# Efficient Approach to Measuring Strength and Deformation of Passively Confined Concrete

Petr Havlásek, Václav Nežerka, Petr Bittnar, Pavel Padevět, Milan Jirásek, Zdeněk Bittnar

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Petr Havlásek, Václav Nežerka, Petr Bittnar, Pavel Padevět, Milan Jirásek, et al.. Efficient Approach to Measuring Strength and Deformation of Passively Confined Concrete. 2012. [hal-04086415](https://hal.science/hal-04086415)

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Distributed under a Creative Commons Attribution 4.0 International License
Efficient Approach to Measuring Strength and
Deformation of Passively Confined Concrete

Petr Havlásek¹*, Václav Nežerka², Petr Bittnar¹, Pavel Padevět¹, Milan Jirásek¹ and Zdeněk Bittnar¹

¹*Department of Mechanics, Czech Technical University in Prague, Faculty of Civil Engineering, Thákurova 7, Prague, 166 29, Czech Republic.

²Department of Physics, Czech Technical University in Prague, Faculty of Civil Engineering, Thákurova 7, Prague, 166 29, Czech Republic.

*Corresponding author(s). E-mail(s): petr.havlasek@cvut.cz;
Contributing authors: vaclav.nezerka@fsv.cvut.cz;
petr.bittnar@fsv.cvut.cz; pavel.padevet@fsv.cvut.cz;
milan.jirasek@fsv.cvut.cz; bittnar@fsv.cvut.cz;

Abstract

This paper presents a novel experimental method developed to deter-
mine the increase in concrete strength and the evolution of both axial
and lateral deformation under confined compression. In contrast to
expensive and time-consuming triaxial experiments, the present method
requires only a uniaxial testing machine with displacement control.
In the proposed setup, a concrete cylinder is surrounded by metal rings,
which are activated by the lateral expansion of concrete and provide
passive confinement. The magnitude of confinement can be easily con-
trolled by the dimensions and spacing of the rings. In contrast to triaxial
tests, the stress history is much closer to that encountered in real struc-
tural members. The most suitable measuring setup is a combination
of conventional and non-contact measurements, namely of the vertical
extensometers for the axial strain and digital image correlation (DIC)
for the hoop strain. The results indicate that the lateral deformation
needs to be averaged over a representative volume as its distribution over
the height of the specimen becomes highly nonuniform in the postpeak.
The proposed setup was successfully verified on 20 concrete cylin-
ders with 4 different ring layouts. The measured strength increase
2 *Strength and Deformation of Passively Confined Concrete*

due to confinement is consistent with models from the literature
and thus with triaxial tests that were used for their development
and calibration. The experimental scatter decreases with increas-
ing magnitude of confinement and decreasing spacing of the rings.

**Keywords:** Confined concrete, Experiment, Passive confinement, Digital image correlation (DIC)
# 1 Introduction

## 1.1 Motivation

Cement production is responsible for approximately 8% of global anthro-
pogenic CO₂ emissions [1]. The urge to limit these emissions led to the adoption
of several mitigation strategies [2]: i) partial replacement of clinker in Portland
cement, ii) utilization of recycled concrete, and iii) adoption of more advanced
methods in the design of concrete structures. All of these methods require a
thorough description of the material's mechanical properties. Moreover, the
increasing volume of concrete production demands a higher consumption of
quality natural aggregates, which are becoming scarce. Incorporating lower-
grade or recycled aggregates as well as Portland cement substitutes directly
results in greater variability of the mechanical properties of concrete.

To avoid inefficiently oversized structures designed to meet structural
safety, and in the spirit of performance-based design, it is essential to determine
the governing mechanical characteristics of concrete more accurately using
readily available experiments. The resulting experimental data can provide a
basis for the calibration of advanced constitutive models for concrete to fully
utilize its structural potential. Such an approach can lead to more efficient
utilization of the material without sacrificing structural safety and, in turn, to
substantial savings in the consumption of raw materials and reduction in CO₂
emissions.

Advanced constitutive models for concrete, such as continuum damage-
plasticity models [3, 4], microplane models [5], or discrete lattice models [6],
can accurately reproduce the response of compressed concrete under lateral
confinement, which can be provided by properly designed transverse rein-
forcement. Such confinement enhances both the strength and the ductility
of concrete [7–13], thereby substantially increasing the load bearing capacity
without increasing concrete consumption. To provide essential data for cali-
bration, a novel experimental setup which allows conducting compressive tests
under confinement has been recently developed at CTU in Prague. As opposed
to conventional tests relying on results from triaxial testing, the new setup
should be more accessible in engineering practice.

## 1.2 State of the art in confined concrete experiments

The experimental setups for testing the response of confined concrete can be
divided into two basic groups. *Active confinement* refers to the case where the
magnitude of lateral confinement can be prescribed and controlled indepen-
dently of the deformation of the tested specimen. A prerequisite for this type
of test is the triaxial machine (Hoek cell [14]), primarily developed for testing
rocks. The target magnitude of confinement is typically imposed already before
dominant loading and is maintained throughout the experiment at a constant
level [11]. There are some exceptions to this rule, e.g., in [8], where conven-
tional triaxial tests are supplemented with a multistep and cyclic history of
4 *Strength and Deformation of Passively Confined Concrete*

confinement. The range of prescribed confinement is very wide and depends on the testing apparatus; it covers the magnitudes common for concrete columns reinforced with spirals (several MPa) as well as for concrete filled steel tubes (possibly tens of MPa).

The need for special experimental equipment is not the only drawback of the active confinement approach. The cell size predetermines the size of concrete cylinders (typically 54 × 108 mm), which might not be sufficient to represent concrete with larger aggregates. Moreover, the testing procedure is laborious and time-consuming, making the experiment expensive and also hindering the testing of a large number of specimens at a specific age. In addition, specimen instrumentation is not trivial and inexpensive. The axial strain can be measured with resistance strain gauges oriented vertically at midheight and regularly spaced along the circumference to determine the average strain. An externally mounted LVDT inherently adds spurious compliance of the supports and leads to undesired averaging of strain over the entire height of the specimen. Both axial and lateral strain gauges often need to withstand strains exceeding $30 \times 10^{-3}$ in magnitude. Furthermore, the length of the hoop strain gauge should encompass the entire circumference of the cylinder because a shorter measurement distance can provide local and misleading information. As the view of the specimen is blocked during loading in the triaxial machine, the formation and propagation of cracks remain obscured, which hinders the classification of failure modes. One must not forget that concrete is a path-sensitive material whose response depends on the entire loading history. Therefore, the response determined under active confinement may differ from the behavior of a real structural member even when the magnitude of confinement is similar [15].

