1. Introduction

In many applications, geomaterials or other rock-like materials (concretes, mortars, rocks, granular materials, ice, etc.) are subjected to an intense loading characterized by high levels of pressure and high or very high rates of loading [1]. For instance, we can mention the vulnerability of concrete structures subjected to hard impact [2] in which the shear resistance and compaction law (irreversible diminution of the volume) of concrete under high pressure is known to condition the penetration of the projectile into thick targets [3–7]. One may also mention the issue of rock blasting in open quarries for the production of aggregates and sand where controlling the block size distribution is an important objective [8], the use of percussive drilling tools in civil engineering that induce high stresses beneath the indenter [9–11] or the dynamic compaction of soils. In all these applications, the geomaterial is subjected to very high confinement pressures ranging from few tens to several hundreds of MPa. A good grasp of the behavior of geomaterials under confined compression is essential to any understanding and modeling of their

performances in order to improve the efficiency of the protective solutions or the industrial applications of concern.

Triaxial tests have been developed for half a century to characterize the mechanical behavior of concretes [12] and rocks [13] under high confinement levels. It consists in applying a purely hydrostatic pressure on a cylindrical specimen by means of a fluid followed by an additional axial compression. In this case, the stress tensor is defined with the two components (σradial, σaxial):

$$
\overline{\sigma} = \begin{bmatrix}
\sigma\_{radial} & \mathbf{0} & \mathbf{0} \\
\mathbf{0} & \sigma\_{radial} & \mathbf{0} \\
\mathbf{0} & \mathbf{0} & \sigma\_{axial}
\end{bmatrix}\_{\left(\overline{U\_r}, \overline{U\_\theta}, \overline{U\_x}\right)},\tag{1}
$$

where Ur �!, U<sup>θ</sup> �!, Uz � � �! corresponds to the frame attached to the cylindrical sample. The deviatoric stress is defined as the axial stress (in absolute value) on withdrawal of the lateral pressure exerted by the confinement fluid:

$$
\sigma\_{deviation} = |\sigma\_{axial} - \sigma\_{radial}|\,,\tag{2}
$$

Thus, it can be remarked that the last point of the "Common concrete" curve requires relatively close levels of radial stress and axial stress (respectively, about 700 and 1000 MPa) due to the small mean stress difference at this end of the test, the last point of BPR600 requires much smaller level of radial stress (about 400 MPa) and much higher level of axial stress (more than 1800 MPa). In conclusion, it appears that the level of axial and radial stresses to be applied during a triaxial or quasi-oedometric tests may need to be adapted as function of the level of the desired hydrostatic pressure and as function of the expected level of strength of

Limit state curves obtained from triaxial tests performed on ordinary concrete (Common concrete), high strength concrete (CRE140) and ultra-high strength concretes (BPR200, BPR300, BPR 600) [24] and

Investigation of the Quasi-Static and Dynamic Confined Strength of Concretes by Means…

corresponding levels of axial and radial stresses to be reached during the test.

DOI: http://dx.doi.org/10.5772/intechopen.89660

The quasi-oedometric compression (QOC) testing method provides a very attractive alternative to triaxial tests. It is based on the use of a cylindrical sample, a confinement cell that is usually designed as a simple metallic ring, two compression plugs and an interface product that should be used to fill the gap between the sample and the inner surface of the cell. Once the sample is inserted in the confinement cell and the compression plugs are put in contact with the top and bottom surfaces of the sample, an axial compression is applied. The specimen tends to expand under the effect of its radial expansion and exerts a lateral pressure against the confinement cell. In the course of the test, a rise of both axial and radial stresses is observed in the specimen, which gives a possible reading of the mean stress difference as a function of the level of applied pressure (the so-called deviatoric behavior) and of the diminution of the sample volume with the level of hydrostatic

A strong limitation must be underlined at that point: since the test is driven only

by the axial strain, it provides a single loading path (i.e. the "quasi-oedometric loading path") corresponding to an almost "1D" uniaxial-strain loading path. However, it cannot be concluded whether the variation of the strength is provoked mainly by the variation of the axial strain independently of the pressure level or by the change of hydrostatic pressure independently of the level of axial strain neither whether the mechanical response might be changed by subjecting the sample to a

The QOC testing technique has been continuously developed for concretes during the last three decades. Among the proposed experimental devices, one may cite the technique developed by Bažant et al. [25] (Figure 2(a)) where a cylindrical concrete specimen is placed in a hole and compressed. However, the lateral pressure exerted between the sample and the inner surface of the hole could not be measured during the test. Burlion [26] devised an instrumented vessel of 53 mm as interior diameter and 140 mm as exterior diameter, which was considered stressed in its elastic domain (Figure 2(b)). An interface product was used between the vessel

the tested material.

