41



1. Introduction - Importance of Hardened Cement Properties

Cement is a unique material. It is placed in the wellbore in a liquid form but ultimately provides long-term function

after it hydrates taking on the characteristic properties of a porous solid. It is important that cement placement is

executed successfully for the cemented annulus to initially protect and support the casing string as well as provide

zonal isolation, but the cement’s hardened properties must be conducive for long-term functionality. An initially

good cement sheath can become compromised when subjected to stress changes experienced in a well undergoing

pressure and temperature fluctuations caused through wellbore operations (drilling, stimulation production,

workover, etc.). Therefore, it is important to characterize the hardened cement’s properties to facilitate estimations

of the stress-strain response of the cement during wellbore operations. These estimates can provide the information

necessary for selecting a cement system that can withstand the thermal and mechanical stresses the cement sheath

will have to endure during the life of the well.

There are two common ways to determine the properties of hardened cement. One technique is via “static”

measurements using a load frame that yields values of Young’s modulus, Poisson’s ratio, and compressive strength

while the second uses acoustic measurements that give values of dynamic Young’s modulus and dynamic Poisson’s

ratio. In general, there is not a published correlation between static and dynamic measurements over a wide variety

of cement compositions. The two methods will be addressed separately.

2. Terms and Definitions

To facilitate communication and avoid confusion, it is important to provide clear definitions to the mechanical

parameters discussed in this report. Please note that only the parameters directly related to mechanical testing of

cement is provided here.

2.1 Stress

Stress is defined as a force applied to a surface per unit area. Normal stress is the stress component normal to a

given plane. Shear stress is the stress component parallel to a given plane.

For a cylindrical specimen under unaxial compression, only normal/axial stress (σa) is produced, which can be

represented as:

σ a=ForceArea

= FA0

(1)

with the axial compressive loading force (F) applied normal to the section (surface A0) of the cement specimen.

2.2 Strain

Strain is defined as the ratio of total deformation to the initial dimension of the material body in which the forces are

being applied. Normal strain is defined as the change in length per unit of length in a given direction. Shear strain is

defined as the displacement of one surface with respect to another divided by the distance between them, or the



tangent of the change in the angle between two material line elements initially perpendicular to each other. For a

cylindrical specimen under uniaxial compression, only normal strains are produced, which can be further divided

into two types: axial strain and transverse strain.

2.2.1 Axial strain

For the cylindrical specimen, the amount of axial dimensional change (ΔL) relative to the original length (L 0) in the

direction of primary axial stress is defined as the axial strain (εa):

ε a=∆ LL0

(2)

2.2.2 Transverse strain

For the cylindrical specimen, the amount of diametrical dimensional change (ΔD) relative to the original Diameter

(D0) in a direction perpendicular to the primary axial stress is defined as the transverse (or radial) strain (εt):

ε t=∆ DD0

(3)

2.3 Elastic constants

Many elastic materials have a tendency to deform linearly (or approximately linearly) as long as the stress does not

exceed the material’s elastic limit. This linear-elastic behavior is described by Hooke’s law, which states that strain

is directly proportional to stress. Elastic constants, which represent the material’s elastic properties, are conveniently

defined to link stress and strain. Some of the most commonly used elastic constants are Young’s modulus, Poisson’s

ratio, shear modulus and bulk modulus. For homogenous and isotropic materials, the material’s elastic properties are

fully described by any two of these elastic constants (all the others can be calculated theoretically). At moderate

stress levels cement can be assumed to exhibit linear-elastic behavior and therefore its elastic constants are often

reported.

2.3.1 Young’s modulus

Young’s modulus (E) is defined by the ratio of the increase in normal stress to the resulting increase in normal strain

in the same direction:

E=σa

εa

(4)

E can be determined experimentally by performing a linear regression analysis on the stress-strain data over a

prescribed stress range. This approach yields the tangent modulus as the slope to the stress-strain curve relative to a

given point is approximated. On the other hand, the slope of a line from any point on the stress-strain curve relative

to the origin (zero net stress) is defined as the secant modulus and the slope of a line connecting any two points on

the stress-strain curve is called the chord modulus. For a perfectly linear-elastic material, Young’s modulus, tangent

modulus, secant modlus and chord modulus are all identical.



2.3.2 Poisson’s ratio

When a material is compressed in one direction, it usually tends to expand in directions perpendicular to the

direction of compression. To characterize such behavior of a cylinder using previously defined normal strains in

Section 2.2, Poisson’s ratio (ν) may be defined as,

ν=−εt

εa

(5)

Poisson’s ratio should be determined experimentally over the same stress range the Young’s modulus is determined.

Remark:

Minus sign for the Poisson ‘s ratio formula is required due to sign convention commonly used for normal strain.

2.4 Unconfined Compressive Strength (UCS)

The unconfined compressive strength is the maximum stress (load per unit of surface area) at which the cement

specimen fails in a compression test without confining pressure. It is determined experimentally by destructively

testing the cement. The maximum stress recorded during the test is the UCS.

UCS=MAX {σ a(unconfined)} (6)

Note:

Materials can deviate from linear elastic relationship at strengths less than the UCS.

3. Mechanical Testing Specimen Preparation3.1 Cement Slurry Preparation

Systems should be mixed in accordance with procedures described in Clause 5 of API RP 10B-2 when possible.

Considerations include:

1. Before preparation of cement specimens, cement slurry design should be checked to achieve minimum free

fluid and sedimentation.

2. When the total volume of desired slurry exceeds the capacity of the mixing device, i.e. 1 liter (1 quart),

then:

a. Follow API RP 10B-2 Annex A, or

b. Consolidate a number of smaller batches (prepared according to Clause 5 of API RP 10B-2)

together and homogenize them by mixing in a low-shear laboratory mixer.

3. When additives are to be mixed requiring deviation from the recommended procedure, i.e. fibers,

elastomers, etc., then

a. Document any deviation from the recommended procedure, including:



i. Addition of additives to the individual blend while in the recommended mixing device

after the standard procedure

ii. Addition of additives to the combined blends during the homogenization process

b. Ensure that the addition of additives is done in a manner that results in a homogenized slurry for

testing.

c. The mixing procedure should be reproducible

4. Document any deviation from API RP 10B-2 Clause 5 and report them.

3.2 Casting Cement Specimens

In order to produce specimens with desired shape and uniformity, the following procedures and requirements shall

be followed when casting cement specimens:

1. Molds can be made from any material as long as they are capable of maintaining their shape in the curing

conditions to which they will be exposed and do not interfere with the cement hardening process.

2. Cylindrical molds with an internal diameter intended to define the sample shape (when sample is not cored

from a larger mold) should comply with the requirements specified in ASTM C470/C470M, except that the

preferred inside height of the mold is approximately 2.5 times the inside diameter to allow for subsidence

and post-processing of the resulting cement specimens. The inside diameter should be large enough to

accommodate any particulate additives such that the resulting specimen provides a homogenous

representation of the composite response of the additives bound by the cement matrix. It is recommended

that the minimum diameter should be at least ten times greater than the largest granular particles in the

slurry.

a. The diameter of a cylindrical specimen used for compression test should be greater than or equal

to 1 inch (25 mm).

b. The preferred diameter of a cylindrical specimen used for splitting tensile test is 2 inch (50mm)

and should be no less than 1.5 inch (38 mm).

3. When a cored sample is cored from a larger hardened cement sample care must be given to the core

diameter. It is recommended that the minimum diameter should be at least ten times greater than the

largest granular particles in the slurry.

4. Briquette (dogbone) molds used for direct tension test shall conform to the dimensional requirements

shown in Fig. 1 (ASTM C307). The molds are designed to produce specimens to fracture at the waist line

(i.e. the weakest/smallest cross section) under tension. The width of the mold, between inside faces at the

waist line, shall be 1 in. ± 0.02 in.. The depth of the mold, measured on either side of the mold at the waist



line shall also be 1 in. ± 0.02 in.. Gang molds may be used. The briquette molds should be tightly attached

to a plate at the bottom. The leak tightness of the molds may be checked by filling them with water.

Fig. 1: Dimensions of briquette specimens for direct tensile strength test (ASTM C307)

5. A thin layer of release agent or lubricate may be applied to the inside surface of the molds before casting

cement specimens.

a. The layer of release agent shall be applied in a thin film with uniform thickness.

i. The release agent shall be thin enough to not change the intended shape and size of the

final cement specimen produced.

ii. There should be no significant irregularities in the release agent that will ultimately be

imprinted on the hardened cement specimen, i.e. brush strokes.

b. The release agent shall be inert to the cement and not interfering with its setting and hardening

process.

