Strength Characterization of Open-Graded Aggregates for Structural Backfills

CHAPTER 2. BACKGROUND

2.1 USE OF OGAs

Manufactured OGAs are used in a variety of transportation applications, including retaining wall backfill, concrete, asphalt, pavement structures, and foundation support. These materials are selected primarily because of their strength, excellent drainage properties, and speed of placement in the field. The first known attempt by AASHTO to standardize gradations for processed aggregates was in 1988, which followed ASTM standard D448 (published in 1986). The standard included 19 gradations, ranging from 4 inches minus material to 0.375 inch minus material. While six additional versions have since come out, the same gradations and nomenclature is used; the biggest difference is the elimination of metric units.

For some projects, contractors and designers have the flexibility to select backfills that meet certain requirements; in other projects, the backfill type is specified by the owner. Many State transportation departments and other transportation agencies have specifications related to the use of AASHTO M 43, but these guidelines are primarily focused on concrete and pavement design requirements.(See references 4 through 7.) For structural backfills, the specifications are typically more open where OG or well-graded aggregates meeting the broad gradation and durability requirements can be used.

2.2 STRENGTH PROPERTIES OF GRANULAR MATERIALS

The shear strength (𝜏) of granular materials is the measure of their resistance to mass deformation developed from a combination of particle rolling, sliding, and crushing.⁽⁸⁾ The interparticle attraction or cohesion (c) and the angle of internal friction (ϕ) are the two commonly used parameters employed to quantify the shear strength. The values of these strength parameters are not constant, varying as a function of the loading condition, stress history, compaction, relative density, confining pressure, grain shape, hardness, and mineralogy, among other factors.

The peak friction angle at a given applied confinement is one of the measured parameters during shear testing that is widely adopted to characterize the shear strength of granular materials. Rowe (1962) proposed that the mobilized peak friction angle can be represented as the sum of the resistance to the interparticle sliding, or true friction angle (ϕ '_u), the resistance to crushing and rearrangement, and resistance due to dilation of the material (figure 1).⁽⁹⁾ It should be noted that figure 1 displays a general trend, and the magnitude and exact shape of the components within the sketch could change slightly at extreme levels of confining stress or for samples with heterogeneous mineral composition and shape.

Figure 1. Chart. Effect of porosity and compaction on the shear strength of granular materials (modified from Rowe, 1962).⁽⁹⁾

As shown in figure 1, the rate of dilation is higher under denser states. The reason is that in a dense medium, rearrangement is limited, forcing particles to climb over each other during shearing and resulting in volume expansion and higher measured friction angles. With the increase in void ratio, the contribution from the dilation component diminishes gradually, and the particles shear primarily by rearrangement of adjacent particles, which results in more contraction and less dilation of the granular material during shear.⁽¹⁰⁾ The general observation is that there is a net increase of the mobilized friction angle with the decrease in initial porosity because the rate of increase of the dilatancy component is higher than the rate of decrease of the rearrangement. The critical state is defined at the density state where the granular materials shear at a constant volume and stress state. At this state, the dilatancy rate diminishes and approaches zero; hence, the friction angle at this critical state is termed the constant volume (CV) friction angle (ϕ'_cv).

Visualizing the shear strength as a function of varying confining stress for a given density state, similar components comprise the mobilized peak friction angle (figure 2). At high effective confining stresses, the relative movement of the particles via dilation will reduce significantly. In addition, a high breakage rate through crushing will result in contraction, shifting the phase from the initially achieved true friction angle to a new phase of non-constant volume.⁽¹¹⁾

Figure 2. Chart. The theoretical determination of the drained shear strength for sands based on the three components that comprise the mobilized friction angle (after Lee and Seed, 1967).⁽¹¹⁾

Knowledge about the contributing factors and the various laboratory shear strength tests, data interpretation, and the application of the strength parameters for designing geotechnical applications with OGAs is therefore important. In-situ tests are available to quantify or correlate with in-place shear strength; however, this study focuses on the laboratory analysis.

Laboratory Testing

The state of in-situ shearing deformations-which can eventually lead to failure-is oftentimes best approximated as a PS problem. For instance, the failures in several geotechnical applications such as landslide problems, retaining walls, earth dams, long foundations, culverts, pipe lines, tunnels, and beam foundations, for the most part, are all cases of PS; however, there is considerable difficulty in designing and conducting PS shear tests. Such tests require the fabrication of a special fixture, membrane, accessories, and preparation of a prismatic soil specimen.⁽¹²⁾ The complexity of the PS shear test leads geotechnical engineering researchers and practitioners to the simpler DS or TX tests to characterize the shear strength of geomaterials.

