# ASR impacts on the behaviour of mortar submitted to a pull-out test inside a X-ray tomograph

Sylvain Langlois, Farid Benboudjema, Maroua Maaroufi, Benjamin

Smaniotto, Fikri Hafid, Amélie Fau

► To cite this version:

Sylvain Langlois, Farid Benboudjema, Maroua Maaroufi, Benjamin Smaniotto, Fikri Hafid, et al. ASR impacts on the behaviour of mortar submitted to a pull-out test inside a X-ray tomograph. Cement and Concrete Composites, 2026, 169, pp.106540. 10.1016/j.cemconcomp.2026.106540. hal-05523144

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ASR impacts on the behaviour of mortar submitted to
a pull-out test inside a X-ray tomograph

Sylvain Langlois<sup>a,*</sup>, Farid Benboudjema<sup>a</sup>, Maroua Maaroufi<sup>a</sup>, Benjamin Smaniotto<sup>a</sup>, Fikri Hafid<sup>b</sup>, Amélie Fau<sup>a</sup>

<sup>a</sup>Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS – Laboratoire de Mécanique Paris-Saclay, 4 Avenue des sciences, Gif-sur-Yvette, 91190, France

<sup>b</sup>RTE, Réseau de Transport d'Électricité, Research & Development, La Défense, 92060, France

Abstract

Multi-scale and multi-physics processes make understanding the mechanical impact of alkali-silica reaction (ASR) on structure challenging. This study investigates ASR's impact on a small-scale mortar foundation subjected to reinforcement pull-out. A 1/50 scale electrical pylon foundation is tested in an X-ray tomograph at different ASR swelling stages. Finite-element-based digital volume correlation is used to analyze the structure's behavior during loading. Results show that the pull-out resistance of small-scale foundations increases with ASR and the failure patterns change. Through measurements of displacements within the mortar, interfacial debonding, and multidirectional swelling, this increase is attributed to reinforcement prestressing caused by ASR swelling. In-situ tests combined with Digital Volume Correlation allow for precise quantification of three-dimensional displacement fields in the specimen. Such a method highlights the effects of alkali-silica reaction, enabling a quantified understanding of the relationship between structural response and pathology progression.

Keywords: Alkali-Silica-Reaction (ASR), Mortar, Pull-out, Computed Tomography (CT), Digital Volume Correlation (DVC)

*Corresponding author
Email address: sylvain.langlois@ens-paris-saclay.fr (Sylvain Langlois)
# 1. Introduction

The construction of concrete foundations and the installation of tetrapod electricity pylons began in the early 20th century in France [1]. These pylons are supported by concrete foundations comprising a chimney and a series of concrete slabs, as illustrated in Figure 1(a). When the tetrapod towers are subjected to overturning moments, two of the four foundations are under tension, as depicted in Figure 1(b), representing the most difficult stress condition for the foundation.

<figure><img src="image_2.png" /><figcaption>Figure 1: Scheme of a typical concrete foundation for high-voltage electricity pylons (a). Pylon forces applied to foundations (b). Only one/two of the four foundations are represented in (a) and (b) figures, respectively.</figcaption></figure>

To meet the growing energy demand, it is essential to guarantee the reliability and resilience of transmission lines, as demonstrated in the study of [2]. Failures of infrastructure components (transmission lines or subsidiary electrical station) can exert a substantially negative impact on the network reliability to meet the energy demand satisfaction, especially in case of correlated failure, when two or more electrical lines linked with the same subsidiary station occurs. As Kliukas et al. highlight [3], an aging infrastructure contributes significantly to mechanical stability issues within the tower/foundation system. The transmission line failures are mainly due to problems inherent to this tower/foundation system, which become evident as the system ages [4].
Several studies have been carried out on pull-out tests of concrete foundation pylons at real or reduced scales, primarily focusing on geotechnical performance, such as soil properties [5], foundation dimensions [6], and the impact of horizontal ground movements [7]. Some studies, like that of Saito [8], examine the failure mechanisms of concrete under anchorage pull-out. However, no research has investigated the impact of concrete aging on its mechanical performance during anchorage pull-out tests.

Regarding the period when the foundations for electricity pylons were built (mainly between the 1940s and the 1960s), many construction defects are suspected, given the lack of national guidelines for the design of concrete foundations subjected to pull-out loading. In the 1940s, Alkali-Silica Reaction (ASR) was first identified [9] and, apart from the knowledge that expansion pressure was generated by the precipitation of a silica gel [10], its mechanisms and mitigation strategies were far from being understood as they are today [11]. Thus, Alkali-Silica Reaction is a pathology that may occur due to the local use of siliceous limestone aggregates and cements with high alkali content. As foundations are subjected to water exchanges with the environment, all criteria are met for alkali-silica reaction to develop. The French operator responsible for high-voltage transmission lines, Réseau de Transport d'Électricité (RTE), has recently begun to investigate the durability of these structures. Internal studies reveals the confirmed presence of silica gel in 10 out of 398 foundations [12].

No comprehensive study has yet been conducted to understand the impact of Alkali-Silica Reaction on the pull-out capacity and cracking behavior of foundations for electrical pylons. The only conducted studies are technical assessments within companies, emphasizing the occurrence of ASR in these structures. These reports concern foundations in the United States [13, 14], as shown in Figures 2(a) and 2(b). The problem can therefore be considered a global issue, although it remains poorly documented. The work focuses on ASR, but the authors wish to emphasize that other pathologies, such as delayed ettringite formation, may also occur. Any pathology other than ASR is beyond the scope of this study.
<figure><img src="image_3.png" /><figcaption>Figure 2: (a) A shallow foundation of a monopod pylon [13] and (b) a shallow foundation of a tetrapod pylon [14], both used for electricity transmission lines. Map cracking due to alkali-silica reaction is visible through the exudation of the white gel.</figcaption></figure>

The Alkali-Silica-Reaction (ASR) is a physico-chemical process that causes significant deterioration of concrete structures worldwide [15]. The mechanisms leading to stress and cracking have been studied for decades [9, 16]. The reaction occurs when the reactive silica contained in the aggregates reacts with the alkalis present in the pore solution. Concrete degradation is a gradual and continuous process described by four main sequential steps [17, 11]. Over time, the alkaline pore solution fosters the dissolution of the metastable silica contained in the aggregates, producing a nano-colloidal silica solution that then precipitates as the so-called silica gel, comprising several types of ASR reaction products. The final step has long been described as the hydration of the silica gel, which was thought to swell and generate expansion pressure on both the aggregates and cement matrix. This hypothesis has recently been invalidated. Studies have shown that the water uptake of ASR products is significantly lower than that of calcium-silicate-hydrate (C-S-H), the main product of cement hydration [18]. The mechanism now identified as responsible for expansion pressure is the solidification pressure exerted by the electrostatic repulsion between negatively charged silicate surfaces and negatively charged polynuclear silica in the pore solution [19]. This solidification pressure induces
cracking of the aggregates and the cement paste, ultimately leading to macroscopic swelling of the material.