The other setup, *passive confinement*, is based on restraining the lateral expansion of loaded specimens, which results from elastic (Poisson effect) and inelastic (plastic deformation and microcracking) processes. The confinement is never as uniform over the specimen height as in the preceding case. Friction in the supports hinders lateral deformation, which in turn leads to a non-uniform distribution of confining-induced stress over the specimen height. The stiffness of the restraint determines the evolution of the confinement and the material strength determines its maximum attainable magnitude. The shape of the specimen cross-section has a strong impact on the distribution of the confinement about the circumference.

In this study, attention is limited to cylinders, for which the lateral confinement (about their circumference) can be idealized as uniform and which can provide a direct insight into the material behavior rather than an understanding of the confinement efficiency, such as in the case with rectangular cross-sections and different corner radii [16, 17]. In contrast to active confinement, the requirements on specimen dimensions are not so strict; the maximum cross-section area is limited by the confined strength and the capacity of the testing machine.
Metallic or composite materials are commonly used to produce a restraint to free lateral expansion of concrete and thereby to generate confinement. The advantages of metallic materials are the consistency of their properties and the elasto-plastic behavior. Additionally, metallic tubes can serve as a mold for concrete, which simplifies the specimen preparation. However, the stress state that develops in the tube wall upon loading is chiefly biaxial. In the axial direction of the specimen, the tube is subjected to compression, which can substantially contribute to the overall measured axial force, while in the circumferential direction the tube is in tension. The ratio between these stresses with similar magnitudes gradually evolves during loading. This biaxial stress state also implies earlier yielding, especially since it combines tension with compression. As a result, the value of the hoop stress and the corresponding confining stress are not easy to determine. Since the objective is not to measure the performance of a concrete-steel composite, but rather to provide data for the identification of concrete behavior, continuous metallic tubes are not suitable for the given purpose.

The problem associated with undesired vertical restraint can be eliminated by using spiral reinforcement [18, 19], which does not require longitudinal reinforcement or spacers as opposed to circular (welded) rings. However, increasing spiral pitch results in a non-uniform distribution of confinement over the height of the specimen and it is more difficult to attain the target magnitude of confinement as the rebars are produced at a discrete scale and changing the spiral pitch disrupts the confinement efficiency factor.

The behavior of composite materials (carbon/glass fiber reinforced poly-
mers, CFRP/GFRP [9, 10, 20]) in tension is elastic-brittle, which implies that
the lateral confinement grows linearly with lateral expansion until the sur-
rounding shell ruptures, typically at maximum load. The history of stress
in concrete is different from typical reinforced concrete structures, but it is
essential to understand the behavior of concrete in retrofitted structures. In
contrast to metallic reinforcement, the properties of FRP are highly vari-
able [21] and can significantly differ from the manufacturer's specifications [9].
The specimens can be cast in standard size molds [22–24], which simplifies
the comparison with the reference uniaxial strength. Furthermore, the FRP
layer(s) can be applied shortly before testing, which eliminates possible shrink-
age strains that might delay the initiation of the confining pressure. However,
this is not a rule and FRP tubes prepared beforehand can also be used as
a mold [25]. Provided that the FRP is uniaxially woven and oriented in the
hoop direction, its stiffness in the axial direction can be neglected. Stiffness
and strength can be controlled by material selection, by the diameter of the
cylinder [24], and by the number of plies of the composite [9].

The instrumentation of passively confined concrete specimens is not stan-
dardized. The measurement setup typically uses two [20, 24], three [10, 22, 25]
or even four [23] externally mounted LVDTs or extensometers with a mea-
surement distance equal to half or the entire specimen height. Occasionally, an
independent technique is used to supplement these measurements, e.g., strain
6 *Strength and Deformation of Passively Confined Concrete*

gauges [10, 20, 23], laser sensors [23] or non-contact image-based methods [24].
Strain gauges of various lengths are by far the most common device for mea-
surements of the hoop strain, especially in the case of FRP whose behavior
is linear until failure. The other techniques include chain extensometers [22],
horizontal LVDTs [10, 17], and non-contact measurements [21, 24, 26]. The
non-contact measurements have demonstrated good agreement with the strain
gauges, but at the same time have revealed extreme variability in the distribu-
tion of the hoop strain, even in the elastic range. Conventional measurements
rely on the hypothesis that the hoop strain measured at mid-height is repre-
sentative of the investigated specimen. The measurements carried out within
the present research indicate that this assumption is not always valid.
# 2 Materials and Methods

## 2.1 Experimental design

In the newly developed experimental setup, a cylindrical concrete specimen is equipped with evenly spaced metal rings that provide axisymmetric passive confinement that improves both strength and ductility.

The benefits of the proposed approach include:

(i) elimination of special or single-purpose testing equipment—the proposed setup requires only a commonly available uniaxial testing machine with displacement control,

(ii) replacement of conventional strain gauges by non-contact measurements,

(iii) simple and fast assembly with quick replacement and fitting of the specimens,

(iv) variability that allows changing the target value of confinement.

A schematic representation of the experimental setup and photographs of specimens with 8 and 12 rings ready for testing are shown in Fig. 1. A similar concept has recently been used to evaluate the influence of ring width and spacing on increased concrete strength [27].

<figure><img src="image_2.png" /><figcaption>**Fig. 1** Outline of the experimental setup and photos of specimens with 12 and 8 metal rings. Red color corresponds to conventional techniques while purple color refers to the image-based measurements.</figcaption></figure>

The proposed design adopts the recommended height-to-diameter ratio $H : D = 2 : 1$ [28]. In this particular case, the diameter of the concrete cylinder, $D_0$, is slightly less than the recommended value of 100 mm, which facilitates the manufacturing process. Every experimental setup should properly represent the behavior of the investigated material; therefore, as recommended in EN 12390-1 [29], the internal diameter $D_0$ should exceed $3.5 \times$ the maximum
8 *Strength and Deformation of Passively Confined Concrete*

aggregate size. According to Van Mier [30], this factor is in the range 3–5, and the minimum dimension of the cross-section should be at least 100 mm [28]. It should be noted that every 1 MPa of lateral confinement increases the strength by ≈ 4 MPa [7], which in combination with a large diameter $D_0$ (required by the aggregate size or by a requirement of a high value of the confinement effectiveness factor, $k_e$ (3)) could easily exceed the capacity of the testing machine.

The magnitude of the lateral confinement can be modified by adjusting the geometry of the metal rings and/or their material properties. The development of passive confinement depends on the lateral expansion of concrete restrained by the rings. Therefore, the confinement builds up from zero in the initial unloaded state and reaches its maximum when the rings reach their tensile strength.