6. The cement slurry should be added to the molds in a way that minimizes voids and air entrapment.

a. The following procedures may be followed when casting a cylindrical specimen



i. Fill the mold up to half-full.

ii. Puddle slurry approximately 30 times (puddling rod should be corrosion resistant with a

diameter approximately ¼ in.).

iii. Stir remaining slurry and fill the mold to overflowing.

iv. Puddle approximately another 30 times

v. Strike off excess slurry

b. The following procedures may be followed when casting a briquette specimen

i. Fill the mold up to overflowing

ii. Puddle slurry to fill voids

iii. Strike off excess slurry

3.3 Cement Curing Procedure

Curing condition has a very strong effect on the mechanical property development of a cement system. Therefore,

standard curing procedures shall be followed during preparation of cement specimens. It is recommended to not

completely seal the top of the molds such that the specimens have access to water during the curing process.

Depending on the purpose of the study, specimens can be cured at either ambient conditions or simulated downhole

conditions.

1. Atmospheric-pressure water bath curing

a. Cover molds with plates or lids.

b. Place molds in water bath set at the desired temperature. Temperature fluctuations of the water

bath should be within ±2 ˚F (±1 ˚C).

c. Off-set molds from the bottom of the bath to allow for uniform temperature distribution around the

specimen

d. Cure for desired time at the desired temperature.

2. Pressurized water bath curing

a. Cover molds with plates or lids.

b. Place molds in a pressurizable curing vessel using water as pressurizing medium.

c. Apply pressure and temperature to the vessel in accordance to the test schedule

i. Make sure the pressure is greater than the vapor pressure at all times to avoid steam

generation



ii. Curing schedule can simulate cement placement conditions

iii. When specific conditions are not available a generic schedule is recommended:

1. Initial step to 1000 psi (6.9 MPa) and 80°F (27°C)

2. Ramp to BHST and 3000 psi (20.7 MPa) over 4 hours.

3. Cure for desired time at the desired temperature.

4. Ramp the pressure and temperature to atmospheric conditions as slow as

possible

a. Try not exceed 10 psi/min (69 KPa/min) ramp down (~ 5 hours from

3000 psi (20.7 MPa))

b. Try not exceed 4.5 °F/min (2.5 °C/min) ramp down

5. Immerse specimens in water at ambient conditions after removing from the

vessel and the molds

6. Prepare cylinders and perform tests in as short of time possible from removing

the specimens

iv. Curing conditions should be documented and presented with the results

1. A chart showing actual conditions is recommended

3. After specified test age has been reached,

a. Remove molds from the water bath.

b. Remove specimens from the molds.

c. Mark up specimens for identification purpose.

d. Store specimens immersed in water at room temperature.

e. Prepare specimens according to Section 3.4 and test them as soon as possible.

Remark:

Curing time should be limited in time. When run in parallel with curing specimen for mechanical testing, A UCA

test can help to determine if the cement is still in a transitional state after the desired curing time or to determine a

minimum curing time which should be the time to reach a plateau.

3.4 Cylinder Preparation

Cylinder specimens can be generated by either molding or coring from a larger specimen. This section describes the

procedures to post-process a cast/molded cylinder specimen for further mechanical testing.



1. For specimens to be tested under uniaxial and triaxial compression, the final specimen should have a length

to diameter ratio (slenderness ratio) of 2.

LD

=2.0 ±0.2(7)

2. For specimens to be tested under splitting tension, the final specimen shape should have a length that is one

half the diameter.

LD

=0.5 ±0.05(8)

a. A longer cylinder can be sliced to generate these specimens.

b. If these specimens are generated by slicing a larger specimen then the specimens can be used as a

quality control check for slurry stability and specimen homogeneity.

3. The specimens should be kept saturated with water from the time they are cured untill the time of testing

except when they are being worked on.

4. Cut the top end of the specimen at appropriate length to remove any weakened top section due to

sedimentation and dilution effect. Grind both ends of the specimen to generate smooth surfaces. Make sure

the final length of the specimen meets the requirements in No. 1 of this section.

a. The actual preparation conditions (core barrel design, rate of penetration, rpm, etc.) will depend on

the specimen properties and the equipment being used.

b. The cut/ground end should result in two smooth parallel ends for testing. Cylindrical specimens

should have ends flat to within ±0.0001 in (±0.025mm), circumference smooth to ±0.02 in

(±0.5mm) and ends perpendicular to the longitudinal axis within ±0.5 degrees.

c. Water should be run over the specimen during the cut/grinding process to cool the cutting surfaces

and remove debris.

d. If preparing specimen for the splitting tensile test, a larger cylinder can be cut into several slices at

the recommended lengths.

5. Measure specimen length, diameter, mass and volume (displacement of water). Refer to the Sedimentation

test in API RP 10B-2 for a way to measure density (Sections 12.5.2.9 through 12.5.2.19).



3.5 Quality Control Check for Specimen Integrity

The quality of the specimens to be tested can be affected by both the quality of the procedures used to prepare the

specimens and the methods used for curing the specimens. This section covers techniques to prevent specimens

from being produced that will yield misleading results.

1. Conventional tests may be run during the cement preparation to ensure the quality and the reproducibility

of the process.

a. Sedimentation and free fluid tests (to validate slurry stability) or using the Archimedes principal to

check the density of the splitting test specimens taken from a cylinder

b. UCA to determine the transient behavior of the hydration process

2. Cylindrical specimens should have ends flat to within ±0.0001 in (±0.025mm), circumference smooth to

±0.02 in (±0.5mm) and ends perpendicular to the longitudinal axis within ±0.5 degrees.

4. Testing Equipment and Common Uniaxial Compression Test Setup4.1 Tesing Equipment

Common equipment for conducting mechanical tests mainly consists of the following items:

1. A load frame that provides reaction forces.

2. A linear actuator (hydraulic or meachnical) to allow load application to the specimens. Either the load

application rate or the deformation rate must be controllable.

3. For compression tests, platens to provide proper contact with the test specimens.

a. The platens should be smooth and free of any imperfections or debris

b. They should be parallel or allowed to swivel such that a uniform load is applied to the test

specimen

4. For tension tests, grips/clamps to secure the end of the specimens.

5. A load cell, or equivalent device, to measure the amount of force applied to the specimen.

6. Displacement transducers to measure the radial and axial deformations of cylindrical specimens under load

(Optional).

a. Several transducer types can be used (i.e. extensometers, LVDTs, etc.).

b. Measurements can also be aided with signal processing and mechanisms, such as cantilevers, to

give the measurement more resolution.

7. Data acquisition system.



Remark: Instrumentation and equipment should be designed to accurately measure the forces and displacements in

order to determine the test specimens properties with little uncertainty.

4.2 Common Test Setup

Uniaxial compression test is the most commonly used test method to characterize cement mechanical properties.

Fig. 2 shows a common setup of such test for a cylindrical specimen (displacement/strain measurement devices are

not shown). As a test is performed, the force (or machine displacement) applied perpendiculary to a flat surface is

changed while the cement specimen’s response is measured. Typically measurements are made of the applied force

(F) and the deformation of the specimen (axial deformation (ΔL) and transverse diametric deformation (ΔD)) until

observation of specimen failure. The obtained test data allows the determination of mechanical parameters of the

specimen including the unconfined compressive strength (UCS), Young’s Modulus (E), Poisson’s ratio (ν).

The common uniaxial compressive setup can be changed slightly to measure other material properties of interest.

For example, a confining cell, or pressure vessel, can be used to apply a hydraulic confining pressure to the

specimen and thus perform triaxial testing; a cylindrical specimen may be flipped on its side to allow applying

diametric compressive forces and conducting splitting tension tests; the compressive platens can be replaced with

grips to allow testing specimens under direct tension.

Fig. 2: Common compressive test setup

Remark:

Test equipment should be calibrated to the manufactures recommended practices.


A0 ΔL

D0 + ΔD

Force

D0

L0Bottom Platen

Spherical Seated PlatenCement Sample

Actuator

Table

LoadCell

Unloaded

Load Frame

Loaded


5. Unconfined Compression Testing

The unconfined compressive strength (UCS) and the stress-strain behavior of cement is usually determined by

applying uniaxial (unconfined) compression loads to cylindrical specimens. The stress-strain data can be used to

derive the elastic constants of Young’s Modulus and Poisson’s Ratio. For determination of these properties,

cylindrical specimens are required to have a length to diameter ratio (slenderness ratio) equal to 2.0 ± 0.2. This

slenderness ratio requirement minimizes the “end effects” on test results (The ends of the specimens are subjected to

triaxial stresses due to constraint of their lateral expansions exerted by the platens). For specimens with smaller

slenderness ratios, the unconfined compressive strength would be overestimated and correction factors are required.