Given the severity of ASR, early detection of this pathology using appropriate methods can help companies significantly reduce repair and rehabilitation costs, while extending the life of affected structures through preventive maintenance programs [20]. In the case of affected old structures, such as the concrete foundations for electrical pylons or nuclear power plant [21], the aim is no longer to prevent ASR but to understand its impact on the mechanical response of the structure. Initially, experimental studies were carried out to quantify the impact of ASR at material level (concrete, mortar) using standardized compression and tensile tests [22, 23, 24]. These measurements are useful for providing sets of parameters for future modeling but do not represent the structural behavior. The results indicate that material properties vary significantly with ASR development, and may be biased by antagonist effect such as cement hydration and accelerated conditions (temperature, humidity, aggregate type and casting direction). The only possible consensus concerns the Young's modulus, which decreases because of the cracking of aggregates and cement paste. The reduction in Young's modulus correlates with both the number and width of cracks, making it a reliable damage indicator compared to other mechanical properties, such as compressive and tensile strength [25].

Besides, studies have been carried out directly at the scale of the structure. Morenon et al. [26] conducted experiments to understand the impact of ASR on the flexural performance of a three-meter reinforced concrete beam. As the beam ages, stiffness remains unchanged and cracking is delayed during a four-point bending test. Ferche et al. [27] led an experimental campaign to investigate the performance of reinforced shear walls composed of reinforced concrete subjected to ASR. The maximum shear strength remained unchanged, but the initial stiffness increased and the ductility decreased. Both authors suggest that the reinforcement bars restrain swelling and undergo stressing due to swelling induced by the ASR. Studies at the structural scale focus only on stiffness and ultimate load capacity derived from measurements of macroscopic
quantities: applied forces, stroke and structure displacement (i.e., vertical and lateral displacements). This leads to limited information on the relationship between ASR expansion and structural response. The effect of the ASR expansion at the structural scale needs to be understood. The findings highlight the need for improved methods that account for restraint and anisotropic expansion.

Experimental studies have been conducted to understand the effect of restraint on ASR-induced swelling. Dunant and Scrivener [28] highlighted how uniaxial stress influences the orientation of lateral surface cracks in cylindrical reactive concrete specimens, noting reduced lateral expansion under longitudinal load. Recent research has focused on the effect of reinforcement bars on reactive concrete, in particular through pull-out tests on prismatic specimens. Takahashi et al. [29] found that longitudinal reinforcement increases lateral swelling without affecting longitudinal expansion. Villemure et al. [24] reported a loss of pull-out strength as ASR develops, attributed to cracks near the interface. Interestingly, the ultimate pull-out force increases for higher ASR swelling, which is supposed to be due to confinement pressure from concrete expansion. These findings contradict those of Li et al. [30], who observed that if restraint swelling occurs longitudinally, the pull-out force first increases with ASR before decreasing beyond an expansion threshold of 0.035%.

These restraint phenomena occurring within the material can only be observed and measured using appropriate experimental techniques. Recently, advanced imaging methods based on Computed Tomography (CT) have proven effective in understanding aggregate and cement matrix cracking due to ASR development [31]. These techniques enable quantifying damage growth in concrete due to ASR, such as pore volume and 3D crack patterns [32]. With this perspective of using images for mechanical studies, Teramoto et al. [33] employed Digital Image Correlation on a flat concrete prism to measure large strains due to ASR cracks. The study demonstrates that image correlation is relevant for assessing crack growth and macroscopic expansion. However, a limitation is that the study only computed 2D quantities under free swelling conditions and without any mechanical loading. Besides, to the authors's knowl-
edge, no information has been obtained at the interface between reinforcement and concrete/mortar. It is crucial to assess this interface to predict the bearing capacity of reinforced concrete structures affected by ASR. In recent years, advances in image correlation techniques have enabled the experimental identification of relevant mechanisms at the microscale, both in 2D [34, 35] and in 3D [36].

The present study aims to understand the behavior of a scaled-down mortar structure affected by alkali-silica reaction (ASR) during a pull-out test. The structure is a 1/50 scale model of an electrical pylon foundation, with a Glass fiber reinforced polymer (GFRP) reinforcement anchored at its center to perform the pull-out test. These tests are conducted at different stages of ASR development and are performed in-situ within an X-ray tomograph. A Finite-Element Digital Volume Correlation (FE-DVC) method with elastic regularization is used to quantify the 3D displacement field of the sample based on an image-based mesh that accounts for the geometry of the foundation and reinforcement. On the one hand, the study shows that tomography coupled with Digital Volume Correlation (DVC) captures the effect of ASR development in the structure, namely the heterogeneous and anisotropic swelling induced by ASR and the opening of the mortar-reinforcement interface. On the other hand, the combined effect of ASR and pull-out loading is assessed by measuring the macroscopic specimen displacements, interfacial debonding, failure modes, and pull-out capacity. This analysis provides a better understanding of the influence of ASR-induced swelling on the pull-out resistance of the small-scale structure.

Section 2 summarizes the formulation and curing protocol for a reactive mortar that induces the alkali-silica reaction within the foundation model. Details of the small-scale structure are provided, along with the experimental setup used for pull-out testing. The complete experimental methodology is described, including time-lapse X-ray tomography during ASR development, in-situ pull-out tests performed within the tomograph, and the global Digital Volume Correlation technique used for post-processing. Section 3 first presents the
mechanical characterization of the reactive mortar using standard procedures.
The main results of ASR development in the foundation model are then pre-
sented, including anisotropic swelling, structural effects, and interface opening
with the reinforcement. Finally, the results of the pull-out tests performed at
different stages of ASR development are analyzed, comprising pull-out capac-
ity, cracking, and interfacial debonding.

## 2. Materials and Methods

The experimental campaign consists of the following steps:

* A mortar is formulated to induce alkali-silica reaction in a short period of time.

* The longitudinal swelling and mechanical properties of the mortar are quantified with standard testing procedures.

* A 1/50 scale model of an electrical pylon foundation is designed and manufactured with the reactive mortar.

* The foundation models are submitted to ASR development ex-situ (outside the X-ray laboratory tomograph). Time-lapse X-ray CT scans are acquired at different stages of ASR development.

* At each stage of ASR development, pull-out tests are performed in-situ within the tomograph on the 1/50 scale foundation models.

This section outlines the formulation of the reactive mortar and the ag-
ing protocol to induce ASR. Afterwards, the design of the foundation model
and the protocol for ex-situ ASR development and in-situ pull-out tests are de-
tailed. Finally, the global Digital Volume Correlation method for quantifying
the three-dimensional kinematic fields is described.
## 2.1. Formulation of the reactive and reference mortars

A reactive mortar is formulated to induce an alkali-silica reaction, resulting in significant swelling in a short period of time. The pessimum ratio is targeted, although the exact mass of reactive silica required is not known. The inert sand used is a limestone sand from the Boulonnais quarry, and the reactive sand is a crushed siliceous limestone sand from the Tournaisis quarry, the latter being known to have caused ASR in the past [37]. Previous studies, carried out with the same inert and reactive sands, have shown that a mortar formulation containing 50% (by mass) reactive and 50% non-reactive sand leads to the highest expansion when reactive particles smaller than 0.63 mm are removed [38]. More recent studies have demonstrated that reactive particles from the same quarry, smaller than 0.16 mm do not induce expansion, whereas aggregates between 0.315 mm and 0.630 mm generate the highest expansion amplitudes [39].