<figure><img src="image_3.png" /><figcaption>**Fig. 2** Symmetric half of the representative segment: assumed distribution of stress and equilibrium of resultant forces in the horizontal direction.</figcaption></figure>

Fig. 2 schematically describes a symmetric half of the representative segment of the specimen with one ring characterized by its height $h$, thickness $t$, and internal diameter $D_0$. The uniform spacing between the rings is denoted as $g$ (gap), and the total height of the representative segment can be expressed as $h + g$. The average value of passive confinement, $\sigma_L$, can be derived from the equilibrium condition

$$F_L = 2F_R \qquad (1)$$

of the stress resultants of lateral confinement in concrete, $F_L$, and tension in the metal ring, $F_R$. After substituting $F_L = \sigma_L D_0(g + h)$ and $F_R = \sigma_R th$, the average confinement is expressed as

$$\sigma_L = \frac{2 \sigma_R th}{D_0(g + h)} \qquad (2)$$
As described in Section 2.2, highly uniform confinement can be achieved by minimizing the gap width, g. However, it needs to be ensured that the gaps can accommodate the high axial deformation and do not close during the experiment and, additionally, that the neighboring rings do not interfere with the vertical (axial) extensometers. The height of the rings should be sufficient to allow for the placement of a strain gauge, which might be necessary for the initial verification of non-contact measurements. An excessive height brings about a potential risk of spurious friction in the vertical direction.

Before yielding, the behavior of rings is elastic and defined by Hooke's law $\sigma_R = E_R\varepsilon_R$ where $E_R$ is the Young modulus of the metal and $\varepsilon_R$ is the hoop strain in the rings, which is equal to the (average) lateral strain in concrete cylinder, $\varepsilon_L$.

Special care should be taken to choose a suitable material for the metal rings. The transition between the elastic and plastic response should be as sharp as possible. Section 3 shows that the confined concrete strength is usually attained close to this transition, so the value of the yield stress, $f_Y$, needs to be known with sufficient precision to properly evaluate the corresponding lateral confinement. Provided the hardening of the metal is not significant, a constant value of stress can be assumed after the onset of the yielding, $\sigma_R = f_Y$.

The last but definitely not least important requirement is the compatibility of the standard mold sizes for the reference unconfined specimens with the range of metal tubes available on the market.

## 2.2 Confinement effectiveness

In axially compressed concrete members reinforced, for example, with spirals or rings, the distribution of lateral confinement is not uniform and depends on the layout of both transverse and longitudinal reinforcement. Even more complex is the confinement in columns with multi-spiral reinforcement [31, 32].

The distribution of confinement is variable in both the lateral and the axial directions. Just below the reinforcement, the concrete is under triaxial compression and the magnitude of confinement is very high; on the contrary, at the surface between the rebars, the lateral stress is negligible. Concrete cover is usually not considered in the analysis at all, as it tends to spall off at very low levels of axial deformation (≈ $-2 \times 10^{-3}$). Toward the center of the member, the homogeneity of the lateral confinement rapidly increases. In practical engineering applications, concrete in the structural member is, for simplicity, divided into two regions—the effectively and ineffectively confined parts—whose behavior is idealized as uniform [33].

The overall structural strength is determined by the weakest section with the highest proportion of ineffectively confined (unconfined) concrete. In the case of circular rings, such a section is between the rings. In the present case, the strength of the unconfined part (red color in Fig. 2) is assumed to be equal to the uniaxial compressive strength, $f_c$. The strength of the effectively confined concrete (shown in the weakest section in green), $f_{c,c}$, is evaluated from the average confinement $\sigma_L$ (2). To reflect this idea in structural analysis
10 *Strength and Deformation of Passively Confined Concrete*

and design, a simple multiplicative factor $k_e$ referred to as the confinement effectiveness is introduced. This factor, proposed in the pioneering work of Mander [33], has been adapted directly or in a modified way into almost every design code of practice [34–36].

The simplest choice would be to consider the confinement effectiveness as the ratio $k_e = A'_c/A_c$ where $A'_c$ is the area of concrete effectively confined in the weakest section and $A_c$ is the total area of concrete bound by reinforcement. With the assumption that (in the elevation view) the boundary dividing the effectively and ineffectively confined concrete is a 2nd-order parabola with a 45° angle intercept at the surface, the maximum width of the ineffectively confined concrete zone is $g/4$ and the diameter of the effectively confined concrete is thus $D_0 - g/2$. The resulting confinement effectiveness factor is then expressed as

$$k_e = \frac{A'_c}{A_c} = \frac{\pi (D_0/2 - g/4)^2}{\pi (D_0/2)^2} = \left(1 - \frac{g}{2D_0}\right)^2 \quad (3)$$

To obtain a uniform stress distribution in concrete, the gap width $g$ should be considerably smaller than the internal diameter $D_0$. For small values of the ratio $g/D_0$, $k_e$ is close to $1 - g/D_0$. For instance, $k_e = 0.95$ corresponds to $g/D_0 = 0.051$, $k_e = 0.9$ to $g/D_0 = 0.102$, and $k_e = 0.85$ to $g/D_0 = 0.156$.

In practice, however, a modified definition of the confinement effectiveness factor

$$k_e = \sigma'_L / \sigma_L \quad (4)$$

is usually preferred. It is then used to evaluate the confined concrete strength on the entire concrete cross section $A_c$ from the reduced effective confinement, $\sigma'_L$. Provided that the increase in concrete strength due to confinement, $\Delta f_{c,c}$, is a linear function of confinement, the two definitions coincide and the compressive strength of the specimen can be computed as

$$f_{c,c}^{\text{spec}} = \frac{f_c A_c + \Delta f_{c,c}(\sigma_L) A'_c}{A_c} = f_c + k_e \Delta f_{c,c}(\sigma_L) = f_c + \Delta f_{c,c}^{\text{spec}}(\sigma'_L) \quad (5)$$

## 2.3 Experimental program

Table 1 summarizes the four different configurations of the experimental setup that were tested. The label that identifies a given configuration specifies the number of rings and their thickness. For instance, '8R_t3' refers to 8 rings, each 3 mm thick. The approximate range of interest for the target confinement was between 2.5 and 5.0 MPa. This range is typical, e.g., in the design of multi-spiral columns developed in Taiwan [31]. Two setups labeled '8R_t3' and '12R_t2' with the same total areas of reinforcement yield very similar average confinement, and so the results should reveal the differences caused by the confinement effectiveness factor.
<table><caption>**Table 1** Geometry of concrete specimens with metal rings.</caption><thead><tr><th>Series</th><th>No. rings, N</th><th>t [mm]</th><th>D<sub>0</sub> [mm]</th><th>g [mm]</th></tr></thead><tbody><tr><td>8R_t2</td><td>8</td><td>2</td><td>96</td><td>16.0</td></tr><tr><td>8R_t3</td><td>8</td><td>3</td><td>94</td><td>16.0</td></tr><tr><td>12R_t2</td><td>12</td><td>2</td><td>96</td><td>7.7</td></tr><tr><td>12R_t3</td><td>12</td><td>3</td><td>94</td><td>7.7</td></tr></tbody></table>

Dimensions common to all series: *H* = 200 mm, *D* = 100 mm, *h* = 9 mm.