For slenderness ratios of 1, the UCS can be overestimated by 15% (ASTM C39/C39M).

5.1 Test Procedures

Both UCS and elastic constants of cement are determined from unconfined compression tests. However, their

determination can require different test procedures. UCS is typically determined from a monotonic loading test

while elastic constants may be determined by a cyclic loading test under the (assumed) elastic limit of the specimen.

Safety precautions: Violent failures of cement specimens can occur when loaded in compression. A protective shield

should be placed around the test specimen to prevent flying cement fragments and injuries.

5.1.1 Loading specimen monotonically

1. Measure the length and diameter of the specimen.

2. If stress-strain curves are to be obtained, apply instrumentation (mainly strain-measuring equipment) to the

specimen.

a. Use a load cell that gives good resolution for the specimen strength for which the test is being

applied.

b. Both axial and radial displacement instrumentation may be used if desired. (For tests where the

only requirement is to determine UCS the use of axial and radial instrumentation is not required.)

c. Verify the instrumentation can precisely measure the small displacements experienced during

testing.

d. Document any pertinent information about the instrumentation, such as:

i. instrument type

ii. resolution

iii. attachment method

3. Place specimen (with the instrumentation attached if appropriate) in the load frame at the center of the

bottom platen and verify that both load and displacement indicators are set to zero.



4. Adjust the test machine to have the top platen to bear upon the specimen.

5. Start data acquisition.

6. Apply a compression load.

a. Document the control method (force or displacement) for the way the load is applied.

b. Document the rate at which the load or displacement is applied.

7. Run test until specimen failure and then stop data acquisition.

Remark:

The fracture pattern of the specimen should be identified and reported according to ASTM C39/C39M.

5.1.2 Loading specimen cyclically

Specimens are typically loaded cyclically within its elastic limit to determine their elastic constants, such as

Young’s modulus and Poisson’s ratio. The first cycle often seats the gages produces different results than

subsequent cycles. It is not recommended to use data for the first cycle for any calculations when gages need to

be set. To minimize the risk of loading the specimen beyond its elastic limit, the UCS of the specimen should

be estimated before such test.

1 Measure the length and diameter of the specimen.

2 Estimate the UCS of the specimen (This is typically done by testing a companion specimen).

3 Apply instrumentation (mainly strain-measuring equipment) to the specimen.

a. Use a load cell that gives good resolution for the specimen strength for which the test is being

applied

b. Both axial and radial displacement instrumentation should be used

c. Document any pertinent information about the instrumentation, such as:

i. Instrument type

ii. Resolution

iii. Attachment method

4 Place specimen (with the instrument attached) in the load frame at the center of the bottom platen and

verify that both load and displacement indicators are set to zero.

5 Adjust the test machine to have the top platen to bear upon the specimen. Start data acquisition.

6 Apply a cyclic compression load:

a. Cycle up to 50% of the UCS of the specimen and back down to a minimum stress of 5% of the

UCS. Note the loading and unloading rates (normally the same)

b. Repeat the cycle multiple times if desired (This is usually done to check the reproducibility of test

results).



c. An additional compressionnal load up to failure (a half cycle) can be done in order to determine

the remaining strength of the specimen.

7 Stop the test and data aquisition.

5.2 Test Result Interpretation

1. The axial stress (σa) in Psi, axial strain (εa), and transverse strain (εt) of a cylindrical specimen during a

typical test can be calculated by,

σ a=F

π∗( D2 )

2 (9)

ε a=∆ ll0

(10)

ε t=∆ DD

(11)

Where

F is the applied load (lb);

D is the diameter of the specimen (in);

l0 is the gauge length of the axial strain measuring device (in);

∆l is the change in the gauge length (i.e. the reading) of the axial strain measuring device (in);

∆D is the change in the gauge length (i.e. the reading) of the transverse strain measuring device (in).

Note: Strain has units of in/in and is therefore often referred to as dimensionless. In the figures within this

document the numbers are represented as a percentage which amplifies the value by 100, i.e. 0.004 in/in

multiplied by 100% is reported as 0.4%.

2. The unconfined compressive strength (UCS) of a specimen is the maximum stress (calculated according to

Eq. (9)) experienced by the specimen before failure occurs.

3. For cyclic loading tests, test data of the first cycle is usually not used for analysis (ASTM C469). Ideally,

after the first loading cycle, the specimen should exhibit linear behavior during stress range from 10% to

50% of the UCS. If this is the case, calculate the Young’s modulus (E) through linear regression on this

portion of the σa - εa curve according to Eq. (4). Otherwise, reduce the portion of the curve used for

regression analysis until it is linear and document the stress range. One method of determining the linear

portion of the stress-strain curve is to plot the tangent modulus as a function of strain (or stress). Fig. 3

shows an example of such plot (SPE101310).



0

2000

4000

6000

8000

10000

0 0.0005 0.001 0.0015 0.002 0.0025 0.003AXIAL STRAIN

YO

UN

G'S

MO

DU

LUS

, MP

a

Cycle Up 1Cycle Up 2Cycle Up 3

Fig. 3: Tangent modulus as a function of axial strain

4. Similarly, Poisson’s ratio (ν) can be calculated through linear regression on a portion of the εt – εa curve

according to Eq. (5). The linear regression analyses used to obtain Poisson’s ratio and Young’s modulus

should be in the same stress/strain range. Alternatively, as will be shown in Section 5.3, the slope obtained

by linear regression on a portion of the σa – εt curve can be combined with previously obtained E to

calculate ν.

5.3 Typical Test Result

When ploting the stress-strain curve of cement, it is convenient to use the nomenclature typical of rock mechanics,

in which compressive stress is defined as positive and a reduction in dimension is presented as a positive strain. Fig.

4 shows a typical stress-strain plot of an unconfined compression test. As shown in the figure, the positive portion of

the strain-axis represents the axial strain (εa) while the negative portion represents the transverse strain (εt).



Fig. 4: Typical stress-strain curve of an unconfined compression test

Based on the definitions given in Section 2, Poisson’s ratio can also be calculated as follows,

ν=−εt

εa=

−σ a

ε a

σa

ε t

=−EM

(12)

where M is the slope of the linear portion of the σa – εt curve. Eq. (12) is particularly useful when there exists two

separate sets of test data, i.e. σa vs. εa and σa vs. εt.

6. Tensile Testing6.1 Test procedures of direct tension test (using briquette specimens)

The most straightforward way to obtain the tensile strength of a material is through direct tension tests. However,

direct tension tests using regular-shaped specimens (such as cylinders and prisms) are very difficult to conduct due

to difficulties of creating a uniform tensile stress in the specimen. ASTM C307 describes a standard method for

performing direct tension tests using briquette (dogbone) specimens, for which it is not necessary to create uniform

tensile stress in the specimen. Test setup is similar to Fig. 1, except that platens are replaced with specially designed

tension grips/clips for holding the test specimens. A generic design for the clips is given in ASTM C307. In order to



avoid breaking the specimen at the grips, friction reduction measures such as those described in Step 2 and 3 of this

Section shall be adopted. Test results of specimens fractured at the grips should not be used.

1. Measure the depth and width at the waist of the specimen.

2. Lubricate the rollers of the tension clips.

3. Electric tape can be attacthed to the specimen at points where the specimen comes in touch with the roller,

with the smooth surface of the tape facing the rollers.

4. Center the specimen in the clips of the testing machine and verify that load indicator is set to zero.


6. Apply a tensile load until the specimen is pulled apart.

a. Document the control method and rate used

i. A rate of 100-200 lb/min can be used for load control

ii. A rate of 0.20-0.25 in./min can be used for displacement control (ASTM C307)

7. Stop the test and data acquisition.

6.2 Test procedures of splitting tension test (Brazilian test)

The tensile strength of cement-based materials can also be conveniently determined using an indirect method,

namely the splitting tensile test method (often called the Brazilain test). This method requires applying a diametral

compressive load along the length of a cylindrical specimen (Fig. 5). Based on the theory of elasticity, this loading

method induces uniform tensile stresses in the specimen on the plane containing the applied load. As will be shown

later (Eq. (14)), the magnitude of the tensile stress is proportional to that of the diametral compressive load. A

detailed derivation of their relationship and the stress state of a specimen under such loading condition may be found

in the work of Timoshenko and Goodier (1951).

Fig. 5: Schematic of splitting tension test (Brazilian test)


Typical

Failurel

Force (F)

D

Force (F)


Specimens are usually loaded onto the press with cardboard backing, 0.16” wide 2ply plywood, or malleable metal

sheet, to distribute the load over a small arc. The specimen should be positioned either using a specific test jig as

described in ASTM C496/C496M or following Step 3 as described below. A metal jig with curved surfaces to

spread the load over a small arc, as described in ISRM document (reference list) may also be used.