Based on these studies, aggregate diameters measured using standardized tests [40] range from 0.25 to 4 mm. They are composed of 50 % (by mass) reactive siliceous limestone aggregates and 50 % non-reactive limestone aggregates. The chemical composition of the reactive aggregate is given in Table 1.

<table><caption>Table 1: Chemical composition of the reactive siliceous limestone (% by mass)</caption><thead><tr><th>Aggregate</th><th>SiO<sub>2</sub></th><th>Al<sub>2</sub>O<sub>3</sub></th><th>Fe<sub>2</sub>O<sub>3</sub></th><th>CaO</th><th>MgO</th><th>Na<sub>2</sub>O</th><th>K<sub>2</sub>O</th><th>SO<sub>3</sub></th></tr></thead><tbody><tr><td>Siliceous Limestone</td><td>15.4</td><td>2.2</td><td>0.9</td><td>42.2</td><td>1.4</td><td>0.1</td><td>0.6</td><td>1.1</td></tr></tbody></table>

The reactive silica content of siliceous limestone sand from the Tournaisis quarry is approximately 6.9 % [41]. The used cement CEM II/A-LL 42.5R has an alkali content of 0.96%, according to the manufacturer data sheet. The mortar is manufactured with a water to cement ratio W/C = 0.5 and a sand to cement ratio S/C = 3, which corresponds to the proportions of a non-reactive standardized mortar according to NF-EN-196-1 [42]. A 1 M sodium hydroxide solution is used instead of water to increase the alkali content in the pore solution, giving an alkali content Na₂Oeq of 9.4 kg.m⁻³mortar, providing an ade-
quate supply of alkaline material for subsequent reactions. Table 2 summarizes the mortar formulation, including the density of each component measured according to standards [43]. The reactive mortar is abbreviated ASR. A standardized non-reactive mortar is also manufactured following [42]; this mortar is abbreviated NR and used for swelling comparison purposes on prism specimens.

<table><caption>Table 2: Formulation of the reactive and non-reactive mortars. (1) Mortar affected by ASR. (2) Sound mortar.</caption><thead><tr><th>Designation</th><th>Density (kg.m<sup>-3</sup>)</th><th>ASR (1) (kg.m<sup>-3</sup>)</th><th>NR (2) (kg.m<sup>-3</sup>)</th></tr></thead><tbody><tr><td>Siliceous limestone 0.25 – 4 mm</td><td>2670</td><td>766</td><td>0</td></tr><tr><td>Limestone 0.25 – 4 mm</td><td>2670</td><td>766</td><td>0</td></tr><tr><td>Limestone 0 – 4 mm</td><td>2700</td><td>0</td><td>1533</td></tr><tr><td>CEM II/A-LL</td><td>3110</td><td>511</td><td>511</td></tr><tr><td>Water</td><td>1000</td><td>0</td><td>0</td></tr><tr><td>NaOH 1M</td><td>1040</td><td>256</td><td>0</td></tr></tbody></table>

The mortar is then poured into molds for mechanical characterization. After demolding, the specimens are stored in autogenous curing conditions using two layers of plastic film and two layers of aluminum foil at 20°C for 28 days to foster cement hydration in a non-aggressive environment. The specimens are then submerged in a 1M NaOH solution to maintain a stable alkaline concentration in interstitial water, fully saturated conditions and prevent alkali leaching. The bath temperature is raised to 60°C to accelerate reaction kinetics [44]. In the following, the term *ASR-aging* refers to accelerated ASR development fostered by the submersion into the alkaline aqueous solution.

## 2.2. ASR-induced swelling on prismatic specimens

ASR swelling is measured on three prismatic specimens of 4 × 4 × 16 cm in accordance with standards to measure shrinkage [45]. The variability between samples is represented by the unbiased standard deviation. The evolution of the longitudinal swelling of the standardized non-reactive and reactive mortars (Table 2) is plotted in Figure 3. First, during the 28-days autogenous
curing period, the reactive mortar experiences autogenous shrinkage of up to 300 µm/m. This shrinkage is much larger than the one of the non-reactive mortar (50 µm/m). Longitudinal swelling is evident for the reactive mortar during curing under 1M NaOH at 60°C, exhibiting rapid kinetics over the first few weeks. It rapidly exceeds (after 4 days of ASR-aging) the threshold of 400 µm/m used to assess the aggregate reactivity in French standard FD P18 542, noting that the procedure itself is not followed because the cure is performed in an aqueous solution of NaOH and not at 100% HR. The swelling rate decreases with time until reaching a plateau. Mortar after 119 days of curing (i.e., 91 days of ASR-aging) is considered as reference for 100% ASR swelling (around 5500 µm/m). Two other swelling stages of interest are 35% ASR swelling and 65% ASR swelling.

The specimen nomenclature is as follows: ASRXXX indicates the time step of ASR-aging at which the specimen is analyzed. XXX specifies the swelling ratio, i.e., the prism longitudinal swelling normalized by the swelling level observed after 91 days of ASR-aging. It can be 0 (0% of swelling), 35 (35% of swelling), 65 (65% of swelling), or 100 (100% of swelling) as seen in Figure 3.

<figure><img src="image_4.png" /><figcaption>Figure 3: Mean longitudinal swelling of reactive and non-reactive specimens (4x4x16 cm) with respect to the age (variability is characterized by the non-biased standard deviation between three specimens).</figcaption></figure>
## 2.3. In-situ pull-out tests and ex-situ ASR-aging

A 1/50 scaled model of an electrical pylon foundation made of reactive mortar is designed. The structures follow the cure to foster the reaction and are monitored by time-lapse X-ray CT. At each ASR-aging stage, in-situ pull-out tests are performed to assess the structural response.

### 2.3.1. Foundation model

The geometry of the specimen shown in Figure 4(a) is directly inspired by electrical pylon foundations of the French network in Figure 1(a) and represents a 1/50 scaled model of these structures. The structure features a Glass Fiber Reinforced Polymer (GFRP) reinforcement with a Young's modulus of 60 GPa according to the manufacturer datasheet, anchored in a mortar foundation whose properties are given in Section 3.1. GFRP was specifically chosen for its chemical composition and density, which enable low X-ray attenuation. Unlike steel, which causes high signal attenuation and can create tomographic artifacts such as beam hardening, the GFRP associated with mortar allows a wide dynamic range to be covered without saturating, maximizing the 8-bit encoding depth available as shown in a previous study [46]. Real-scale foundation anchorage is typically made of steel, which has a Young's modulus approximately seven times greater than that of mortar, compared to approximately twice that of GFRP. Since the anchorage remains within its elastic domain during the pull-out loading, the use of GFRP results in a decrease in structural stiffness and a reduction in strain discontinuity at the interface compared to steel. Consequently, the loss of chemical adhesion and mortar cracking are expected to occur at higher pull-out forces when using GFRP.