Both DS and TX methods have been widely accepted for design and research to determine shear strength. The wide popularity of TX compression tests is partially because of the numerous structures designed and constructed based on the strength data from TX that perform well after many years, the ability of TX tests to combine simplicity with versatility, the ability to allow drainage control, the reproduction of the effects of most common field loading conditions, and the application of the desired major and minor principal stresses.⁽¹³⁾ The wide application of DS tests in characterizing the strength parameters of granular materials is attributed to their simplicity, requirement of shorter experimental run times, and ability to predetermine the orientation of the failure surface as desired and allow determination of the residual strength.⁽¹⁴⁾ However, the inability to control the drainage and the non-uniformity of stress and strain in DS tests relative to PS and TX tests inhibits the suitability of DS apparatuses in studies that involve the stress-strain behavior of granular materials.

Note that there are several drawbacks associated with TX and DS tests relative to tests using a PS apparatus. One of the major differences between TX and PS is that in TX-based tests, the applied stresses are axisymmetric, leading to the absence of intermediate principle stresses. The DS tests are closer to the PS condition, but the geometry and boundary conditions of the DS test predetermine the localized region of high strains through which failure is forced to happen; failure is not allowed to occur along its natural plane.⁽¹⁵⁾ The PS tests are better suited to help us understand the in-situ strain localization problems and shear band formations.⁽¹⁶⁾ Several studies have reported the formation of shear bands along a well-defined shear failure plane in PS compression tests, whereas samples sheared in a TX apparatus rarely developed a distinct shear plane.^(17,18,19) Instead, some microscale observations using advanced imaging techniques proved the prevalence of complex fan-shaped patterns in samples subjected to TX-based compression tests.^(20,21)

The other difference among the different laboratory shear tests is the imposed lateral boundary conditions.⁽²²⁾ Both PS and DS tests have a rigid boundary condition that significantly reduces the grain movements during shearing. The flexible membrane boundary in TX tests allows lateral movement of the particles, which inhibits mobilization of the friction angles. The other marked difference of the testing methods is their effect on post peak strain behavior. For sand, Sterpi (2000) indicated that TX-based tests suggest a perfectly plastic behavior, whereas the PS results showed marked strain softening effects, in particular for the denser samples or for high values of confining stress levels.⁽²³⁾ In general, the measured shear strength from PS testing is greater than that measured from DS testing, which is greater than that measured from TX testing.

Regardless of test device, the determination of strength and deformation parameters for granular materials that contain particles of larger sizes such as rockfill materials and OGAs requires equipment of unconventional dimensions.⁽²⁴⁾ To be characterized by the conventional DS and TX apparatuses, which require smaller-sized specimens, the sizes of particles are reduced based on various modeling techniques. As cited by Honkanadavar and Sharma (2013), four modeling techniques are used to reduce the size of the prototype material: the scalping technique, the parallel gradation technique, the generation of a quadratic grain size distribution curve, and the replacement technique. (See references 25 through 29.) Following the findings of Ramamurthy and Gupta, which indicated that the parallel gradation was the best method, several other researchers have conducted shear tests on modeled materials based on the parallel gradation technique. (See references 30, 29, 24, and 31.) The results from these modeled materials could potentially lead to inaccurate deformation behavior and failure modes because of the inevitable size-dependent dilation and different mechanisms of particle crushing.⁽³²⁾ Therefore, the use of large-scale triaxial and direct shear apparatus is imperative for a realistic depiction of the strength and deformation characteristics of aggregates with large-size grains such OGAs.

Data Interpretation

The shear strength of granular materials is usually characterized by the angle of internal friction (ϕ) and cohesion (c). Because of the high drainage rate in OGAs, shear studies for OGAs should be conducted under drained condition, and for this reason, the stresses and strength parameters will be presented in their effective stress forms (e.g.,ϕ', c', σ'₁,σ'₃). There are three concepts of presenting the values of friction angles for any shear test. First, a secant or peak friction angle ( ϕ'_s) can be determined for a given test subjected to a specific effective consolidation stress and assuming a zero c-value due to the absence of cohesion in OGAs (figure 3). Secondly, a combined or tangent friction angle (ϕ '_t) can also computed for the same aggregate type (examined as the best-fit across a series of stress levels) to form the MC failure envelope (figure 3). Lastly, a CV friction angle can be computed as the friction angle in which there is zero dilation, termed the zero dilation angle (ZDA) approach.⁽³⁾

Figure 3. Chart. Secant (ϕ's) and tangent (ϕ't) friction angle illustration for DS testing

The MC failure criterion is the most commonly adopted approach to determine ϕ'_t (equation 1).