## 2.4 Materials

### 2.4.1 Concrete

The composition of the concrete mixture with the 0.42 water-to-cement ratio is specified in Table 2. Basic material properties measured at the age of 28 or

<table><caption>**Table 2** Concrete composition.</caption><thead><tr><th>Ingredients</th><th>Quantity [kg/m<sup>3</sup>]</th></tr></thead><tbody><tr><td>CEM I 42.5R (Mokrá, Czech Republic [37])</td><td>410</td></tr><tr><td>Water</td><td>170</td></tr><tr><td>Aggregates 0–4 mm, 4–8 mm, 8–16 mm</td><td>796.4 + 450.0 + 524.2</td></tr><tr><td>Superplasticizer Stachement F</td><td>4.1</td></tr></tbody></table>

29 days on standard cylinders 100 × 200 mm stored under sealed conditions are summarized in Table 3. In this table, the basic numbers are the mean values while the corresponding standard deviations are in parentheses. The reported properties of plain concrete include density, ρ, uniaxial compressive strength, *f*<sub>c</sub>, the strain (magnitude) at peak stress, ε<sub>fc</sub>, and the secant modulus of elasticity evaluated at 40% of the peak stress, *E*<sub>40</sub>. The axial strain was measured by two 100 mm long extensometers installed on the opposite sides of the specimen at its mid-height. The present concrete can be classified as C40/50, as the characteristic strength *f*<sub>ck</sub> = *f*<sub>cm</sub> – 1.64 × stdev = 46.576 – 1.64 × 2.406 = 42.629 [MPa].

<table><caption>**Table 3** Average concrete properties at the age of 1 month measured on cylinders 100 × 200 mm.</caption><thead><tr><th>Property</th><th>Unit</th><th>Mean value (stdev)</th></tr></thead><tbody><tr><td>ρ</td><td>[kg/m<sup>3</sup>]</td><td>2375.2 (8.0)</td></tr><tr><td>E<sub>40</sub></td><td>[GPa]</td><td>37.68 (1.62)</td></tr><tr><td>f<sub>c</sub></td><td>[MPa]</td><td>46.58 (2.41)</td></tr><tr><td>ε<sub>fc</sub></td><td>[10<sup>-3</sup>]</td><td>1.92 (0.24)</td></tr></tbody></table>

### 2.4.2 Metal rings

The metal rings, which are the source of passive confinement, were cut from AW6060 T66 aluminum tubes with external diameter *D* = 100 mm and wall thickness *t* = 2 or 3 mm, which are commonly available on the market. The
rings were first cut with a band saw and then finished with a lathe to achieve
the desired height $h = 9$ mm.

The tensile behavior of aluminum AW6060 T66 was verified experimentally
on 100 mm long coupons, with a cross section 1.8 × 15 mm. The specimens
were cut from a square hollow section in the direction perpendicular to its
longitudinal axis. The measured stress-strain diagram is shown in Fig. 3. In
contrast to high-ductility reinforcing steel (e.g. B500C or SD420W) used in
seismic areas, the transition from elastic to plastic behavior is much smoother,
but the advantage is that the subsequent hardening is very slow, and thus the
confinement during the late stages of the test remains almost constant.

The recorded stress-strain diagram agrees nicely with the standard char-
acteristics of this alloy (E = 69.5 GPa, minimum tensile strength 215 MPa).
Deformation was evaluated from the elongation of a 25 mm long extensometer
(solid lines with points) and from the cross-head displacement (dashed lines).
In the main experimental study on the behavior of concrete under passive con-
finement, the hoop strain in the metal rings at the peak axial load level is
typically between 3 × 10⁻³ and 4 × 10⁻³; see Figs. 10 and 13. For this reason,
the value of the yield stress used in further analyses is set to fY = 190 MPa,
which is considerably higher than the initial yield stress (approx. 160 MPa)
but lower than the stress at the yield plateau (approx. 200 MPa). On aver-
age, the tensile strength 220 MPa is attained at strain 80 × 10⁻³, which is in
accordance with the standard specifications (fu = 215 MPa). On the basis of
the two measurements, the strain at failure is approx. 140 × 10⁻³.

<figure><img src="image_4.png" /><figcaption>Fig. 3 Detailed (left) and overall (right) view of the experimental stress-strain diagram of AW6060 T66 aluminum alloy coupons subjected to uniaxial tension.</figcaption></figure>

**2.5 Specimen preparation**

Compatibility of the outer diameter *D* of the rings with the inner diameter of the standard cylinder mold 100 × 200 mm allowed for a simple and accurate assembly of the aluminum and 3D-printed plastic rings with height *g* (or *g*/2). Before that, the inner surface of the aluminum rings was treated with floor wax to prevent a chemical reaction.
Approximately 4 hours after concrete casting (and properly vibrating), the molds were wrapped with foil to minimize evaporation. The next day, the specimens were demolded, and the spacer rings were removed. The specimens were then transferred to a closed container with relative humidity ≈ 95% and room temperature. Two days prior to testing, the horizontal load bearing surfaces were ground [38].

## 2.6 Instrumentation and testing program

### 2.6.1 Conventional measurements

To measure the hoop strain of the passively confined specimens, the four middle rings (T2, T1, B1, B2 in Fig. 1) were equipped with strain gauges HBM-1-LY41-10/120 (measuring length 10 mm, width 8 mm) oriented in the circumferential direction. Only 3 of 5 specimens (Nos. 7, 8 and 9) in each series were instrumented in this way. Additionally, axial shortening was recorded by two 100 mm long extensometers placed at mid-height and attached to the surface of the concrete cylinder. In the case of plain concrete specimens, only axial deformation was measured.