The reinforcement denoted ① in Figure 4(a) has a diameter of 0.8 cm, and 0.9 cm if the ribs are included. The reinforcement is anchored over a length of 4.3 cm in the foundation, designated by ②. The foundation consists of a chimney and two slabs (slab 1 and slab 2) of 2.8 cm, 1 cm, and 1 cm high, respectively. The lower part of the mortar foundation (3 cm high) is glued directly to an Acrylonitrile Butadiene Styrene (ABS) collar, which is then attached to the
bottom platen of the testing machine. A steel clamp, designed according to the ER collet standard (ISO 15488-2003), is used to hold the GFRP reinforcement and is attached to the testing machine, as illustrated in Figure 4(b). The region of interest (highlighted in yellow in Figure 4(a)) comprises the upper part of the mortar foundation and the lower part of the reinforcement, thus minimizing boundary effects. Displacement is imposed by the lower platen, allowing the foundation to be pulled out of the reinforcement, as shown in Figure 4(c).

<figure><img src="image_5.png" /><figcaption>Figure 4: Specimen composed of a GFRP reinforcement ① and a mortar foundation ②, region of interest in yellow (dimension in cm) (a), in-situ testing machine and specimen inside the tomograph (b), boundary conditions applied on the specimen (c).</figcaption></figure>

The mortar is poured into an ABS mold. A fixing template ensures the reinforcement is sealed, centered, and vertical in the foundation. The specimen is removed from the mould after 24 hours.

### 2.3.2. *Sole effect of ASR swelling on the structure*

This project aims to study the impact of ASR on small-scale foundations. The foundation models follow the curing protocol described in Section 2.1. The effect of swelling due to the alkali-silica reaction alone on the structure is assessed (Section 3.2.1) by scanning the same structure at the different ASR-aging stages. The same sample is scanned when it reaches 35%, 65%, and 100% ASR swelling, and compared with the reference stage (0% swelling). For each specimen, following the acquisition of the first scan, a successive scan is performed
in the same tomographic configuration to quantify measurement uncertainties
associated with the tomographic acquisition and the DVC method (see Sec-
tion 2.4).

2.3.3. *Combined effect of ASR swelling and pull-out on the structure*

To understand the impact of ASR on the mechanical response of the struc-
ture model, pull-out tests are carried out at each time step (0%, 35%, 65%, and
100% swelling). Three models are tested for each stage of ASR-aging to assess
the variability.

The tension-compression-torsion machine (Figure 4(b)) is employed in-situ
in the X-ray tomograph (North Star Imaging X50+). The foundation is loaded
incrementally with a vertical stroke displacement at a speed of 2 µm/s. Seven
CT scans are performed at intermediate loading steps to observe changes in
the microstructure under the effect of mechanical stress. Each scan, consisting
of 1,200 projections, lasts 30 minutes. Tomograph parameters are given in Ap-
pendix A in Table A.5.

All the tests have the same overall sequence. Two examples illustrating
the force-displacement curves of the pull-out test before ASR-aging (0% ASR
swelling) and after ASR-aging (100% ASR swelling) are shown in Figures 5(a)
and 5(b), respectively. A preload of 50 N is applied to ensure correct contact
between all setup parts and stabilize the specimen for the first scan. A 10-
minute dwell time is observed before each scan to minimize relaxation effects
during scans. Scan 0 is a reference scan for computing displacement fields
by Digital Volume Correlation (DVC). Immediately after Scan 0, a repeat scan
(Scan 00) is performed to assess measurement uncertainties (see Section 2.4).
Subsequent scans are performed as follows: Scan 1 after a load of 200 N, Scan 2
after a load of 550 N, Scan 3 after a load of 920 N, and Scan 4 as close as possible
to the maximum load. Finally, a post-mortem scan (Scan 5) is performed after
the specimen has been completely broken. The force measured at the beginning
of each scan will hereafter be denoted as F.
<figure><img src="image_6.png" /><figcaption>Figure 5: Overall in-situ test sequence exemplified on two pull-out force vs stroke curves before ASR-aging (0% ASR swelling) (a) and after ASR-aging (100% ASR swelling) (b)</figcaption></figure>

### 2.3.4. Summary of the experimental campaign

In addition to the measurements on the foundation models, various specimens are prepared to perform standardized mechanical characterization of the reactive mortar. The measurements include Young's modulus *E* (initial secant modulus during the first loading cycle) with compressive strength *f*<sub>c</sub> along the longitudinal direction on 11 × 22 cm cylindrical specimens (in accordance with standards [47, 48]), and flexural strength *R*<sub>f</sub> determined by three-point bending tests on 7 × 7 × 28 cm prismatic samples (following RILEM recommendations [49]). Each measure is repeated on three specimens.

The experimental campaign is outlined in Figure 6. All the tests are summarized in Table 3 with their corresponding accelerated aging.

<figure><img src="image_7.png" /><figcaption>Figure 6: Experimental campaign with the time steps of each experiment</figcaption></figure>
The specimen labelling scheme is as follows: ASRXXX-Y, where XXX refers to the swelling ratio observed on the 4 × 4 × 16 cm prisms compared to the swelling at 91 days of ASR-aging. The number Y identifies the specimen number among the three tested specimens.

The foundation model scanned along the ASR-aging process (as explained in Section 2.3.2) is designated ASR100-1. This specimen is finally subjected to a pull-out test after 91 days of accelerated aging.

<table><caption>Table 3: Experiments conducted along with the corresponding accelerated aging and swelling ratio.</caption><thead><tr><th>Specimen's name</th><th>Time of accelerated aging (days)</th><th>Swelling ratio</th><th>Test</th></tr></thead><tbody><tr><td>ASR0-[1;3]</td><td>0</td><td>0%</td><td>Compressive test<br>Bending test<br>Model pull-out</td></tr><tr><td>ASR100-1</td><td>0</td><td>0%</td><td>Model CT scan during aging</td></tr><tr><td>ASR35-[1;3]</td><td>14</td><td>35%</td><td>Compressive test<br>Bending test<br>Model pull-out</td></tr><tr><td>ASR100-1</td><td>14</td><td>35%</td><td>Model CT scan during aging</td></tr><tr><td>ASR65-[1;3]</td><td>35</td><td>65%</td><td>Compressive test<br>Bending test<br>Model pull-out</td></tr><tr><td>ASR100-1</td><td>35</td><td>65%</td><td>Model CT scan during aging</td></tr><tr><td>ASR100-[1;3]</td><td>91</td><td>100%</td><td>Compressive test<br>Bending test<br>Model pull-out</td></tr><tr><td>ASR100-1</td><td>91</td><td>100%</td><td>Model CT scan during aging</td></tr></tbody></table>
## 2.4. Computation of displacement field with Digital Volume Correlation

To exploit the 4D (space and time) information provided by the time-lapse X-ray CT scans during ASR-aging (Section 2.3.2) and the X-ray CT scans acquired during in-situ pull-out test (Section 2.3.3), global DVC is employed to measure the three-dimensional displacement fields at different time points. Two volumes $f(\mathbf{x})$ (in the reference configuration) and $g(\mathbf{x})$ (in the deformed configuration) are correlated by considering the gray level residuals

$$ \rho(\mathbf{x}, \mathbf{u}) = f(\mathbf{x}) - g(\mathbf{x} + \mathbf{u}(\mathbf{x})). \quad (1) $$