Whe using flat plattens with bearing strips:

1. Draw diametric lines on each end of the specimen using a suitable device that will ensure that they are in

the same axial plane (Design of such device is provided in ASTM C496/C496M).

2. Measure the length and the diameter of the specimen in the plane containing the lines marked on the two

ends (typically 2.0 in (50mm) diameter and 1.0 in (25 mm) thick).

3. Center one of the bearing strips at the bottom plate. Place specimen on the bearing strip and align so that

the diametric lines marked on the ends of the specimen are vertical and centered over the bearing strip.

Place a second bearing strip parallel to the first one and centered on the vertical lines. Verify that load

indicator is set to zero.

4. Adjust the test machine to have the top platen to bear upon the top bearing strip. Before applying load to

the specimen, adjust the spherically seated platen such that the bearing face of the top platen is parallel to

the top bearing strip.


6. Load the specimen until failure occurs.

a. Document control method.

b. Document control rate.


When using a metal jig:

1. Measure the length and the diameter of the specimen in the plane containing the lines marked on the two

ends (typically 2.0 in (50mm) diameter and 1.0 in (25 mm) thick).


3. Load the specimen until failure occurs.

a. Document control method.

b. Document control rate.




Remark:

When performing Brazilian tests, it is important to stop the test as soon as possible after fracture occurs and to

examine the form of the break. Ideally, the specimen should break at the plane containing the applied force and the

two marked lines. Minor irregularities and deviations from this plane is permited. Test data should be discarded if

the specimen does not show the appropriate break pattern.

Fig. 6: Example of a good test (left) and poor test (right).

6.3 Test Result Interpretation

1. The direct tensile strength (DTS) in Psi of a briquette specimen is calculated by:

DTS= Fb∗d

(13)

where,

F is the maximum load at failure (lb);

b is the width at the waist of the briquette (in);

d is the depth at the width of the briquette (in).

2. The splitting tensile strength (STS) in Psi of a cylindrical specimen is calculated by:

STS= 2∗Fπ∗L∗D

(14)

where,

F is the maximum load at failure (lb);

D is the diameter of the specimen (in);

L is the length of the specimen (in).

7. Triaxial Testing

Compressive testing can also be performed with stresses applied in more than one direction, often called triaxial

loading. The most common way to apply a second stress is through using a pressurized vessel on the load frame to



apply fluid pressure on a sleeved test specimen (Fig. 7). This results in a stress (σ 3) along the curve surface equal to

the fluid pressure. The primary stress (σ1) can still be applied mechanically through the axial system. It is obvious

that the unconfined compression test is a simplified version of the triaxial test; with σ3 equal to zero. The

engineering parameters, previously discussed for unconfined testing, can also be determined for a confined test

result where the stress-strain relationship is recorded.

Fig. 7: Schematic of confined compression test

7.1 Confined Compressive Strength

Confined testing is a type of triaxial testing. Initially, the fluid pressure and the mechanical load are simultaneously

brought to a predetermined value, the confining pressure(σ3). Then the mechanical load (σ1) is increased until

specimen failure occurs (while the fluid pressure (σ3) is held constant).

7.1.1 Typical triaxial test results

Triaxial compressive results are normally presented by the stress versus strain curves. Their representations are

similar to those of unixaxial compressive test (Clause 4) (Fig. 8). It is convenient to use the nomenclature typical of

rock mechanics, in which compressive stress is usually defined as positive; thus, a reduction in dimension is

presented as a positive strain. For the example stress-strain curve, the positive strain (ε) portion of the x-axis

represents the axial strain (εa); the negative strain represents the transverse strain (ε l an expansion) . The deviator

stress (∆σ) (called in some cases net stress), the difference between the loading stress (σ 1) and the confining stress

(σ3 ) is reported to the y- axis.

The maximum load the specimen withstood (MAX{ σ1}) minus the confining stress (σ3) is defined as the confined

compressive strength. It is often found for cement that the Young’s modulus E and Poisson Ratio υ are very similar

for both confined and unconfined tests (i.e. unaffected by confining loads); whereas the compressive strength is

influenced by various confining loads. The example in the nearby figure illustrates compressive test at three

confining pressures: 0 (or unconfined), 500, and 1,000 psi. The slope of the linear portion of the stress-strain curves


σ3 =

σ2 =

Pre

ssur

e

σ3 =

σ2 =

Pre

ssur

e

σ1 = F/A


change marginally while the ultimate stress (Deviator stress on y-axis) experienced is greatly different. As

confining pressure increases, the net compressive strength increases

0

500

1000

1500

2000

2500

3000

3500

4000

4500

-0.40% -0.20% 0.00% 0.20% 0.40% 0.60% 0.80% 1.00% 1.20%

Net

Stre

ss (p

si)

Strain (in/in)Axial Strain (in/in) Lateral Strain (in/in)A Strain L Strain

Fig. 8: Triaxial compressive strength test results (Note: Deviator stress (net stress) ∆σ = σ1 – σ3)

7.2 Triaxial test interpretation

Introduced by Augustin-Louis Cauchy, stress at a point in a solid body is physically represented as a 2 nd order

tensor. It has components consisting of both shear and normal stresses. Analysis of the stress-state in the simple

test specimen exposed to normal stresses of σ1 and σ3 at the boundary actually results in both shear and normal

stresses at a point within the specimen.

Otto Mohr found that the transformation equation relating the shear and normal stresses takes the form of a circle.

Once this “Mohr’s circle” is defined the stress at a point is fully understood. This concept is important for cement

testing because physical observations of failed specimens subjected to normal stresses are typically found to fail in

shear. This is especially true when cement is tested in a confined state. Therefore, several confined tests, each

yielding a Mohr-circle, are performed (Fig. 9). The normal stresses at the time of failure are points on the x-axis. In

the example, the confining pressure (σ3) is the smallest principal stress and the beginning of each half circle and the

maximum stress at failure (σ1) is the end of each half circle. Each circle has a radius equal to, τ max=(σ1−σ3)/2,

the maximum shear stress experienced during the test. Center of the Mohr circle is positioned on the x-axis at a

stress value equal to (σ 1+σ3)/2 . Without confining pressure, in that case σ 3=0, and the Mohr circle diameter σ 1


ConfiningPressure (σ3 = σ2)

Confined Compressive

Strength

Max Stress

(σ1)Psi Psi Psi0 3750 3750

500 3940 44401000 4180 5180

ε αε t

Strain (in/in) x 100%


is equal the UCS. It is also possible to draw a Mohr circle with tensile stresses. In that case the tensile test can be

represented by a circle with negative stress and a diameter equal to the tensile strength T o. At failure, τ max, which

is the apex of the circle, establishes what is called a failure limit. The failure limit for each case is used to establish

a failure envelope (Fig. 10). Subsequently any stress state which is represented by a Mohr circle can be compared to

the failure envelope. If the circle crosses the envelope then a failure is expected. The failure envelope can be

mathematically represented by several models such as Mohr-Coulomb, Drucker-Prager, Munson-Dawson, etc..

Fig. 9: Mohr circles and Mohr failure envelop

7.2.1 Mohr-Coulomb shear failure

Under certain limits of stresses the failure envelope can be modeled as a linear line : this is defined as the Mohr-

Coulomb shear failure criteria. Any stress state represented by a Mohr circle crossing the Mohr-Coulomb line,

should result in a shear failure.

This line’s y-intercept is the “Cohesion” (C) and the slope is the tagent of the “Friction Angle”(Φ). Mohr-Coulomb

shear failure line is represented by the relationτ=c+σ n tanΦ


T o 0 σ3 σ1= UCS σ1

σ

τ Failure envelope


0

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500

She

ar S

tress

(psi

)

Normal Stress (psi)

Cohesion = 1568 psi Friction Angle =

10.2

Fig. 10: Mohr’s Circles for confined tests bounded by the Mohr-Coulomb shear failure criteria.

7.3 Friction Angle (Φ) and Cohesion (c)

Defining the Mohr–Coulomb shear failure parameters, friction angle and cohesion are calculated from multiple sets

of triaxial compressive tests. A linear regression of the maximum axial stress (σ1) versus the confining stress (σ3) is

used to determine the friction angle and cohesive strength. The slope, tanα, of the linear least squares fit is used to

calculate friction angle (Φ).

sin Φ= tan α−1tan α +1

Cohesive strength (c) is determined using UCS and the friction angle (Φ).

c=UCS∗¿¿

Remark: Other methods to interpret confined test results can be used, for example Drucker-Prager, Munson-

Dawson, etc.