### 2.6.2 DIC measurements

The secondary aim of the presented research was to demonstrate that simple and cheap 2D DIC measurements can extract valuable data from uniaxial tests on cylindrical specimens if carried out and evaluated properly. The evolution of deformation was recorded as a sequence of images taken in 5-second intervals using a high-definition camera Canon 70D equipped with a 200mm objective lens, minimizing the fish-eye distortions. The observed specimens, sprayed with black and white speckles to provide a random pattern needed for DIC, occupied the entire image frame when placing the camera approximately 10 m from the tested specimens. This setup yielded a pixel resolution of 16.95 px/mm.

A suite of open-source noncommercial software, Ncorr [39] and Ncorr_post [40], was used for the evaluation of the displacement and deformation fields and for data extraction. To quantify relative displacements, virtual extensometers were used to gather the data (Ncorr_post), while the distributions of strains and displacements along a line were calculated by averaging the displacement/strain matrix values within a strip parallel to that line (Ncorr_post_CSTool); see Fig. 4.

Assuming a uniform distribution of hoop strain over the circumference of the aluminum rings, the in-plane projection can be used to evaluate hoop strain. The strains on the rings are calculated as $\epsilon = \Delta L/L$ where L is the length of the extensometer and $\Delta L$ is its change, and both $\Delta L$ and L are reduced by the same factor to obtain the 2D projection. The same approach was adopted for hoop strain measurements on FRP wraps used as confinement for cylindrical specimens using particle image velocimetry (PIV) [21, 24, 26]. A demonstration of this conjecture is provided in Fig. 5; the study was performed on the rings T1 and B4 of 12R_t2-8 specimen. Although the results in Fig. 5
14

Strength and Deformation of Passively Confined Concrete

<figure><img src="image_5.png" /><figcaption>**Fig. 4** Placement of virtual extensometers for extraction of displacements at discrete locations (left) and a 60 mm wide averaging strip for evaluation of displacement/strain distribution along a red line (right), on a map of vertical displacement (mm) at the peak load for the 12R_t2-8 specimen. Extensometer couples 1a-1b and 2a-2b (located near edges ~ EXT<sub>L/R</sub> length) were used for evaluation of vertical displacements, while extensometer couples 3a-3b to 14a-14b were placed on the rings 60 mm apart to evaluate their horizontal deformation.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 5** Hoop strain measured on the 12R_t2_8 specimen rings T1 and B4 (Fig. 1) demonstrating the independence of measured values on the length of virtual extensometers.</figcaption></figure>

are almost independent of the length of the extensometer, the hoop strain is highly variable about the circumference, therefore, it is important to maximize the extensometer length.

### 2.6.3 Testing

The specimens were tested at the age of 28 days (12 rings) and 29 days (8 rings). Every specimen series with rings (5 specimens) was supplemented with a set of 4 reference plain concrete specimens tested on the same day; altogether the
experimental program comprises 16 plain concrete specimens and 20 specimens with rings.

A loading frame with 2.5 MN maximum force was used for testing. The instrumented specimens were properly centered (max. 10% difference in reading of extensometers under 40 kN load) and loaded at a constant rate of 100 kN/min until the load of 200 kN was reached. The test was then switched to displacement control at a rate of 0.48 mm/min. (Note that this rate corresponds to the displacement of the loading cylinder, while the actual imposed displacement is about 2 times less.) The test was terminated once several rings had ruptured (typically at less than 25% of the maximum force). One run of the experiment (excluding centering) took approx. 15–30 minutes.
# 3 Results and Discussion

To achieve maximum clarity of the results presented, the following conventions are adopted. Positive values of stress and strain denote tension and extension, respectively. The axial stress is computed as the loading force divided by the net area of the concrete cross-section; this area differs for the setups with 2 and 3 mm thick rings. The rings are numbered from the center towards the bases according to Fig. 1. The axial strain corresponds to the average of two extensometers, physical (contact measurements) or virtual (DIC). The designation introduced in Table 1 characterizes the geometry of the experimental setup. Where applicable, an additional number refers to particular specimens: 1–4 to companion plain concrete specimens and 5–9 to specimens with rings. Specimens 5 and 6 were not equipped with strain gauges to measure hoop strain.

## 3.1 Stress-strain response

This section presents the axial stress-strain response of the specimens with metal rings. Here, the axial strain was measured using a pair of (contact) extensometers whose consistent readings indicated well-centered specimens and their symmetric behavior even in the post-peak. The rupture of the first ring, which typically occurs at axial strains between $-20 \times 10^{-3}$ and $-25 \times 10^{-3}$, defines the measuring range of this experimental setup. This is fully sufficient and comparable to other experiments in the literature [8, 9, 11] at similar confinement magnitudes.

Fig. 6 illustrates the statistically processed results, different colors denote the individual experimental setups. Solid lines correspond to the mean response of specimens with satisfactory failure mode. The scatter (standard deviation, shaded area) increases approximately linearly with axial strain in the post-peak. The minimum and maximum responses (dashed lines) are very close to the bounds of this shaded region.

Except for the discarded specimens exhibiting shear failure, the results are very consistent in terms of strength, maximum strain (ductility), strain at peak stress, and the softening rate in the post-peak. The noisy character of the lines in the late post-peak range is due to the removal of the failed specimens from the statistical evaluation.

Only a portion of the experimental data is presented. The data was typically trimmed after the rupture of the first ring, resulting in a sudden drop in confinement and rapid propagation of damage in unrestrained concrete. In addition to this, the uniformity of readings between the extensometers was lost and the measured data could become misleading.

Consistent with other studies, e.g. [8, 9, 11], the compressive strength and the corresponding strain (Table 4) increase with confinement. Series 8R_t3 and 12R_t2, which have a very similar reinforcement ratio (the same cross-sectional area of the rings but different internal diameter $D_0$), reach similar strength. Owing to better confinement efficiency, the strength is higher in the case with
<figure><img src="image_7.png" /><figcaption>**Fig. 6** Statistically processed stress-strain diagrams for all specimen groups. Solid line is the average, dashed lines are the minimum and maximum responses, shaded area is the average ± standard deviation.</figcaption></figure>

closely spaced rings, whereas the setup with loosely spaced rings results in higher strain at peak stress. Additionally, the standard deviation of strength is rapidly decreasing with higher confinement and closer ring spacing (Table 4).

The summary presented in Table 4 reveals that the number of discarded specimens that failed in shear decreases with an increasing number of rings and/or confinement. Furthermore, from the available data it appears that the inappropriate failure mode does not affect the strength and corresponding strain, but significantly influences post-peak behavior, which is characterized by higher softening rate. Therefore, any deviation from the prevailing stress-strain behavior might serve to detect an inappropriate failure mode, which, in contrast to plain concrete specimens, is more difficult to detect, even from a sequence of (uncorrelated) digital images.