The displacement $\mathbf{u}(\mathbf{x})$ is expressed in terms of finite-element discretization using 4-nodes tetrahedra (T4). It is computed by minimizing the image residual $\Phi_c$ over the entire Region Of Interest (ROI) highlighted in yellow in Figure 4(a)

$$ \Phi_c^2(\mathbf{u}) = \sum_{\text{ROI}} (f(\mathbf{x}) - g(\mathbf{x} + \mathbf{u}(\mathbf{x})))^2. \quad (2) $$

To quantify voxel-scale information over a refined discretization, DVC was regularized using a regularization length by adding an elasticity-based term derived from the equilibrium gap to the cost function [50]. This penalization restricts the search space for displacement fields to be mechanically admissible over a selected regularization length. Regularization including damage allows displacements to be measured with low uncertainties in the vicinity of cracks [51, 52]. The development and robustness of the method are detailed in a separate publication [46] and will therefore not be discussed further here. Digital Volume Correlation parameters are given in Appendix A in Table A.6.

The finite-element mesh is created from the segmentation of the reference scan (Scan 0) using Avizo® data visualization and analysis software. The mesh for the ASR0-1 specimen is given in Figure 7(a); it accurately represents the geometry of the GFRP reinforcement and mortar foundation and involves split nodes at the interface to allow for displacement jumps between both materials. The mesh properties used for analyzing the pull-out tests ASR0-1 and ASR100-1 are detailed in Appendix B in Table B.7.
<figure><img src="image_8.png" /><figcaption>Figure 7: (a) Mesh for the DVC procedure from the reference Scan 0. (b) Debonding measurement with displacement jump $\llbracket u \rrbracket$ between split interfacial nodes of the mesh.</figcaption></figure>

By splitting the nodes at the interface, debonding can be quantified through displacement jumps $\llbracket u \rrbracket$ between mortar and GFRP reinforcement. For the further study, the vertical component of the displacement jump (i.e., in the direction of the pull-out test) and the normal debonding component (i.e., the normal of the interfacial node seen in Figure 7(b)) will be quantified to analyze the interfacial behavior. The method for computing debonding is detailed in Appendix B.

Since volume correlation gives access to quantitative measurements of displacement fields, it is crucial to assess the noise floor level associated with its implementation. Measurement uncertainties on the quantity of interest ●, where ● refers to the full-field displacement $u(x)$ or any kinematic quantity computed from it (such as debonding), are quantified as three times the non-biased standard deviation $\text{std}(●)$ of the quantity ● by registering two scans [53] in the reference configuration (Figure 5). All kinematic quantities are defined at the nodes of the finite-element mesh for the calculation. By assuming the measurement noise as a Gaussian normal distribution, 99% of the displacements of interest ● of the repeat scan are below the measurement uncertainty.

In the following DVC results, all reported displacements correspond to the so-called mechanical fields after subtracting the rigid body motions from the
measured displacement, and will be written **u**. All the equations of the rigid body motions formulation are detailed in Appendix C.

### 3. Results

This section presents and analyzes the most significant results of the experimental campaign. First, the evolution of the mechanical properties of the mortar is discussed. Then, the DVC method is applied to the CT scans acquired at different instants during ASR-aging and to the CT scans obtained during in-situ pull-out tests to investigate the impact of ASR on the mechanical behavior of the foundation model. Given the (very) rich experimental dataset provided by the in-situ pull-out tests, only the ASR0 (before ASR-aging) and ASR100 (after ASR-aging) structure models are analyzed using the DVC method.

#### 3.1. *Evolution of the mechanical properties of the reactive mortar*

Experiments are carried out to characterize the mechanical properties of the reactive mortars (Table 2). Mechanical properties are identified at the four swelling stages of interest: 0%, 35%, 65%, and 100% of the swelling measured at 91 days of ASR-aging.

Compressive strength is equal to 28.9 MPa after cement hydration (28 days) as shown in Figure 8(a). Then, during ASR-aging, the compressive strength increases almost linearly with the swelling. The increase in compressive strength can be explained in several ways. Cement hydration continues for several months after manufacturing [54], improving the mortar's mechanical properties over time. The silica gel produced during the reaction migrates into the interconnected porosity between the aggregate and the cement paste. Once filled with gel, this porosity increases the strength of the material, since the gel has a non-zero elastic modulus [55, 56]. To verify these hypotheses, experiments were conducted on the same mortar (ASR in Table 2) after a 28-day autogenous cure. These samples were then submerged in water at 20°C for 35 days, assuming that ASR is far less fostered than for specimen submerged in
60°C aqueous solution of NaOH. The corresponding measurements are shown in green in Figure 8. At the same age, the reactive mortar exhibits 7% higher compressive strength. Not only does the hydration reaction continue, but the silica gel produced appears to fill the air voids and the cracks caused by the reaction.

After cement hydration (at 28 days), Young's modulus, presented in Figure 8(b), is measured at 26.2 GPa. It undergoes 31% of reduction after 14 days of ASR-aging, followed by a slight recovery as the reaction progresses. Cracks due to ASR, as well as dissolution of aggregates induce a decrease of the Young's modulus, surpassing the aforementioned positive effects which explained the increase of compressive strength. As expected, the Young's modulus of the sample stored in water at 20°C for 35 days increased due to the ongoing hydration of the cement.

The Poisson ratio $v$ (Figure 8(c)) is measured on 11 × 22 cm cylindrical specimens using LVDT sensors placed in the extensometer to measure transverse strain $\epsilon_t$ and longitudinal strain $\epsilon_l$ during the test. The initial value of the Poisson ratio is about 0.27. The Poisson ratio decreases with ASR-aging by 9% and 22% after 14 days and 35 days of ASR-aging, respectively. The average value increases after 65% swelling to 0.22 at 100% swelling.

The flexural strength shown in Figure 8(d) decreases slightly from 5,450 N to 4,800 N after 14 days of ASR-aging. It then increases to 5,800 N and returns almost to its initial value at 100% swelling. Overall, the ultimate flexural load remains constant during ASR-aging, given the standard deviation of the measurements. The results of the sample without reaction, after 35 days of water curing, show a 23% increase in flexural strength compared to the aged sample. This demonstrates that hydration is occurring, although it is offset by the previously explained negative effects of the reaction.

It should be noted that the characterization of the reactive mortar is performed on specimens of different sizes. ASR-induced expansion is measured on 4 × 4 × 16 cm prism specimens, while compressive strength and Young's modulus are measured on 11 × 22 cm cylindrical specimens and flexural strength
on 7 × 7 × 28 cm prism specimens. However, specimen size and shape are known to influence ASR expansion, namely small-sized specimens exhibit lower expansion, and cylindrical specimens expand less than prismatic ones [38]. Various explanations have been proposed to explain this phenomenon, including gel permeation effects [57] and alkali-leaching effects [58]. In particular, at 60 °C, the rate and amount of alkali leaching have been identified as the main factors controlling ASR expansion.