            (1)

Where:

𝜏_f = Shear stress at failure.
c' = Effective cohesion.
σ'_n = Effective normal stress.
' = Effective angle of internal friction.

For OGAs that are cohesionless, the cohesive term is zero. This approach assumes that shear failure starts at a point in a mass of soil when, on some surface passing through the point, a critical combination of shearing and normal stresses is reached.⁽¹⁰⁾ The TX and DS equipment are developed to determine and investigate these critical combinations; the results are then used to compute the strength parameters.

In TX compression tests, it is assumed that only principal stresses are applied to the boundaries of the specimen, with the strength parameters extracted from the measured major (σ'₁) and minor (σ'₃) principal stresses at failure. The shear stress path (q) and mean stress path (p') representations are computed for a series of tests according to equation 2 and equation 3, respectively.⁽³³⁾

            (2)

            (3)

When looking at stress paths, a modified failure envelope based on the p and q values was developed, commonly called the K_f line.⁽³⁴⁾ The envelope is defined by equation 4.

            (4)

Where:

α = Angle that the modified (stress-path) failure envelope makes with the horizontal.

The relationship between the tangent effective friction angle (ϕ '_t) and α is shown in equation 5.

            (5)

For TX tests, the value of the secant or peak friction angle (ϕ '_s) for each specific test is computed using equation 6, which is developed from Mohr's circles by applying trigonometric relationships.⁽³⁴⁾

            (6)

Unlike in TX tests, the major and minor principal stresses in DS tests are not measured. Hence, the applied normal stress and measured shear stress at failure are used to compute these strength parameters. Similar to TX test, the individual pairs of 𝜏_f and σ'_n from a series of tests of the same aggregate type as a function of various confining stress are plotted, and the MC linear failure envelope is developed as the best fit line of the peak shear and normal stress values at these different stress points (figure 3). The ϕ'_t is then computed as the arctangent of the slope of the linear fit. The ϕ'_s value for each specific shear test is determined according to equation 7.

            (7)

The linear MC failure criterion is the linear representation of the otherwise nonlinear failure envelope of the strength behavior. Several approaches have been developed to describe this nonlinear increase in peak shear strength of granular materials as a function of the increasing confining stress. The power strength function (equation 8) that was developed by Charles and Watts has been also adopted by other several other researchers with some modifications to the original equation. (See references 35 through 38.)

            (8)

Where:

A and b = nonlinear material constants that are determined by curve fitting of the experimental data. This power curve strength model can be used to interpret data from both TX and DS tests.

Other models, such as the Hoek-Brown model, have been established to characterize strength of rock materials in terms of major and minor principal stresses. Therefore, they are more valid to TX data.^(39,40,41) This model also has material constants that need to be estimated from the geological data and additional tests like uniaxial compressive strength. Nicks and Adams (2013) employed a ZDA that is based on the linear relationship between the friction angles and the dilation angles as a function of varying consolidation stresses for the same aggregate.⁽³⁾ According to Bolton (1986), the y-intercept of the best-fit linear envelope in this approach corresponds to the constant volume or critical state friction angle (ϕ'_cv).⁽⁴²⁾ The advantage of this technique is that the effect of dilation is negated and a conservative shear strength value results without relying on an apparent cohesion value as in the linear MC approach.

This study focuses on the simple approaches that are used to determine common shear strength parameters (e.g. ϕ'_s, ϕ'_t,and ϕ'_cv) applicable for both TX and DS tests to have an unbiased comparison and an approach that does not require any additional strength tests. The MC linear relationship is widely used and accepted because of its reasonable tolerance for the majority of geotechnical applications.⁽³⁶⁾ This approach also does not require any other strength test or geological data and can be used to extract ϕ'_s and ϕ'_t for both TX and DS tests. The ZDA is another simple method to compute ϕ'_cv. Therefore, these two approaches are adopted and compared in this study to characterize the strength parameters of the OGAs based on the TX and DS apparatuses.

Design Practices

The design practices in problems involving the application of stresses to soils may be divided into (a) deformation-controlled design (e.g., settlement), and (b) failure-controlled design (e.g., bearing resistance).⁽⁴³⁾ In other terms, the service and strength limit states must be satisfied in design. For applications involving relatively rigid structures such as bridge foundations and retaining walls, where deformations are expected to be low, the strength limit of the backfill or underlying soil is especially important. The shear strength of the backfill is therefore a key parameter in design.