8. Acoustic measurements

Equipment is available to allow the determination of the dynamic Young’s modulus (Ed) and dynamic Poisson’s

ratio (υd) of set cement from the velocity of shear (VS) and compressionsal (VP) waves through the set cement. Ed

and υd can be determined from VP and VS and the set cement density () using the following equations:

υd=(V P

2 −2V S2 )

2 (V P2 −V S

2 )



Ed=2 ρV s2 (1+υd )

Which can be written as

Ed=2ρV s2 (3V P

2 −4V S2 )

(V P2 −V S

2 )

For porous media these values are generally higher than measurements made under static conditions (Plona). It

should be noted that no universal correlation exists, all sonic measurements should be correlated to static

measurements.



9. Reporting

It is suggested that the following information be recorded and presented with mechanical testing results.

- Rheology after mixing

- Sedimentation test or density measurements of the slices for Splitting tests using Archimedes principle

- UCA chart

- Curing chart (Temp & pressure vs. time)

- Molds type

- Molds-release agent used

- Load frame reference, loading control system, loading rate

- Type of measurement devices (gauges, MTS chain, LVDT…)

- Sonic measurements (if available)

- Specimen dimensional measurements

- Specimen pictures (before & after crushing)

- Stress-Strain data for unconfined tests

- Calculated values: Poisson’s ratio, Young’s Modulus and unconfined compressive strength.

- Maximum force and calculated Tensile Strength for splitting tests

- Stress –strain data for triaxial tests

- Failure mode



References

ASTM Standard C307, 2003, “Standard Test Method for Tensile Strength of Chemical-Resistant Mortar, Grouts,

and Monolithic Surfacings,” ASTM International, West Conshohocken, PA, 2003.

ASTM Standard C39/C39M, 2001, “Standard Test Method for Compressive Strength of Cylindrical Concrete

Specimens,” ASTM International, West Conshohocken, PA, 2001.

ASTM Standard C469/C469M, 2010, “Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio

of Concrete in Compression,” ASTM International, West Conshohocken, PA, 2010.

ASTM Standard C470/C470M, 2009, “Standard Specification for Molds for Forming Concrete Test Cylinders

Vertically,” ASTM International, West Conshohocken, PA, 2009.

ASTM Standard C496/C496M, 2004, “Standard Specification for Splitting Tensile Strength of Cylindrical Concrete

Specimens,” ASTM International, West Conshohocken, PA, 2004.

ASTM Standard D3967, 2008, “Splitting Tensile Strength of Intact Rock Core Specimens,” ASTM International, West Conshohocken, PA, 2008.

ISRM Commission on Standardization of Laboratory and Field Tests, “Suggested Methods for Determining Tensile

Strength of Rock,” Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., (1978) 15, 99.

T.J. Plona and J.M. Cook, “Effect of Stress Cycles on Static and Dynamic Young’s Moduli in Castlegate

Sandstone,” in Rock Mechanics, ed. Daemen and Schultz, 1995, Balkema, Rotterdam.

Others for consideration

ASTM C684 Test Method for Making, Accelarted Curing, and Testing Concrete Compression Test Speciments.

ASTM C918/C918M Test Method for Measuing Early-Age Compressive Strength and Projecting Later-Age

Strength.

ASTM E178 Standard Practice for Dealing with Outlying Observations.

Timoshenko, S. and Goodier, J. N., Theory of elasticity, McGraw-Hill, 2nd Ed., New York, 1951, pp. 107.



10. Appendix 1 – Cooperative Testing Results

In order to check the variability of the mechanical property test results in the laboratory, a cooperative testing

program is conducted with a total of seven participating labs. To ensure the uniformity of the material, the dry blend

(cement and additive) is shipped from a single source. The composition of this slurry is shown in Table 2. All labs

are required to cure the specimen at a simulated downhole condition (140 ˚F and 3000 psi) for a period of 7 days.

The specific testing parameters, such as the mixing procedure, molds, and testing equipment, vary widely from one

lab to another. In this appendix, test results from different labs are summarized and compared. The participating labs

are designated as Lab 1 through Lab 7. Two separate batches are made in Lab 1 and Lab 4 and are designated as I

and II, respectively. Large scale blenders were used in Labs 1, 2, and 7 such that all samples were produced from the

same batch. Slurries were mixed in 2 or 3 regular small blenders in Labs 3, 4, and 5 and homogenized either by a

spatula or by a low-shear mixer.

Table 2: Slurry Composition (in percent by weight of cement)

Material Class H cement (Larfarge) Water Suspending aid additive

Amount 100 69.38 0.1

10.1Slurry stability

Sedimentation tests are typically performed to check the stability of the slurry and make sure that the produced

specimens have uniform density. The sedimentation test results from four different labs are listed in Table 3. As

seen in the table, test data from all labs suggest that the density variations along the longitudinal direction of the

cylindrical specimens are very small, with coefficients of variation less than 0.01. The maximum density variation

observed is less than 2%. The obtained average densities in different labs are also very consistent except for Lab 7.

It is not clear why this sample used for sedimentation test has a lower density. But the other samples produced in

Lab 7 have an average density of 14.32 lb/gal, which is more consistent with other labs.

Table 3: Variation of specimen density along the axial direction (units in lb/gal)

Test No. Lab 1-I Lab 1-II Lab 4-I Lab 4-II Lab 3 Lab 7

Mold Size 2’’ by 5’’ 2’’ by 5’’ 3” by 4”* 3” by 4”* 1.625’’ by 10’’ 1.4’’ by 2.8’’

Top 14.27 14.27 14.33 14.66 14.27 14.05

Middle14.29 14.28 14.41 14.41

14.28 14.0214.34 14.33 14.33 14.58

Bottom 14.53 14.45 14.41 14.41 14.30 13.99

Average 14.36 14.33 14.37 14.52 14.28 14.02

COV 0.008 0.006 0.003 0.009 0.001 0.002



*: Molds are 3’’ diameter and 4’’ high with samples cored and cut to required size.

10.2 Uniaxial monotonic compression tests

Uniaxial monotonic compression tests were performed in six different labs (Lab 1 through Lab 6). Test results from

Lab 5 is not presented as there seemed to be instrumentation problems regarding specimen deformation

measurments. Radial deformations were only measured in Labs 1, 2 and 6. Test results of different labs are shown

in Fig. 10 through Fig. 14. The most accurate method of measuring specimen deformation (strain) is by using

extensometers directly attached to the specimens. Such method is adopted in Labs 1, 2, and 6. As shown in Figs. 10

and 11, stress-strain curves obtained in these labs exhibit very good reproducibility. However, there appear to be

some outliers in Fig. 11, which may be due to specimen defect and/or mounting issues with the extensormeters. In

Lab 3 and Lab 4, specimen (axial) deformation is obtained from the piston/cross-head displacement during tests to

failure. Stress-strain curves obtained in these labs are given in Fig. 12 through Fig. 14.

Fig. 15 and Fig. 16 compare the specimen axial strain measured by directly attached extensometers and by piston

displacement in Lab 1 and Lab 2, respectively. Probably due to the fact that both the test frame and the piston

deforms during the test, it is apparent that piston displacement measurement significantly overestimate the axial

strain of the specimen (maybe machine stiffness should be reported). The difference between the two measurements

also seem to depend on the test system as the difference appears to be much larger in Lab 2 compared with that in

Lab 1. The effects of loading rate on test results were studied in Lab 3 and Lab 4. However, a conclusion cannot be

reached due to the small number of samples tested and the poor reproducibility of test results. The effects of control

mode on test results were investigated in Lab 1. As shown in Fig. 17, for the rates studied here, control mode has

virtually no effect on the stress-strain curve (and the calculated elastic constants) of the specimen in the linear-elastic

range. However, the average compressive strength obtained from displacement control is found to be about 6%

lower than that obtained from load control. This is primary because the effective loading rate varies during

displacement control and becomes much lower than that used with load control (10 psi/sec in this case) during the

later stage of the test (Fig. 18).