Considering the ASR size effect, it is possible that the cementitious matrix was already cracked at ASR35 for the 11 × 22 cm and 7 × 7 × 28 cm specimens. Furthermore, the silica gel may have diffused through these cracks without generating sufficient expansive pressure to fracture the material further. As a result, the measured properties may benefit more from positive antagonistic effects (previously discussed) than from the negative effects of ASR, which could explain the rebound of the Young's modulus observed from ASR65. ASR size effect, together with quasi-brittle material size effect [59] prevent a direct extrapolation of the following mortar properties to the structure model, as well as the amplitude and kinetics of expansion measured on 4 × 4 × 16 cm prism specimens. The foundation models are expected to exhibit slower and lower expansion than the 4 × 4 × 16 cm prisms. This effect will be investigated using Digital Volume Correlation in the following Section 3.2.1.
<figure><img src="image_9.png" /><figcaption>Figure 8: Evolution of the mechanical properties of the mortar with ASR progression, compressive strength (a), Young's Modulus (b), Poisson ratio (c), and flexural ultimate load (d). Error bars represent the non-biaised standard deviation between the three specimens.</figcaption></figure>

## 3.2. Impact of Alkali-Silica Reaction on the Mechanical Behavior of the Foundation Model

The effect of the alkali-silica reaction on a structure, a foundation model in this case, is studied. First, the behavior of the structure during internal swelling is assessed. Then, pull-out tests are conducted on foundations at various aging stages.

### 3.2.1. DVC study of foundations affected by ASR swelling at various aging stages

The foundation model ASR100-1 is scanned at four aging stages of the alkali-silica reaction (Table 3), i.e., at 0, 14, 35 and 91 days of ASR-aging. A sagittal section of the CT scans is reported in Figure 9 for each aging stage. The section slice is the same for the four images. One may see that rigid body motions with an amplitude of some voxels occurred between scans due to an
expected misplacement when placing the specimen in the tomograph. These motions are removed from the DVC analysis as given by Equation C.1.

Figure 9(a) shows the specimen prior to ASR-aging. The mesostructure of the mortar is clearly visible, including aggregates, cement paste, and air voids. This composition associated with the tomograph parameters results in a strong material phase contrast within the mortar. The GFRP reinforcement, on the other hand, exhibits a lower contrast at the current resolution, and the observed heterogeneities are attributed to the resin matrix. Overall, the gray levels of the specimen effectively utilize the full dynamic range, enhancing the visualization of mesostructural details. At 35% of maximum swelling, Figure 9(b) shows numerous cracks. These cracks occur mainly in the aggregates, with some extending into the cement paste. Cracking is the main cause of the decrease in Young's modulus [60], explaining the significant drop of the mortar Young's Modulus observed in the ASR35 samples. In addition, it can be seen in Figure 9(c) that cracks extend into the cement paste. A comparison of sections at different aging stages reveals that the gray levels of some aggregates have decreased. It is unlikely that this effect is due to the precipitation of ASR products within aggregate cavities, as this phenomenon occurs at a scale much finer than the effective resolution of 45 µm/vx, and the uptake of calcium is believed to be too small to produce a measurable change in the gray-level residual [61]. Moreover, such a phenomenon would increase X-ray attenuation and therefore the gray level. In the present case, the observed decrease in gray level is instead attributed to partial dissolution of the aggregate caused by the highly alkaline pore solution. Figure 9(d) reveals significant crack propagation in the mortar. It is also worth noting that the gray level intensity of some of the air voids has increased. These pores appear to be filled with a fluid or a solid that could be silica gel [31]. It is unlikely to be water alone, as both sub-surface and bulk air voids are filled.
<figure><img src="image_10.png" /><figcaption>Figure 9: Sagittal sections of CT scans (ASR100-1 specimen) at different stages of ASR-aging</figcaption></figure>

Displacements due to swelling are computed using DVC from the reference scan $f(\mathbf{x})$ at 0% of swelling (Figure 9(a)) and deformed scans $g(\mathbf{x})$ at 35%, 65% and 100% of swelling (Figures 9(b), 9(c), 9(d)). To assess the reliability of the measured displacements, uncertainty analysis is conducted at each time step (0%, 35%, 65%, and 100% of swelling) from two successive CT scans under similar loading conditions. The uncertainties are obtained by averaging the standard deviations of the displacement field components $u_x, u_y$, and $u_z$. The
resulting uncertainties are 1.9, 1.4, 0.9, and 1.2 µm for the four instants, respectively.

The components of swelling displacement in the sagittal plane (Oxz) (cartesian reference frame depicted in Figures 4(c) and 7(a)) are displayed in Figure 10 for the 100% affected specimen, i.e., at 91 days of ASR-aging. The displacement $u_x$ (Figure 10(a)) is heterogeneous in the chimney, with a slight increase near the interface. The change in diameter due to the slab results in a heterogeneous displacement, also visible in the displacement $u_y$ (symmetry of $u_x$ if the axisymmetry was perfect) in Figure 10(b). Figure 10(c) shows the displacement $u_z$, indicating that the mortar moves due to ASR-induced swelling. Displacements $u_x$ and $u_y$ vanish in the reinforcement, but not the displacement in vertical direction $u_z$ which corresponds to the restraint of mortar swelling.

<figure><img src="image_11.png" /><figcaption>Figure 10: Sagittal sections of the displacement field $u_x$ (a), $u_y$ (b), $u_z$ (c) (in µm) for the reference ASR swelling (Specimen ASR100-1). Green dots represent the interface between the GFRP reinforcement and the mortar foundation.</figcaption></figure>

The maximum principal strains measured are shown in Figure 11 for all stages of swelling: 35% (Figure 11(a)), 65% (Figure 11(b)), 100% (Figure 11(c)). These strains are not uniformly distributed within the foundation. High strain levels are concentrated near the interface and near the edges where the foundation diameter changes.
<figure><img src="image_12.png" /><figcaption>Figure 11: Sagittal sections of the maximum principal strain $\epsilon_1$ (Specimen ASR100-1) at 35% of swelling (a), 65% of swelling (b), and 100% of swelling (c)</figcaption></figure>

To better understand the multidirectional swelling, the strain $\epsilon_{xx}$, $\epsilon_{yy}$, $\epsilon_{zz}$ are shown in Figure 12 at the last aging stage. In the reinforcement, $\epsilon_{xx}$ in Figure 12(a) and $\epsilon_{yy}$ in Figure 12(b) are near 0. In the mortar, those values are near the maximum principal strain. Indeed, the mortar can expand freely in the radial direction; there is no radial confinement as the reaction develops. If the axisymmetry was perfect, $\epsilon_{xx}$ would be exactly equal to $\epsilon_{yy}$. It appears in Figure 12(c) that the mortar has lower strains $\epsilon_{zz}$ than in the other two directions $\epsilon_{xx}$ and $\epsilon_{yy}$. The reinforcement is in extension in direction z, especially in the chimney part, with strong strain discontinuities at the interface. These measurements indicate that the reinforcement creates axial restraint of the mortar with an imperfect interface between the reinforcement and the mortar. While the mortar features free surfaces at the outer boundaries of the foundation, its interface with the reinforcement transfers axial forces. Thus, the vertical strains $\epsilon_{zz}$ in the mortar have a lower amplitude near the reinforcement.
<figure><img src="image_13.png" /><figcaption>Figure 12: Sagittal sections of the strain field $\epsilon_{xx}$ (a), $\epsilon_{yy}$ (b), $\epsilon_{zz}$ (c) at 100% swelling (Specimen ASR100-1 after 91 days of ASR-aging)</figcaption></figure>