<table><caption>**Table 4** Compressive strength and corresponding strain of concrete cylinders with metal rings. The specified values represent the average and the standard deviation (in parentheses) evaluated from the specimens with the correct failure mode.</caption><thead><tr><th>Series</th><th>passed/total</th><th>f<sub>c,c</sub><sup>spec</sup><br>[MPa]</th><th>ε<sub>fc,c</sub><br>[10<sup>-3</sup>]</th></tr></thead><tbody><tr><td>8R_t2</td><td>3/5</td><td>63.77 (2.32)</td><td>3.98 (0.33)</td></tr><tr><td>8R_t3</td><td>5/5</td><td>67.06 (1.61)</td><td>5.20 (0.35)</td></tr><tr><td>12R_t2</td><td>4/5</td><td>69.94 (0.99)</td><td>4.88 (0.13)</td></tr><tr><td>12R_t3</td><td>5/5</td><td>76.93 (0.93)</td><td>7.42 (0.44)</td></tr></tbody></table>
## 3.2 Distribution and evolution of axial and lateral strain

This section presents the results obtained using a noncontact DIC with a 60 mm wide averaging strip (depicted in Fig. 4b), which allowed efficient processing of the hoop strain and vertical (axial) displacement over the entire specimen height. As demonstrated in Table 4, the behavior of specimens with 12 rings is more regular than with 8 rings. Furthermore, with ring thickness $t = 2$ mm the confinement (see Table 6) becomes more representative of the present experimental program. For this reason, specimen 12R_t2.8 was selected as an example to illustrate the typical behavior both visually and by means of the DIC measurements.

The photos shown in Fig. 7, taken at the beginning of loading and then in the post-peak at 80% and 60% of the peak load, illustrate typical behavior. Until the peak load, no damage is visible except for local and very limited concrete spalling between the rings. Lateral deformation starts to be visually noticeable in the post-peak (Fig. 7b). This deformation is uniformly distributed in the middle part between the springs (≈ 100 mm). Shortly before the failure of the metal rings (Fig. 7c), concrete becomes severely damaged in the central part, while the outer (top and bottom) regions remain undamaged. Damage is diffuse and uniform; no localized deformation is apparent. Towards the end of the experiment, the rings start to bend, the lateral strain is no longer uniform, and concentrates at the mid-height.

<figure><img src="image_8.png" /><figcaption>**Fig. 7** 3 snapshots from the experiment on a specimen with 12 rings with thickness 2 mm (12R_t2.8): (a) prior to loading; (b) postpeak, 80% strength, visually noticeable lateral deformation; (c) postpeak, 60% strength, shortly before rings rupture.</figcaption></figure>
The results of the DIC analysis provide detailed insight into the evolution and distribution of deformation, which is shown at several time snaps in Fig. 8. The response at the peak load is drawn by a solid black line, the numbers in the legend indicate the fraction of the peak load. To facilitate orientation, the horizontal gray bands represent individual rings. The values were obtained by averaging over a 60 mm wide band; the drops to zero around $H = 50$ and 150 mm are caused by external springs blocking the view of the specimen.

The evaluated vertical (axial) strain was very noisy. Therefore, the left part of Fig. 8 shows the vertical displacement. The graph reflects the loading setup in which the top surface is supported and an upward displacement is imposed at the bottom. The right part of Fig. 8 presents the distribution of the hoop strain over the height. Local peaks between the rings signal concrete damage and associated spalling in that region.

<figure><img src="image_9.png" /><figcaption>Fig. 8 Distribution of vertical displacement (left) and hoop strain (right) over height of specimen 12R_t2_8.</figcaption></figure>

To improve the clarity of the DIC results and to eliminate the noise due to concrete damage, both quantities—the axial (vertical) displacement and the hoop strain—are evaluated in the middle of the ring height. Additionally, the axial displacement is zeroed with respect to the top ring. The persistent irregularities can probably be attributed to the sliding of the rings on the concrete cylinder. Horizontal dashed lines indicate the 100 mm long central part of the specimen monitored by a couple of external extensometers.

The evolution and distribution of vertical displacement is, for the experimental setup 12R_t2, presented in Fig. 9. Different line types are used to distinguish the individual specimens while the colors mark the specific load levels (normalized with respect to the corresponding strength). Except for large magnitudes of axial strain, the distribution in the central part can be idealized as linear and at the same load levels as parallel and without strain localization. Therefore, it can be concluded that the measurements with 100 mm long external extensometers can deliver representative data of the central part of the specimen which is sufficient to characterize the material behavior.
20

Strength and Deformation of Passively Confined Concrete

<figure><img src="image_10.png" /><figcaption>**Fig. 9 Distribution of vertical displacement over the height of specimens 12R_t2.**</figcaption></figure>

For the experimental setup 12R_t2, the distribution of hoop strain over the specimen height is shown in Fig. 10. The left part shows the response up to the peak and the right part up to 70% of the specimen strength in the post-peak, which typically corresponds to an axial strain exceeding in magnitude $20 \times 10^{-3}$. Similarly to the previous graphs, colors correspond to individual load levels and line types serve to distinguish individual specimens. As shown in the figure, the response is almost perfectly regular and the hoop strain is nicely symmetric about the horizontal axis of the specimen. The maximum is typically attained in one of the middle rings (B1 or T1). In the pre-peak, the distribution of the hoop strain is almost uniform in the central part of the specimen. When approaching the maximum load level, this distribution gradually evolves to parabolic and finally, in the post-peak, the overall distribution over the height is highly nonlinear and resembles a bell shape. To properly capture the behavior of the representative concrete volume, the hoop strain needs to be averaged. The responses of the other experimental setups which show similar trends are presented in the supplementary material [41].

<figure><img src="image_11.png" /><figcaption>**Fig. 10 Distribution of hoop strains over the height of specimens 12R_t2.**</figcaption></figure>
## 3.3 Conventional measurements vs. DIC

This section compares the results obtained with conventional measurements (i.e., external axial extensometers and lateral resistive strain gauges) and the non-contact DIC method. The aim is to validate the DIC measurements and to select a suitable and reliable combination of experimental techniques to accurately describe the evolution of axial and lateral deformation of the representative concrete volume.

In the literature [8, 9, 11], the response of confined concrete is usually presented in terms of an extended stress-strain diagram. In this diagram, both the axial and the hoop strains are linked to the axial stress. An example of such a diagram is presented in Fig. 11a for specimen 12R.t2.8 (shown previously in Figs. 7 and 8). This overall view demonstrates that a very similar evolution of the average axial strain was measured with both physical (100 mm long, red lines) and virtual DIC (84 mm long, purple points) extensometers. In this particular case, the DIC method offers a longer range ($45 \times 10^{-3}$ instead of $25 \times 10^{-3}$) but on the other hand the extensometers attached to the concrete provide more uniform behavior (dashed red lines vs. tiny purple points).