-0.2% -0.1% 0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7%0

200

400

600

800

1000

1200

1400

1600

1800

Radial Strain Axial Strain

Stre

ss (p

si)

Fig. 11: stress-strain curves of three different samples

(Lab 1-I, 0.0001 in./sec displacement rate, 2’’ by 4’’ sample size)

-0.2% -0.1% 0.0% 0.1% 0.2% 0.3% 0.4% 0.5%0

200

400

600

800

1000

1200

1400


Axia

l Str

ess (

psi)

Fig. 12: stress-strain curves of five different samples

(Lab 2, 0.0001 in./sec displacement rate, 2’’ by 4’’ sample size)



0 0.2 0.4 0.6 0.8 1 1.20

200

400

600

800

1000

1200

1400

1600

1800Loading rate 35 psi/sec Loading rate 85 psi/sec

Strain, %

Axia

l str

ess (

psi)

Fig. 13: stress-strain curves of four different samples (Lab 4-I, 1’’ by 2’’ sample size)

0 0.2 0.4 0.6 0.8 1 1.20

200

400

600

800

1000

1200

1400

1600

1800

2000Loading rate 35 psi/sec

Strain, %

Axia

l str

ess (

psi)

Fig. 14: stress-strain curves of four different samples (Lab 4-II, 1’’ by 2’’ sample size)



0.0% 0.2% 0.4% 0.6% 0.8% 1.0% 1.2%0

200

400

600

800

1000

1200

1400

1600

Displacement rate 0.000033 in./secDisplacement rate 0.00016 in./sec

Axial Strain

Axia

l Str

ess (

psi)

Fig. 15: stress-strain curves of two different samples (Lab 3, 1.6’’ by 3.2’’ sample size)

0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7% 0.8%0

200

400

600

800

1000

1200

1400

1600

1800

Axial Strain

Stre

ss (p

si)

Measured by Extensometers

Measured by piston displacement

Fig. 16: Comparison of specimen axial strain measured by extensometers and by piston displacement



0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7% 0.8% 0.9%0

200

400

600

800

1000

1200

1400

Axial Strain

Stre

ss (p

si)

Measured by Extensometers

Measured by pis-ton displacement

Fig. 17: Comparison of specimen axial strain measured by extensometers and by piston displacement

-0.03% 0.00% 0.03% 0.06% 0.09% 0.12%0

100

200

300

400

500

600

700

800

900

Load control, 10 psi/secDisplacement control, 0.0001 in./min


Axia

l Str

ess (

psi)

Fig. 18: Comparison of stress-strain curves obtained with different control mode



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

Normalized time to failure

Effec

tive

load

ing

rate

(psi

/sec

)

Fig. 19: Effective loading rate of a typical test performed with displacement control

(Lab1-I: 0.0001 in./sec displacement control, 2’’ by 4’’ samples)

10.3 Uniaxial cyclic compression tests

Cyclic uniaxial compression tests were conducted in three different labs (Labs 1, 4, and 7). Lab 1 uses

extensometers directly attached to the specimens to measure both axial and radial deformations (with the later

measured using a circumferential chain). Lab 4 uses LVDTs to measure axial deformations (platen-to-platen) and

cantilever with strain gauges to measure radial deformations. Lab 7 uses LVDT’s to measure both axial and radial

deformations. Multiple-cycle loading were performed on each sample in Lab 4 and a representative plot is presented

in Fig. 19. Test results show that the slopes of the stress-strain curves, which are directly related to measured elastic

constants, do not change significantly after the first half-cycle (i.e. the first ramp-up section). In the other two labs,

only one complete cycle was performed before the sample was tested to failure. Figs. 20, 21 and 22 show stress-

strain plots of the first cycle obtained in different labs.

Table 4 and Table 5 list variations of elastic contants of different samples calculated from different segments of the

loading process (namely the load, unload, and reload segments). These calculations were done for two different

stress ranges, namely 10% to 50%, and 15% to 40%, of unconfined compressive strength. It should be noted that it

is impossible to accurately estimate the ultimate strength of a sample before the test. Therefore, the maximum stress

level used during the cyclic loading process can be much lower than 50% in some cases. As shown in Table 4,

Young’s moduli calculated from the unload segments tend to be higher than those calculated form the reload

segments while those calculated from the initial load segments tend to be lower. On the other hand, Table 5 shows

that variation of Poisson’s ratio calculated from different segments appears to be more random. In Lab 1, where

strain measurements were taken by specimen mounted extensometers, Young’s moduli calculated from the different

segments varies no more than ±1.6% if the stress range used for calculation is 15% to 40% of UCS. Test results in



Lab 1 also suggest that Poisson’s ratios calculated from the first two segments are typically slightly higher (no more

than 6%) than that calculated from the third segment. Fig. 23 further indicates the excellent reproducibility of the

stress-strain curves in Lab 1. In Lab 7, where three LVDT’s were used (compared with two normally used) for axial

deformation measurement, Young’s moduli calculated from the unload segments are reasonably close to those

calculated from the reload segments, while those calculated from the initial load segments are significantly lower.

This is probably due to compressions of the irregularities at the sample-platen interface during the first loading

cycle. In Lab 4, variations of calculated Young’s moduli from different segements appear to be much larger than

those in other labs. Variations of Poisson’s ratio obtained from different segements are alsomuch higher in Lab 4

and Lab 7, compared with Lab 1. Some of the observed differences is mostly due to measurement of the axial

strain. Lab 4 measures the entire sample and this seems to give larger deformation for the same load (end effects).

The measured Young’s modulus is lower but also the Poisson’s ratio is proportionately lower.

-0.03% 0.00% 0.03% 0.06% 0.09% 0.12% 0.15%0

100

200

300

400

500

600

700


Axia

l str

ess (

psi)

Fig. 20: Representative stress-strain curve of the first three cycles

(Lab 4-I, 0.05 mm/min displacement rate, 1’’ by 2’’ samples)



-0.03% 0.00% 0.03% 0.06% 0.09% 0.12% 0.15%0

100

200

300

400

500

600

700

800

900


Axia

l Str

ess (

psi)

Fig. 21: Stress-strain curves of three different specimens during the first cycle

(Lab 1-II, 10 psi/sec load rate, 2’’ by 4’’ samples)

-0.05% 0.00% 0.05% 0.10% 0.15% 0.20% 0.25% 0.30%0

100

200

300

400

500

600

700

800


Axia

l Str

ess (

psi)


(Lab 4-II, 0.05 mm/min displacement rate, 1’’ by 2’’ samples)



-0.03% 0.00% 0.03% 0.06% 0.09% 0.12% 0.15%0

100

200

300

400

500

600


Axia

l Str

ess (

psi)


(Lab 7, 0.01 mm/min displacement rate, 1.4’’ by 2.8’’ samples)

Table 4: Calculated Young’s Modulus (YM) and percent changes compared to reference values calculated from

reload segment (i.e. second ramp-up section)

Lab

No.

Stress range for calculation 10%-50% 15%-40%

Segment of loading

Load

(% chg)

Unload

(% chg)

Reload

(YM, ksi)

Load

(% chg)

Unload

(% chg)

Reload

(YM, ksi)

Lab 1-II

Specimen 1 -0.8% 2.3% 709 1.0% 0.0% 716

Specimen 2 -2.5% 1.8% 681 -0.9% -0.6% 683

Specimen 3 -2.9% 1.6% 685 -1.6% -0.9% 689

Lab 7

Specimen 1 -19.9% 2.2% 557 -17.5% 5.9% 577

Specimen 2 -16.7% 1.5% 671 -16.9% 1.9% 674

Specimen 3 -14.3% 4.4% 643 -14.2% 6.0% 646

Lab 4-II*Specimen 1 -18.0% 11.6% 517 -18.6% 15.1% 531

Specimen 2 -26.9% 13.1% 527 -25.7% 16.3% 540

*: Only the first one and a half cycle (i.e. the first three load segments) were considered to be consistent with the

other two labs



Table 5: Calculated Poisson’s Ratio (PR) and percent changes compared to reference values calculated from reload

segment (i.e. second ramp-up section)

Lab

No.

Stress range for calculation 10%-50% 15%-40%

Segment of loadingLoad

(% chg)

Unload

(% chg)

Reload

(PR)

Load

(% chg)

Unload

(% chg)

Reload

(PR)

Lab 1-II

Specimen 1 -0.6% 2.8% 0.179 0.0% 4.5% 0.179

Specimen 2 2.3% 5.1% 0.176 2.3% 4.0% 0.176

Specimen 3 3.3% 5.6% 0.180 2.2% 3.9% 0.181

Lab 7

Specimen 1 3.9% 20.4% 0.103 4.4% 13.2% 0.114

Specimen 2 17.4% -14.9% 0.161 18.9% -12.6% 0.159

Specimen 3 10.6% -18.6% 0.161 8.0% -17.8% 0.163

Lab 4-II*Specimen 1 -23.7% 17.3% 0.139 -23.1% 18.4% 0.147

Specimen 2 -22.2% 6.7% 0.135 -14.3% 15.0% 0.133

*: Only the first one and a half cycle (i.e. the first three load segments) were considered to be consistent with the

other two labs

-0.2% 0.0% 0.2% 0.4% 0.6% 0.8%0

200

400

600

800

1000

1200

1400

1600


Axia

l Str

ess (

psi)

Fig. 24: Stress-strain curves of three different specimens during the second half-cycle (reload)

(Lab 1, 10 psi/sec load rate, 2’’ by 4’’ samples)



10.4 Mechanical property test results

Table 6 and Table 7 show the mechanical properties of the cement reported by different labs based on uniaxial

monotonic compression tests and uniaxial cyclic compression tests, respectively. The detailed test conditions

adopted in different labs are also listed in these tables. For the tests where specimen deformation was measured by

cross-head movement, Young’s moduli were not calculated due to the known inaccuracies of the strain

measurement. Standard deviations of the test results were calculated when 3 or more samples were tested under the

same condition. For all the properties studied, test data obtained by Lab 1 had the smallest coefficients of variation.