The macroscopic longitudinal strain $\epsilon_l$ of the mortar and reinforcement and the radial strain of the mortar due to ASR swelling (which includes the restraint by the GFRP) can be derived from the displacement field. The macroscopic average longitudinal strain is estimated from the vertical displacement averaged over the top $\overline{u_z^{top}}$ and bottom $\overline{u_z^{bottom}}$ surfaces and the vertical distance $h$ between these two surfaces

$$ \epsilon_l = \frac{\overline{u_z^{top}} - \overline{u_z^{bottom}}}{h} \qquad (3) $$

The top and bottom nodes are the blue nodes in Figure 13(a) for mortar and the green nodes in Figure 13(b) for GFRP reinforcement.
<figure><img src="image_14.png" /><figcaption>Figure 13: Nodes used to estimate swelling (a) of mortar (blue and yellow nodes for longitudinal and radial swelling, respectively), (b) of reinforcement (green nodes for longitudinal swelling)</figcaption></figure>

The radial strain $\epsilon_{rr}(z, \theta)$ is computed from the radial displacement of the outward perimeter nodes highlighted in yellow in Figure 13(a). Each node highlighted in yellow has an opposite node in the (Oxy) plan, detected by maximizing the distance between the two. The radial swelling depends on the vertical coordinate $z$ and the angular coordinate $\theta$; it is known from the radial displacement of the pairs of node $\{u_r(z, \theta), u_r^{opp}(z, \theta)\}$ and the distance between them denoted $d(z)$, which is in fact the diameter of the slab (or chimney) of the foundation

$$ \epsilon_{rr}(z, \theta) = \frac{u_r(z, \theta) - u_r^{opp}(z, \theta)}{d(z)} \quad (4) $$

Figure 14 shows the average macroscopic radial strain due to ASR swelling along the height of the foundation with a vertical moving average over 50 voxels. The opacities around the curves represent measurement uncertainties (Section 2.4). Radial strain exhibits minimal values at the top of the foundation and reaches its maximum at the bottom. Changes in diameter cause abrupt variations in radial swelling as structural effects.
<figure><img src="image_15.png" /><figcaption>Figure 14: Macroscopic radial swelling of the foundation along the height of the foundation (Specimen ASR100-1). The measurement uncertainties, defined as three times the standard deviation of the swelling of two scans in the same configuration, are shown by opacity around the curves.</figcaption></figure>

To compare longitudinal and radial swelling at the structural level, the radial strain $\epsilon_{rr}$ is also averaged over the height of the specimen to obtain the transverse strain denoted $\epsilon_t$,

$$ \epsilon_t = \overline{\epsilon_{rr}} = \left( \frac{u_r(z) - u_r^{opposite}(z)}{d(z)} \right). \qquad (5) $$

Macroscopic swelling components are compared with the longitudinal swelling measured on 4 × 4 × 16 cm prisms in Figure 15. Uncertainties given by the standard deviation between measurements on the three samples are represented by error bars (Section 2.4). Swelling is anisotropic whatever the age of the sample: the radial swelling is significantly larger than the longitudinal swelling because the reinforcement restrains swelling. After 14 days and 35 days of ASR-aging in NaOH at 60°C, the swelling within the small-scale structure remains lower than the longitudinal swelling measured on the prism. From 91 days, the radial swelling of the foundation becomes more significant than the longitudinal swelling measured on prisms. These DVC measurements validate the ASR size effects described in Section 3.1. After 14 days and 35 days of ASR-aging
in NaOH at 60°C, the swelling within the small-scale structure remains lower than the longitudinal swelling measured on the 4 × 4 × 16 cm prism. Nevertheless, from 91 days, the radial swelling of the foundation becomes more significant than the longitudinal swelling measured on prisms, revealing an *expansion transfer* mechanism that greatly amplifies the radial expansion [62], outweighing the ASR size effect.

In addition, the longitudinal strain within the reinforcement is $\epsilon_l^{GFRP} = 0.20\%$ after 91 days of ASR-aging which differs significantly from the longitudinal strain within the mortar. Thus, an interfacial jump between mortar and reinforcement has been created by the ASR swelling.

<figure><img src="image_16.png" /><figcaption>Figure 15: Evolution of the swelling of the foundation specimen (Specimen ASR100-1) and prism specimens with ASR-aging. Average longitudinal swelling of 4x4x16 cm prism mortar and variability uncertainty on three specimens. Longitudinal and transverse strain of the foundation and reinforcement with their respective measurement uncertainties.</figcaption></figure>

Debonding $[u]$ at the interface between reinforcement and foundation is calculated during the development of the alkali-silica reaction. Figure 16(a) shows the vertical displacement jump $[u_z]$ assessed over the circumference with a moving vertical average over a 50-voxel window, with measurement uncertainties represented by shading around the curves. At 35% swelling, the interface exhibits a small vertical debonding of less than 20 µm. Negative values of the vertical debonding indicate that the mortar has moved further downwards than the reinforcement (Equation (B.1) and Figure 4(c)). At 65%
swelling, the upper half of the interface shows a small vertical debonding similar to that of the specimen with 35% swelling. Vertical sliding between mortar and reinforcement increases with the ASR-aging in the lower part of the small-scale structure. It reaches -50 µm and -80 µm for 65% and 100% of the reference swelling, respectively. At 100% of the reference swelling, positive displacement jumps occur in the upper part of the structure up to an amplitude of 15 µm. Positive jump values indicate that the mortar nodes have a larger vertical displacement than the reinforcement interfacial nodes in the positive z-direction.

Figure 16(b) shows the normal debonding [[u_n]] for the various stages of swelling. Whatever the swelling stage, this component of the debonding is positive over the whole interface since the interface is opening. Swelling of the mortar leads to a significant interface opening with an amplitude of about 30 µm already at 35% swelling. It increases significantly with swelling up to 50 µm and 90 µm at 65% and 100% of the reference swelling, respectively. The interface opening varies with position; it is minimal at the top of the foundation and maximal in the first slab. This interface opening leads to a lack of contact between mortar and reinforcement.

<figure><img src="image_17.png" /><figcaption>Figure 16: Displacement jump profiles along the height of the reinforcement (Specimen ASR100-1) for 35%, 65% and 100% of the reference swelling (at 91 days of ASR-aging): [[u_z]] (a) and [[u_n]] (b)</figcaption></figure>
### 3.2.2. Pull-out tests on sound and ASR-affected foundation models

Three pull-out tests are carried out, in-situ within the tomograph, for the four aging stages (0%, 35%, 65% and 100% of the swelling at 91 days of ASR-aging). The average pull-out ultimate force, defined as the maximum force sustained by the sample during the test, is shown in Figure 17. The uncertainties, defined as one time the standard deviation between the three tests, are 23.5%, 27.8%, 43.5%, and 19.5%, respectively, of the average value for the four stages. The pull-out resistance is 1,200 N (average of three tests) for the sound sample and remains barely unchanged at 35% swelling. The pull-out resistance increases with ASR swelling by 22% and 44% at 65% and 100% reference swelling, respectively.