A detailed view of the stress vs. axial strain relationship shown in Fig. 11b reveals that the present DIC measurements suffer from irregular oscillations, which are common to both extensometers. These oscillations are most profound in the first half of the loading branch and are responsible for a spurious offset in this diagram.

The measurements of the hoop deformation are drawn in green and blue in Fig. 11a and c. Only the results for the central 4 rings (top to bottom: T2, T1, B1, B2) are shown, because these were examined by both methods. A detailed view of the loading branch indicates that the magnitudes of the oscillations are similar for both axial and hoop deformations. In the latter case, they become more apparent because the magnitude of the lateral deformation is initially scaled by the Poisson ratio. In contrast to a good agreement of the axial deformation, the hoop deformation exhibits large differences between the two methods. This inconsistency is attributed to variations in the hoop strains along their perimeter, as reported by Bisby and Take [21]. The strain averaging procedure over a 60-mm projection using DIC provides more reliable data than strain gauges of very limited length (10 mm in this case).

The evolution of axial and hoop strain was evaluated for all specimens with metal rings. The axial strain measured by the two methods exhibits a symmetric scatter of approx. 25%. The measuring range of both methods is comparable but the reusable external extensometers can deliver more consistent and smoother data not polluted by the noise of the DIC. For this reason, the physical extensometers should be preferred.

On the other hand, in the case of hoop strain the DIC technique is found superior to conventional measurements with strain gauges. First, the conventional measurements are not representative in the post-peak because the non-uniform strain distribution over the circumference becomes amplified by the material behavior of the rings. Owing to their very little hardening, the
<figure><img src="image_12.png" /><figcaption>**Fig. 11** Evolution of axial and hoop strain on specimen 12R-t2_8; overall view (a), detailed view (b) and (c). Smooth lines correspond to conventional measurements, noisy lines with points to DIC.</figcaption></figure>

rings start yielding in some areas whereas remain elastic elsewhere. Second, DIC delivers more consistent results among specimens with the same setup. The accuracy can be considerably improved if the readings from the central rings are averaged. Finally, the strain gauges are not reusable, their price rapidly increases with measuring length and their usage is overall cumbersome (laborious gluing and soldering, slow transition between specimens during testing).

The final data, which can be used for further analysis and calibration of constitutive models for confined concrete, are presented in the form of combined graphs in Fig. 12. The axial strain is the average of the physical 100 mm long extensometers. The hoop strain is the average of the DIC measurements from the middle region equal to the length of the physical extensometers. In this global view, the noise of the DIC completely vanishes. In contrast to typical graphs from the literature, the lateral strain is here plotted as a function of the axial strain, not of the axial stress. In this way, the rate of lateral dilation can be directly assessed. The volumetric deformation, which is often presented, combines numbers with opposite signs and similar magnitudes, which could lead to large errors. However, even in this respect the results are consistent with data from literature [8, 11, 42], the material strength is reached approximately at zero volumetric strain [41].
<figure><img src="image_13.png" /><figcaption>**Fig. 12** Relations between the stress, conventionally measured axial strain and the average hoop strain measured using DIC. Dashed lines correspond to elasticity with $\nu = 0.2$.</figcaption></figure>
## 3.4 Increase in strength due to confinement

This section compares the present experimental data with selected models from the literature and design codes or recommendations, to support the credibility of the proposed experimental setup. Since most of the selected models were developed for steel reinforced concrete and the present experiment uses aluminum with a distinctly different stress-strain relationship, the only quantity that can be objectively compared is the increase in strength due to confinement. The experimental setup presented here does not produce a perfectly uniform distribution of the lateral confinement. Therefore, to establish a meaningful comparison, this structural effect which causes a strength reduction needs to be properly considered by all models.

Table 5 presents slightly modified formulae of the selected models. In particular, the confinement effectiveness factor $k_e$ has been added to Richart's model and, in the code expressions, the characteristic or design strength has been replaced by the mean compressive strength.

<table><caption>**Table 5** Increase in concrete strength due to lateral confinement according to the selected models.</caption><thead><tr><th>Recommendation</th><th>Strength increase Δf<sup>spec</sup><sub>c,c</sub> [MPa]</th><th></th></tr></thead><tbody><tr><td>Richart [7]</td><td>4.1k<sub>e</sub>σ<sub>L</sub></td><td>(6)</td></tr><tr><td>Mander [33]</td><td>f<sub>c</sub> (2.254√(1 + (7.94k<sub>e</sub>σ<sub>L</sub>)/(f<sub>c</sub>)) - 2(k<sub>e</sub>σ<sub>L</sub>/(f<sub>c</sub>) - 2.254)</td><td>(7)</td></tr><tr><td>MC 1990/99 [43, 44], EC2 [34]</td><td>5k<sub>e</sub>σ<sub>L</sub> for k<sub>e</sub>σ<sub>L</sub> < 0.05f<sub>c</sub><br>0.125f<sub>c</sub> + 2.5k<sub>e</sub>σ<sub>L</sub> otherwise</td><td>(8)</td></tr><tr><td>MC 2010 [36]</td><td>3.5(k<sub>e</sub>σ<sub>L</sub>)<sup>3/4</sup> f<sub>c</sub><sup>1/4</sup></td><td>(9)</td></tr><tr><td>Draft of EC2 [35]</td><td>4k<sub>e</sub>σ<sub>L</sub> for σ<sub>L</sub> < 0.6f<sub>c</sub><br>3.5k<sub>e</sub>σ<sub>L</sub><sup>3/4</sup> f<sub>c</sub><sup>1/4</sup> otherwise</td><td>(10)</td></tr></tbody></table>

All models presume that, at compressive strength, the reinforcing steel is yielding at constant stress. In contrast with steel reinforcement, for aluminum, the transition between elastic and plastic behavior is very smooth, and the compressive strength in all four setups is attained at this transition. Therefore, the value of lateral confinement $\sigma_L$ needs to be determined carefully, and its compatibility with the hoop strain at peak stress must be established. As shown in Fig. 13, a combination of the stress vs. axial and lateral strain diagrams (Fig. 12) and the stress-strain curve for aluminum (Fig. 3) has been used to correctly estimate the corresponding average value of the hoop stress in the metal rings, $\sigma_R$.