The compressive strength obtained in different labs ranges from 1201 psi to 1856 psi. The relatively large variations

are expected considering all the different test parameters used in different labs. More consistent test results should

be obtained if a standardized test procedure was followed.

Table 6: Reported average mechanical properties from uniaxial monotonic compression test

LabSample size(Diameter and Width)

Strain Measurement Loading rate No. of

samplesStrength(std), psi

Young’s modulus(std), ksi

Poisson’s ratio(std)

Lab 1-I 2’’ by 4’’ Extensometers 0.0001 in./sec 3 1687 (25) 728 (22) 0.208 (0.009)

Lab 2 2’’ by 4’’ Extensometers 0.0001 in./sec 5 1275 (207) 643 (51) 0.172 (0.030)

Lab 3 1.6’’ by 3.2’’ Cross-head0.05 mm/min 1 1365 - -

0.25 mm/min 1 1400 - -

Lab 4-I 1’’ by 2’’ Cross-head35 psi/min 2 1798 - -85 psi/min 2 1624 - -

Lab 4-II 1’’ by 2’’ Cross-head35 psi/min 2 1856 - -85 psi/min 2 1806 - -

Lab 5 1.5’’ by 3’’ LVDT ? 3 1246 (31) - -Lab 6 1.5’’ by 3’’ Extensometer ? 3 1652 (70) 490 (17) 0.183 (0.025)

Table 7: Reported average mechanical properties from uniaxial cyclic compression test

LabSample size(Diameter and Width)

Strain Measurement Loading rate No. of

samplesStrength(std), psi

Young’s modulus(std), ksi

Poisson’s ratio(std)

Lab 1-II 2’’ by 4’’ Extensometers 10 psi/sec 3 1548 (3) 694 (19) 0.182 (0.004)

Lab 4-I 1’’ by 2’’ LVDT 0.05 mm/min 1 1588* 582 0.14Lab 4-II 1’’ by 2’’ LVDT 0.05 mm/min 2 1813 514 0.13Lab 7 1.4’’ by 2.8’’ LVDT 0.01 mm/min 3 1201 (26) 605 (58) 0.155 (0.012)

*: Average of two specimens



Splitting tensile tests were conducted in all labs while direct tension tests with Briquette samples were only

performed in Lab 1 and Lab 6. Test results and specific test parameters of the splitting tension tests are listed in

Table 7. The average tensile strength test results obtained in Lab 1 are nearly identical for the two different test

methods. Due to the different sample sizes and loading conditions, the variation of test results between different labs

are fairly large, with the obtained average splitting tensile strength varying from 167 psi to 342 psi. The majority of

the tensile strength test data fall in the range from 205 psi to 310 psi. Therefore, standardized test methods (with L/D

ratio, loading conditions, etc. defined) need to be followed in order to generate more consistent test results among

different labs.

Table 7: Tensile strength test results in different labs

Tests

Splitting tension testDirect tension

(Briquette samples)

Sample size

(Dia and Width)Bearing material* Loading rate

Strength

(psi)

Std.

(psi)

Strength

(psi)

Std.

(psi)

Lab 1-I 2’’ by 1’’ Cardboard 100 psi/min 247 8 244 5

Lab 1-II 2’’ by 1’’ Cardboard 100 psi/min 228 22 221 37

Lab 2 2’’ by 1’’ Steel 0.006 in./min 302 19

Lab 3

1.6’’ by 3.2’’ Wood 0.05 mm/min 309 38

1.6’’ by 1.6’’ Wood 0.25 mm/min 308 17

1.6’’ by 0.8’’ Wood 0.25 mm/min 342 14

Lab 4-I 2’’ by 1’’ Curved Steel 100 psi/min 305 18

Lab 4-II 2’’ by 1’’ Curved Steel 200 psi/min 305 10

Lab 5 1.5’’ by 0.75’’ Steel ? 206 29

Lab 6 1.5’’ by 0.75’’ ? ? 265 5 218 50

Lab 71.4’’ by 0.7’’ ? 0.1 mm/min 215 21

2’’ by 2’’ ? 0.1 mm/min 167 42*: Width of the bearing material is irrelevant here, as it is far larger than the contact area for all the tests conducted

here.



11. Appendix 2 - TASK GROUP PARTICIPANTS

Table 1 - Participants.

Name Company Email

Robert Darbe Halliburton [email protected]

Deryck Williams Chevron [email protected]

Simon James Schlumberger [email protected]

Bernard Fraboulet Total Technology Specialists [email protected]

Jim Davidson Ametek Chandler Eng. [email protected]

Fred Sabins CSI Technologies [email protected]

John St. Clergy Consultant

Camille Lerouge Trican [email protected]

Tim Johnson Messina Chemicals [email protected]

Dan Mueller Conoco Phillips [email protected]

Ramy Eid Repsol [email protected]

Vicente Ciccola PDVSA [email protected]

Clara Mata 3M [email protected]

Axel-Pierre Bois Curis Lab [email protected]

Andre Garnier Total [email protected]

Rick Lukay Ofite [email protected]

Robert Martin Baker Hughes [email protected]

Jeff Moon Ametek Chandler Eng. [email protected]


mailto:[email protected]











5.5 Quality Control Check for Sample Integrity

Even if the cement sample preparation procedure would reduce internal defaults of cement sample subject to

mechanical testing a quality control procedure on the sample itself should allow to select samples to be subject to

testing and mechanical parameter determination. These internal defaults affects sample bulk homogeneity. They

are mainly air bubbles and microfissures, they reduce the values of mechanical parameters and it results in a

potential large measurement variance. A non-destructive procedure which can evaluate the possible presence of

these defaults allows to select and to reduce the number of sample to be crushed.

The ultimate non destructive procedure is a tomography image but a scanner is not common laboratory equipment.

A scanner image of a cement sample with air bubbles and microcracks is shown figure hereafter .

Figure X : Tomography image of a cement sample with internal defaults

5.5.1 Sonic sample integrity control

A quality control procedure based on measurement of sonic velocities through the cement sample is providing good

information related to sample integrity. The velocity of compressional sonic P-waves travelling through a sample is

reduced if the material is not homogeneous and waves intercept very low impedance material such as air.

Using a sonic bench, axial and radial sonic P-wave velocities across the cement sample (cylinder) subject to quality

control are measured and compared. Multiple measurements are done. Through a homogeneous and isotropic

sample the sonic velocity measurements are identical whatever the measurements points. At the opposite, if a non-

homogeneous specimen, when heterogeneities (air bubbles, microcracks) are intercepted by the sonic wave, its

velocity is reduced.

An acceptance criteria based on the difference between axial and radial P-wave velocities is set . It is considered that

with a difference lower than 5% the cement sample is qualified for mechanical parameter determination. If a

difference higher than 5 % is observed the cement specimen is classified as suspect and should not be used to

perform mechanical tests.

Apparatus and procedure for sample integrity control is given in annex XX


Entraped air bubbles microcraks


Remark : Using the proposed apparatus, compressional P-waves are used for quality control. In addition shear S-

wave velocity measurements should be done allowing to determine dynamic Young’s modulus as dynamic

Poisson’s ratio parameters of the cement sample (see clause 10)

Annex xx

Sonic Sample Integrity control

1. Principe

The velocity of compressional sonic P-waves travelling through a sample is reduced if the material is not

homogeneous and waves intercept very low impedance material such as air.

Axial and radial sonic P-wave velocities across the cement sample (cylinder) are measured and compared. Multiple

measurements linked to specimen size are done. Through a homogeneous and isotropic sample the sonic velocity

measurements are identical whatever the measurements points. At the opposite, if a non homogeneous specimen,

when heterogeneities (air bubbles, microcracks) are intercepted by the sonic wave, its velocity is reduced.