Failure-controlled design for geotechnical applications involves the determination of the internal angle of friction (ϕ), which is one of the fundamental engineering parameters. The friction angle is critical because it is used to compute lateral pressures and bearing resistance. For transportation applications, the AASHTO Load and Resistance Factor Design Bridge Design and Constructions Specifications are primarily employed.^(44,45,46) For mechanically stabilized earth (MSE) walls, the design specifications note that a value of 34 degrees may be assumed for the friction angle, with a limit of 40 degrees if tested. The construction specifications require verification of the design assumption that the material exhibits a friction angle of at least 34 degrees on the portion passing the No. 10 (0.08-inch) sieve, as determined by the standard direct shear (SDS) test.⁽⁴⁵⁾ No testing is required for backfills where 80 percent of the sizes are greater than 0.75 inch. While the AASHTO specifications do not prohibit the use of OGAs, FHWA guidelines for MSE walls, which are adopted by many transportation agencies, recommend the use of well-graded materials.^(47,48) For geosynthetic reinforced soil walls and abutments, both OGAs and well-graded aggregates meeting a minimum friction angle of 38 degrees can be used in construction. No maximum limitation is imposed if appropriately tested in the laboratory.

Based on a survey of State transportation departments, approximately 74 percent responded that they use assumed strength parameters for backfills in retaining wall design, with 65 percent of the respondents assuming a friction angles of 34 degrees or less.⁽⁴⁹⁾ When testing is performed, 60 percent and 70 percent stated that they use direct shear and triaxial devices, respectively. A review of the literature found reported friction angles for poorly graded granular materials tested using DS and TX devices (table 1). Despite the availability of vast strength data that demonstrate friction angles higher than the default of 34 degrees for various granular materials conducted using all kinds of shearing tests devices, there is very limited data on large-sized aggregates with a narrow gradation, such as the AASHTO M43 aggregates (e.g., OGAs). Three studies were found that examined materials close to the No. 7, No. 56, and No. 57 aggregates.^(50,51,52)

For the approximate No. 7 aggregate, the difference between standard DS and TX tests was about 7 degrees; the TX results were 15 percent less than the DS results (table 1). For the approximate No. 56 aggregate, the difference was significantly larger between the two types of tests, with the TX 25 degrees, or 33 percent, lower than the DS. The researcher acknowledged that in most reported works in literature, the difference in friction angles are much lower, but the researcher concluded that such reports are not valid for the tested Bremanger sandstone.⁽⁵¹⁾

Two researchers reported friction angles for the No. 57 aggregate; however, both focused on either TX or DS testing, with no comparison.

Limited studies do show the comparison of ϕ' values from both TX and DS tests for OGAs. From table 1, the maximum reported is 33 percent, with TX values being lower than DS; while high, this finding is consistent with other research findings showing that TX friction angles are lower than DS, which are lower than PS. (See references 53 through 56.) Based on a compilation of various studies on sand, Kulhawy and Mayne (1990) presented the relationship for DS and TX compression testing, also as a function of the CV friction angle (equation 9).⁽⁵⁷⁾

            (9)

This relationship is based on sands and standard testing devices. Because of the lack of a sufficient database of the strength and stress-strain properties of the AASHTO M 43 designated aggregates, there is an absence of any established relationships of strength data between PS condition (as well as DS test) and the axisymmetric loading condition of TX tests. Therefore, the scarcity of such data is one of the major motivations of this work.

Table 1 . Reported friction angles from DS and TX testing.

¹Unless specified for a single confining pressure, ϕ' refers to the tangent friction angle obtained from the Mohr-Coulomb failure envelope.
DS = Direct shear.
TX = Triaxial.
- = Information not provided

2.3 DESIGN IMPLICATIONS

As previously discussed, the strength of these materials is an important design consideration. For OGAs, the strength is primarily defined by the internal friction angle (ϕ). The selection of friction angle, therefore, has significant impacts on the design of geotechnical features. It plays a role in the earth pressure coefficients, used in the determination of lateral earth pressures. In retaining wall design, the active earth pressure coefficient (K_a) is often used for failure conditions (equation 10). The higher the friction angle, the lower the coefficient, and thus the lower the lateral pressures that need to be resisted in design.

            (10)

The internal friction angle is also important in determining bearing capacity factors (table 2) used in the conventional equation to estimate nominal bearing resistance, described by Munfakh et al. (2001).^(44,45) As the bearing factors increase in value, the bearing resistance also increases, thus reducing the required size of the foundation. Table 3 illustrates the impact of using higher friction angles on K_a and the bearing capacity factors, N_c, N_q, and N_ϒ . The difference in K_a between 34 degrees and 45 degrees is a factor of 1.6; the differences in bearing resistance are even higher. By utilizing the actual strength properties of OGAs rather than defaulting to 34 degrees, more cost-effective designs can be realized.

Table 2. Bearing capacity factors.⁽⁴⁴⁾

Table 3. Impact of friction angle on geotechnical constants in design.