The metal rings start yielding (proof stress, dashed arrows) shortly prior to reaching the peak load. At compressive strength (solid arrows), the stress in the rings is approximately 190 MPa. In the post-peak, the insignificant material hardening guarantees an almost constant magnitude of the confinement.
The lateral confinement was subsequently calculated using (2) and the reduction confinement effectiveness factor $k_e$, defined in (3), was evaluated from Mander's formula (7) for all models compared. The values of lateral confinement and effectiveness factor for the individual setups are summarized in Table 6. A graphical comparison of the selected models with the experimental

<figure><img src="image_14.png" /><figcaption>**Fig. 13** Relations between the vertical stress in concrete, axial and average hoop strain, and tangential stress in rings. Solid arrows correspond to the peak load and dashed arrows to the proof stress.</figcaption></figure>

<table><caption>**Table 6** Increase in compressive strength due to lateral confinement.</caption><thead><tr><th>Designation</th><th>Δf<sub>c,c</sub><sup>spec</sup><br>[MPa]</th><th>σ<sub>L</sub> (2)<br>[MPa]</th><th>k<sub>e</sub> (3)<br>[-]</th><th>σ'<sub>L</sub> (4)<br>[MPa]</th></tr></thead><tbody><tr><td>8R_t2</td><td>17.20</td><td>2.85</td><td>0.840</td><td>2.40</td></tr><tr><td>8R_t3</td><td>20.49</td><td>4.37</td><td>0.837</td><td>3.65</td></tr><tr><td>12R_t2</td><td>23.37</td><td>4.28</td><td>0.922</td><td>3.94</td></tr><tr><td>12R_t3</td><td>30.35</td><td>6.55</td><td>0.920</td><td>6.03</td></tr></tbody></table>

Average confinement computed assuming $σ_R = f_Y = 190$ MPa.

data is shown in Fig. 14. The reduced effective confinement $σ'_L$ from (4) and Table 6 is used on the horizontal axis to emphasize the structural effect of the ring layout.

Formula (7), derived by Mander from the failure surface proposed by Willam and Warnke [45], is in best agreement with the present experimental data. This is a good message because it promotes the soundness of the experimental setup developed. Except for the final draft of the Model Code 2010, which nicely matches the three setups with the smallest confinement, the other purely empirical models slightly underestimate the strength increase due to confinement.
<figure><img src="image_15.png" /><figcaption>**Fig. 14** Dependence of the specimen strength on the effective lateral confinement: comparison of experimental data (error bars indicate standard deviation) and prediction models.</figcaption></figure>
# 4 Conclusions

The paper describes an experimental setup recently developed to test concrete cylinders under passive confinement. In contrast to a triaxial test, the proposed setup requires only an ordinary uniaxial testing machine with displacement control, a pair of extensometers, a (single!) high-quality camera, and a computer for data processing. In addition to this, the stress history becomes much closer to that encountered in real structural members, and the specimen size can be almost arbitrary, provided that it remains large enough to properly represent the material and small enough to comply with the capacity of the testing machine. Comparison of the main features of the proposed method with the triaxial testing machine is summarized in Table 7. Despite the numerous differences outlined in this Table, the strength increase due to confinement determined from the proposed tests is in accordance with the widely accepted models from the literature (see Fig. 14) and therefore also with the triaxial tests that were used for their development and calibration.

<table><caption>**Table 7** Comparison of the proposed experimental setup with triaxial testing.</caption><thead><tr><th></th><th>Proposed method</th><th>Triaxial machine</th></tr></thead><tbody><tr><td>Testing machine</td><td>Versatile testing machine with displacement control</td><td>One-purpose and expensive Hoek cell</td></tr><tr><td>Specimen size</td><td>Limited only by the capacity of the testing machine</td><td>Determined using the Hoek cell</td></tr><tr><td>Visual control during testing, onset of localisation</td><td>Direct</td><td>Hindered</td></tr><tr><td>Confinement magnitude</td><td>Sufficient for typical RC members</td><td>Almost arbitrary</td></tr><tr><td>Confinement evolution</td><td>Typical for RC members, triggered by lateral expansion of concrete</td><td>Almost arbitrary, typically constant throughout the experiment</td></tr><tr><td>Confinement distribution</td><td>Non-uniform over the specimen height (friction at supports and hoop spacing)</td><td>Uniform</td></tr><tr><td>Vertical strain measurement</td><td>Reusable extensometers</td><td>Foil strain gauges</td></tr><tr><td>Hoop strain measurement</td><td>DIC analysis for all metal rings</td><td>Foil strain gauges at mid-height</td></tr><tr><td>Needed time for preparation</td><td>Short (only centering)</td><td>Long (instrumentation, assembly, pressure medium, and cleanup)</td></tr></tbody></table>

The confinement is provided by evenly spaced aluminum rings prepared from a tube commonly available on the market. The magnitude of confinement can be adjusted by balancing the tube wall thickness, the spacing, and the yield stress. The uniformity of the spacing was achieved with a set of dummy 3D printed plastic rings removed after casting. Metal rings did not cause spurious restraint in the vertical direction, but provided a very uniform lateral confinement. Additionally, the rings were suitable for applying a random pattern needed for DIC measurements that yielded consistent results with sufficient accuracy and measurement range.

The robustness of the proposed experimental setup was successfully validated using 20 concrete cylindrical specimens with 4 different layouts of
the rings. The experimental scatter decreased with increasing magnitude of confinement and decreasing spacing of the rings.

The results indicate that the most suitable measuring setup is the combination of vertical (physical) extensometers for the axial strain with the DIC tracking the evolution of the hoop strain of the rings. The axial strain is almost constant in the middle half of the specimen height throughout the experiment. In contrast to this, the initially uniform distribution of hoop strain over the specimen height becomes highly nonlinear close to the peak and in the post-peak. Very consistent data can be obtained by averaging the hoop strain of the rings in the region given by the extensometers.

The original research data published in this paper are available at Mendeley Data [41]. This dataset contains also responses of the other experimental setups and presents examples of displacement contours obtained with DIC to illustrate the satisfactory and shear failure modes.

## Funding

Financial support for this work was provided by the Czech Science Foundation (GA ČR), project number 19-25312S (Compression tests with confinement for advanced modeling of concrete columns).

## Declarations

**Conflict of interest** The authors have no conflicts of interest to declare that are relevant to the content of this article.

**CRediT author statement PH:** Conceptualization, Methodology, Formal analysis, Data Curation, Writing - Original Draft, Visualization, VN: Investigation, Writing - Original Draft, PB: Investigation, PP: Investigation, MJ: Conceptualization, Writing - Review & Editing, ZB: Conceptualization, Project administration.

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