The cement specimen is placed between axial sonic transducers and radial ones. Compressional sonic P wave travel

times (axial and radial) are measured, velocities are calculated and compared. If a difference higher than 5 % is

observed the cement specimen is classified as suspect and should not be used to perform mechanical tests.

Compressional P waves are used for quality control. In addition shear S6wave velocity measurements should be

done allowing to determine dynamic Young’s modulus as dynamic Poisson’s ratio parameters of the cement sample

(see clause 10).

2. Apparatus2.1 Sonic Bench

Bench with sonic transducers for axial and radial measurements, it allows to support the test sample and to establish

the contacts between the transducers and the surface of the sample and to displace the contact points. Displacement

and the contact pressure of transducer faces to the sample can be using a mechanical device or through an air jack.



Figure : Typical sonic bench

2.2 Axial Ultrasonic transducers, 2: 1 Mhz dual transducers ( P and S waves) ( minimum P wave) minimum diameter 25 mm

2.3 Radial ultrasonic transducers , 2: 1 MHz P wave with cylindrical face as per sample diameter

Figure : Typical P ultrasonic transducer for radial measurements (cylindrical

face as par sample diameter )

2.4 Ultrasonic pulser-receiver, high energy2.5 Ultrasonic switch P/S waves 2.6 Oscilloscope 2 bands2.7 Coupling agent, water soluble

Used to improve the transit of ultrasonic wave between the transducer and the sample

2.8 Caliper with an accuracy of 0.01 mm

3. Procedure

3.1 Determine for axial transducers t0,a, P P wave zero transit time (without sample) and optionally t0,S S wave zero transit time. t0 is the time required to detect the P ( or S) wave by the receiving transducer.

3.2 Determine for radial transducers t0,r, P P wave zero transit time (without sample).This 0 time is determined using a cylinder of ultrasonic P wave velocity known value . Cylinder diameter should be equal to the diameter of cement sample to test.

3.3 Prepare the sonic bench to received the samples to be tested (length and diameter):


Fixe dual P-S transducer

Radial P transducers P

Mechanical displacement

+ air jack

Mobile Dual P –S transducer

Air jack


3.4 Measure length and diameter of the sample using caliper 3.5 Lightly coated the sample contact surfaces with coupling agent 3.6 Place the sample against the fixe axial transducer and establish contact with the mobile one using air jack

or mechanical device. The sample is hold in place; enough pressure is applied by the transducers to allow good ultrasonic wave transmission.

3.7 Activate the P wave pulse through axial transducers From oscilloscope, determine and report the P wave first arrival pick and then axial P wave travel timeδ t P,a

in microseconds. Within the cement sample, P wave travel time∆ tP ,ais calculated as it needs to correct the

measurement by subtraction of axial P zero transit time.

∆ tP ,a=δ tP , a−t 0 , P

With ∆ tP ,a δ tP, a ¿t 0 , P in microseconds

Record P wave axial transit time.

Figure : Typical P-wave reception

Note: With large diameter plugs (3 to 6 in), axial P wave travel time should be determined on reported on

the axis but also on at least 3 off center directions at 120 °

Calculate and record the minimum and the maximum travel time ∆tP,a, min and ∆tP,a , max

3.8 Optional : Axial S wave transit time measurement used for dynamic modulus and Poisson’s ratio determination

Activate S wave pulse through axial transducers. From oscilloscope, determine the S wave first arrival pick.

However the pulser is also emitting a compressionnal parasite pulse, then it is necessary not to consider the

P wave and select the shear wave first pick to determine axial S wave transit timeδ t S ,a in microseconds.

Note that in some cases it is not easy to dissociate on arrival of the S wave from the P wave.

Within the cement sample, S wave travel time∆ t S ,ais calculated as it needs to correct the measurement by

subtraction of axial S zero transit time.

∆ t S ,a=δ t S ,a−t 0 ,S


Initial Pulse

First arrival P wave

Measured

travel time


With ∆ t S ,a δ t S , a¿ t 0 , S in microseconds

Report S wave axial transit time.

Figure : Typical S-wave reception

3.9 Put in position the 2 radial transducers and establish contact on cement sample using air jack or mechanical device

Activate the P wave pulse through radial transducers. From oscilloscope, determine and report the P wave

first arrival pick and then radial P wave travel timeδ t P,r1 in microseconds.

In order to increase the potential interception of microcracks, radial P wave travel time should be determined

for at least 2 diameters at 90° (δ t P ,r 1 , δ tP , r 2¿and up to 4 diameters (δ t P,r 1 , δ tP , r 2 , δ t P ,r 3¿δ t P ,r 4)for

large diameter cylinders. According the length of the plug radial wave travel times should be determined and

reported for 1, 2 , 3 or 4 sections.

For quality control purpose from the series of measurement of radial S travel time δ t P,r , i , the lowest and

the highest radial P wave travel time will be recorded δ tP,r, min and δtP,r , max

These values are used to calculate within the cement sample, minimum and maximum P wave radial travel

time (∆t ¿¿ P , r ,min ∆ t P ,r , max )¿ as it needs to correct the measurement by subtraction of radial P zero

transit time.

∆ tP ,r , min=δ tP , r , min−t 0 , r , P ,

∆ tP ,r , max=δ tP , r ,max−t 0 ,r , P ,

With ∆ tP ,r , min ∆ tP, r , max δ tP , r ,min δ tP , r ,max∧t 0 ,r ,P in microseconds

3.10 Remove cement cylinder from the sonic bench


Initial Pulse

First arrival S wave

parasite P wave

S wave


3.11 Remove coupling agent by washing with water3.12 Place and keep the cement sample in water (preferably calcium saturated water) till the time to test it and

to determine mechanical parameters.

4. Interpretation : Sample quality control

4.1 P-wave velocity

From recorded P wave transit times and sizes of the cylinder P wave velocities are calculated. If more than one

measurements is done (axial or radial) minimum and maximum P wave velocities are calculated.

V P ,a=1,000 L∆ tP ,a

and V P ,r=1000 D∆t P,r

WithV P,a axial P wave velocity and V P ,r radial P wave velocity in m/s

L cylinder length and D cylinder diameter in mm

∆ tP ,a axial P wave transit time and ∆ tP ,r radial P wave transit time in µs

4.2 Quality control criteria:

If for a given cement sample, the quality criteria is not within the limits as stated hereafter, the cement sample

should not be used to perform mechanical tests and discarded.

4.2.1 Multiple axial or radial measurements

When more than two measurements is done in a direction (axial, or radial with more than one section), the minimum

and the maximum values of P wave velocities (radial and or axial) are compared together. The ratio maximum P-

wave velocity to minimum P-wave velocity should be lower than 1,05.

V P , a ,max

V P, a ,min<1,05 and

V P , r , max

V P, r ,min<1,05

With

V P,a , max and V P,a , min respectively maximum and minimum axial P-wave velocity through the cement

cylinder sample , expressed in m/s

V P ,r , max and V P,r , min respectively maximum and minimum radial P-wave velocity through several

cross sections of the cement cylinder sample , expressed in m/s

4.2.2 General acceptance criteria

As a general rule, the ratio of the axial P-wave velocities to the radial P-wave velocity measurement through

diameter 1 or through diameter 2 at 90° from diameter 1 should be higher than 0,95 and lower than 1,05



0,95<V P , a

V P ,r 1<1,05 and 0,95<

V P , a

V P ,r 2<1,05

With

V P ,a axial P-wave velocity through the cement cylinder sample , expressed in m/s

V P,r 1 and V P,r 2 radial P-wave velocities across one section respectively through a diameter 1 and

through a diameter 2 at 90° of the diameter 1, expressed in m/s

When more than one axial P-wave measurements is done and more than 2 radial P-wave measurements are done on

more than 1 cross section, the quality control criteria is written as

0,95<V P ,a , max

V P,r ,min<1,05 and 0,95<

V P, a ,min

V P ,r , max<1,05

With

V P,a , max and V P ,a , min respectively maximum and minimum axial P-wave velocity through the cement

cylinder sample , expressed in m/s

V P ,r , max and V P,r , min respectively maximum and minimum radial P-wave velocity through several

cross sections of the cement cylinder sample , expressed in m/s

Remark: With specialized cement system where large particles can be mixed, by nature the set cement matrix is not

homogeneous on a macroscopic point of view. Even it was not yet observed, cement system with fibers could be the

case. It can result measurement resulting in a ratio criteria lower than 0,95 or higher than 1,05. In such cases and

only the recommended preparation procedure is followed and only when the set cement can be considered as a non

homogeneous matrix, cement sample selection will be based on the comparison of the calculated criteria ratios.

Cement samples with a similar ratio value would be selected for mechanical test. Cement sample exhibiting a

different ratio should be discarded.


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