Figure 1.

different loading path.

69

pressure (the so-called compaction law).

and the hydrostatic pressure is defined by averaging the three principle stresses:

$$P\_{\text{hydrostatic}} = \frac{-\sigma\_{\text{axial}} + 2\sigma\_{\text{radial}}}{3} \tag{3}$$

The deviatoric strength is usually taken as the maximum deviatoric stress reached during the test and a series of triaxial tests performed at different lateral pressure provides several end-points that makes possible to deduce the limit state curves of the tested sample under static loading [14] or dynamic loading [15]. During the last decade, triaxial tests have been conducted in the 3SR laboratory with a high-capacity triaxial press (the GIGA press) able to generate a maximum confining pressure of 0.85 GPa and an axial stress of 2.3 GPa applied to cylindrical concrete specimen 7 cm in diameter and 14 cm long. As observed with quasi-oedometric compression tests [16, 17], the triaxial experiments conducted with dried, partially-saturated and fully-saturated ordinary concrete samples revealed that, under high confinement, the presence of free water in the sample affects the volumetric stiffness and reduces a lot the strength capacity [18, 19]. The role of water to cement ratio [20], cement matrix porosity [21], coarse aggregate size [22] and shape [23] in concrete samples under high triaxial compression loading was also explored with the same triaxial test apparatus. However, triaxial tests present some limitations which make them costly and difficult to perform specially under dynamic loading conditions. Indeed, they demand a very high pressure chamber (100–1000 MPa) coupled to a rigid load frame and they require impermeability between the confining fluid and the specimen that is not easy to carry out, in particular under high loading-rates. Figure 1 provides several limit state curves obtained from triaxial tests conducted with ordinary concrete (Common concrete), high strength concrete (CRE140) and with several types of ultra-high strength (reactive powder) concretes (BPR200, BPR300, BPR 600) [24]. These experimental results illustrate the sharp increase of concrete strength as a function of the applied hydrostatic pressure. The levels of axial stress and radial stress needed to reach any points in Figure 1 can be easily deduced considering the following equations (cf. red solid arrows and blue dotted arrows):

$$|\sigma\_{axial}| = P\_{hydrostatic} + \frac{2}{3}\sigma\_{deviation},\tag{4}$$

$$|\sigma\_{radial}| = P\_{hydrostatic} - \frac{1}{3}\sigma\_{deviatoric} \cdot \tag{5}$$

Investigation of the Quasi-Static and Dynamic Confined Strength of Concretes by Means… DOI: http://dx.doi.org/10.5772/intechopen.89660

Figure 1.

performances in order to improve the efficiency of the protective solutions or the

3 7 5

� � �! corresponds to the frame attached to the cylindrical sam-

ple. The deviatoric stress is defined as the axial stress (in absolute value) on with-

and the hydrostatic pressure is defined by averaging the three principle stresses:

Phydrostatic <sup>¼</sup> �σaxial <sup>þ</sup> <sup>2</sup>σradial

The deviatoric strength is usually taken as the maximum deviatoric stress reached during the test and a series of triaxial tests performed at different lateral pressure provides several end-points that makes possible to deduce the limit state curves of the tested sample under static loading [14] or dynamic loading [15]. During the last decade, triaxial tests have been conducted in the 3SR laboratory with a high-capacity triaxial press (the GIGA press) able to generate a maximum confining pressure of 0.85 GPa and an axial stress of 2.3 GPa applied to cylindrical concrete specimen 7 cm in diameter and 14 cm long. As observed with quasi-oedometric compression tests [16, 17], the triaxial experiments conducted with dried, partially-saturated and fully-saturated ordinary concrete samples revealed that, under high confinement, the presence of free water in the sample affects the volumetric stiffness and reduces a lot the strength capacity [18, 19]. The role of water to cement ratio [20], cement matrix porosity [21], coarse aggregate size [22] and shape [23] in concrete samples under high triaxial compression loading was also explored with the same triaxial test apparatus. However, triaxial tests present some limitations which make them costly and difficult to perform specially under dynamic loading conditions. Indeed, they demand a very high pressure chamber (100–1000 MPa) coupled to a rigid load frame and they require impermeability between the confining fluid and the specimen that is not easy to carry out, in particular under high loading-rates. Figure 1 provides several limit state curves obtained from triaxial tests conducted with ordinary concrete (Common concrete), high strength concrete (CRE140) and with several types of ultra-high strength (reactive powder) concretes (BPR200, BPR300, BPR 600) [24]. These experimental results illustrate the sharp increase of concrete strength as a function of the applied hydrostatic pressure. The levels of axial stress and radial stress needed to reach any points in Figure 1 can be easily deduced considering the following

Ur �!, U<sup>θ</sup> �!, Uz � � �!

σdeviatoric ¼ σaxial � σradial j j, (2)

<sup>3</sup> (3)

σdeviatoric, (4)

σdeviatoric: (5)

, (1)

Triaxial tests have been developed for half a century to characterize the mechanical behavior of concretes [12] and rocks [13] under high confinement levels. It consists in applying a purely hydrostatic pressure on a cylindrical specimen by means of a fluid followed by an additional axial compression. In this case, the

stress tensor is defined with the two components (σradial, σaxial):

drawal of the lateral pressure exerted by the confinement fluid:

equations (cf. red solid arrows and blue dotted arrows):

68

σaxial j j ¼ Phydrostatic þ

<sup>σ</sup>radial j j <sup>¼</sup> Phydrostatic � <sup>1</sup>

2 3

3

σradial 0 0 0 σradial 0 0 0 σaxial

industrial applications of concern.

Compressive Strength of Concrete

σ ¼

where Ur

�!, U<sup>θ</sup> �!, Uz 2 6 4

Limit state curves obtained from triaxial tests performed on ordinary concrete (Common concrete), high strength concrete (CRE140) and ultra-high strength concretes (BPR200, BPR300, BPR 600) [24] and corresponding levels of axial and radial stresses to be reached during the test.

Thus, it can be remarked that the last point of the "Common concrete" curve requires relatively close levels of radial stress and axial stress (respectively, about 700 and 1000 MPa) due to the small mean stress difference at this end of the test, the last point of BPR600 requires much smaller level of radial stress (about 400 MPa) and much higher level of axial stress (more than 1800 MPa). In conclusion, it appears that the level of axial and radial stresses to be applied during a triaxial or quasi-oedometric tests may need to be adapted as function of the level of the desired hydrostatic pressure and as function of the expected level of strength of the tested material.

The quasi-oedometric compression (QOC) testing method provides a very attractive alternative to triaxial tests. It is based on the use of a cylindrical sample, a confinement cell that is usually designed as a simple metallic ring, two compression plugs and an interface product that should be used to fill the gap between the sample and the inner surface of the cell. Once the sample is inserted in the confinement cell and the compression plugs are put in contact with the top and bottom surfaces of the sample, an axial compression is applied. The specimen tends to expand under the effect of its radial expansion and exerts a lateral pressure against the confinement cell. In the course of the test, a rise of both axial and radial stresses is observed in the specimen, which gives a possible reading of the mean stress difference as a function of the level of applied pressure (the so-called deviatoric behavior) and of the diminution of the sample volume with the level of hydrostatic pressure (the so-called compaction law).

A strong limitation must be underlined at that point: since the test is driven only by the axial strain, it provides a single loading path (i.e. the "quasi-oedometric loading path") corresponding to an almost "1D" uniaxial-strain loading path. However, it cannot be concluded whether the variation of the strength is provoked mainly by the variation of the axial strain independently of the pressure level or by the change of hydrostatic pressure independently of the level of axial strain neither whether the mechanical response might be changed by subjecting the sample to a different loading path.

The QOC testing technique has been continuously developed for concretes during the last three decades. Among the proposed experimental devices, one may cite the technique developed by Bažant et al. [25] (Figure 2(a)) where a cylindrical concrete specimen is placed in a hole and compressed. However, the lateral pressure exerted between the sample and the inner surface of the hole could not be measured during the test. Burlion [26] devised an instrumented vessel of 53 mm as interior diameter and 140 mm as exterior diameter, which was considered stressed in its elastic domain (Figure 2(b)). An interface product was used between the vessel

particle-reinforced cement composites, but also to analyze the role plaid by free-water on the quasi-static and dynamic confined responses of microconcrete [16, 30], ordinary concrete [33] and high-performance concrete [34] and to study the effect of coarse aggregates strength on the static and dynamic behavior of

Investigation of the Quasi-Static and Dynamic Confined Strength of Concretes by Means…

In this chapter, the principle of QOC tests, the data processing technique and some validation tools are presented. Next, some main obtained results are gathered. Finally, all this data allows highlighting the main microstructural parameters influencing the mechanical behavior of concretes under quasi-static or dynamic

The introduction of the sample into the confining ring constitutes a very delicate

stage. Indeed, to be sure that the entire gap between the sample and the inner surface of the ring is filled, it is necessary to cover the inner volume of the ring prior to inserting the sample. In addition, the sample needs to be carefully introduced without any contact with the confining cell under pain to block the sample into the ring by bow buttress. For this purpose, a special procedure was developed, as detailed in [16], to align the ring, the sample and the two plugs. First, the concrete sample is scotch tape to the upper plug. A special device (Figure 3) is used to introduce the concrete specimen within the ring previously partially filled by the bi-components epoxy resin named "Chrysor® C6120". During this stage, this resin is slowly extruded out and the internal gap between the specimen and the ring is totally fulfilled by the Chrysor®, which hardens in less than 24 hours. Next, the lower and upper frames are disassembled and the assembly is ready for testing.

concrete under high confinement [35].

DOI: http://dx.doi.org/10.5772/intechopen.89660

quasi-oedometric compression loadings.

2.1 Mounting procedure

Figure 3.

71

2. Principle and data processing of QOC tests

Schematic of the device to set the sample, the ring and the steel plugs [16].

#### Figure 2.

Quasi-oedometric compression testing devices applied to concrete. (a) Technique method developed by Bažant et al. [25]. (b) Instrumented vessel used in [27], (c) smaller confining cells used under quasi-static and dynamic loading conditions [28].

and the specimen to fill the gap between the sample and the vessel, which allows for correcting any possible defects of cylindricality of the sample. The interface product was an epoxy bi-component resin, Chrysor® C6120, commonly used for structural applications, and once polymerized, eliminates any internal play. The radial stress in the specimen was deduced from the measurements provided by strain-gauges attached to the outer surface of the vessel [27] based on the well-known analytical solution of an elastic tube subjected to a uniform pressure applied against its whole inner surface. So, the 'barrel' deformation of the vessel was not taken into account in this analysis. Smaller confining cells, 30 or 50 mm as inner diameter and 50 or 70 mm as outer diameter, were used in [28] to test a micro-concrete under quasi-static and dynamic loadings (Figure 2(c)). A maximum axial strain up to 30% was reached before unloading. Later, a new processing method was proposed in [29] and applied to these experimental data to evaluate the level of radial stress in the specimen from the hoop strain measured on the outer surface of the confining cell, taking into account the sample shortening. Both deviatoric and hydrostatic responses of this microconcrete were obtained from the processed data, which showed a quite limited influence of the rate of loading on the strength, even at a strain-rate of 400 s<sup>1</sup> [30].

The testing procedure and data processing method were substantially improved in several works and applied to successively investigate the influence of particles size and shape [31, 32] and of the porosity [6] on the confined behavior of

Investigation of the Quasi-Static and Dynamic Confined Strength of Concretes by Means… DOI: http://dx.doi.org/10.5772/intechopen.89660

particle-reinforced cement composites, but also to analyze the role plaid by free-water on the quasi-static and dynamic confined responses of microconcrete [16, 30], ordinary concrete [33] and high-performance concrete [34] and to study the effect of coarse aggregates strength on the static and dynamic behavior of concrete under high confinement [35].

In this chapter, the principle of QOC tests, the data processing technique and some validation tools are presented. Next, some main obtained results are gathered. Finally, all this data allows highlighting the main microstructural parameters influencing the mechanical behavior of concretes under quasi-static or dynamic quasi-oedometric compression loadings.