<figure><img src="image_18.png" /><figcaption>Figure 17: Pull-out ultimate force with respect to the swelling stages (uncertainties represent the variability between samples as one time the standard deviation)</figcaption></figure>

Loading curves for the three pull-out tests without expansion (ASR0) and after complete ASR-aging (ASR100) are shown in Figures 18(a) and 18(b), respectively. Magenta lines indicate force vs. stroke during scan acquisitions. Failure is unstable, with a straight force drop. However, failure is slightly more stable for sound samples.
<figure><img src="image_19.png" /><figcaption>Figure 18: Pull-out force vs stroke during the in-situ tests for the three specimens ASR0 (a) and ASR100 (b)</figcaption></figure>

Digital Volume Correlation is performed to measure the evolution of the
mechanical displacement **u**(**x**) during each test. The uncertainty is obtained
by correlating the repeat scan (Scan 00) with the reference scan (Scan 0), both
acquired under a preload of 50 N. For the sound samples ASR0-1, ASR0-2, and
ASR0-3, the uncertainties about the displacement are 2.1, 6.9, and 2.4 µm, re-
spectively. For the affected samples ASR100-1, ASR100-2, and ASR100-3, the
uncertainties are 0.9, 1.4, and 1.5 µm, respectively. The unusually high uncer-
tainty observed for sample ASR0-2 results from the metallic filament in the X-
ray tube (the cathode used to emit electrons), which had to be replaced during
the corresponding pull-out test.

The macroscopic response of the specimens is characterized in Figure 19.
The macroscopic displacement $u_z^{\text{specimen}}$ of the specimen is defined as the rela-
tive displacement in the $z$ direction between the upper part of the GFRP rein-
forcement (highlighted in blue in Figure 13(a)) and the bottom part of the mor-
tar foundation (highlighted in green in Figure 13(b)). A few post-peak scans
have been acquired, but piecewise linear interpolation is particularly known
to be unrealistic for post-peak behavior under tension loading [60].

For each aging stage, the force-displacement curves exhibit a similar trend
for the three samples tested. The repeatability of the experiments is satisfy-
ing. Displacement uncertainties are represented at the top of the figure with an
error bar. The load uncertainty is equal to 0.02 % of the 20 kN load capacity, i.e., 4 N. The macroscopic displacement of the specimen is lower than the dis- placement imposed by the machine because, during loading, deformations in the machine's components induce parasitic displacements, which in this case exceed the specimen's displacement. Additionally, the displacement at peak force is lower for ASR100 samples (Figure 19(b)) than for ASR0 samples (Fig- ure 19(a)). These results highlight a significant difference in rigidity between sound and ASR-affected samples, with sound samples exhibiting damageable behavior rather than purely elastic behavior.

<figure><img src="image_20.png" /><figcaption>Figure 19: Macroscopic displacement of the three specimens ASR0 (a) and ASR100 (b) measured by DVC</figcaption></figure>

Among all performed tests, two will be examined in detail using Digital Volume Correlation, the sample without ASR-aging ASR0-1 from Figure 18(a), and the sample after 100% of swelling ASR100-1 from Figure 18(b). The lat- ter corresponds to the sample scanned throughout the ASR-aging process, as outlined in Section 3.2.1.

Figure 20 presents the sagittal sections of the specimen before the peak load (Scan 4) and after the specimen failure (Scan 5) of samples ASR0-1 and ASR100-1. The progression of cracks induced by the pull-out test can then be analyzed visually in 2D. In the ASR0-1 sample at Scan 4 (Figure 20(a)), cracks appear in the chimney (highlighted by a red arrow). Despite the higher force applied
at Scan 4 of the affected sample ASR100-1, no cracks appear due to the pull-out test. However, the CT scan reveals cracks resulting from the alkali-silica reaction (ASR), with many aggregates showing cracks extending into the mortar. At Scan 5, after failure, both samples show significant damage. The sound sample (Figure 20(c)) exhibits a crack at the junction between Slab 1 and Slab 2, it is responsible for the specimen failure. For the affected sample (Figure 20(d)), a crack also forms at this junction. An additional crack extends from the chimney edge to the base of the reinforcement, deviating from the horizontal crack observed in ASR0 (Figure 20(a)), indicating a change in failure mode. These various pull-out cracks propagate through the mortar and aggregate interfaces.
<figure><img src="image_21.png" /><figcaption>(a) ASR0-1 - Scan 4 (F=1,102 N) - Pre-failure</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>(b) ASR100-1 - Scan 4 (F=1288 N) - Pre-failure</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>(c) ASR0-1 - Scan 5 (F=397 N) - Post-mortem</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>(d) ASR100-1 - Scan 5 (F=333 N) - Post-mortem</figcaption></figure>

Figure 20: ASR and pull-out cracks observed in the sound ASR0 (a,c) and 100% affected ASR100 (b,d) mortars for Scans 4 (a,b) and Scans 5 (c,d). Forces are measured at the beginning of the scans. Cracks have been highlighted in red to improve visibility.

Regularized Finite-Element based Digital Volume Correlation computes the
mechanically admissible displacement field by solving Equation 2. It assumes
that each voxel of the deformed scan $g$ can be transported to the reference scan
$f$ by adding a displacement $u$. The high values of the gray-level residual $\rho(x)$
from Equation (1) indicate variations that are not accounted for by the displacement field **u**. For ex-situ experiments performed outside the tomograph, such as ASR-aging in Section 3.2.1, these residuals can stem from chemical changes with the partial dissolution of several aggregates in Figure 9(c). In mechanical tests performed in-situ within the tomograph, residuals primarily result from a displacement field **u**(**x**) that is not mechanically admissible, preventing full minimization of ρ(**x**). In the present study, the finite-element mesh assumes a continuous displacement field in the mortar on one side and in the reinforcement on the other side. The measured displacements may be discontinuous at the interface due to image-based meshing. The continuity of displacement in the mortar is no longer valid as soon as cracking occurs [63]. Thus, the application of DVC between the reference Scan 0 and the post-mortem Scan 5 provides a scalar field ρ(**x**) that informs on crack locations and damage mechanisms due to the pull-out loading. One advantage of the scalar field is that it provides information related to crack resolution, namely a higher gray-level residual corresponds to a wider crack under opening conditions [64]. For this reason, no segmentation of this scalar field is performed.

Figures 21(a) and 21(b) show post-mortem gray level residual for the sound ASR0-1 and aged ASR100-1 samples, respectively. This location of cracks validates the change of failure modes according to ASR-aging: the crack does not propagate into the chimney for the aged sample. Appendix D presents the same sagittal sections from the pre-failure and post-mortem CT scans, and crack location for the four other tests, ASR0-2, ASR0-3 and ASR100-2, ASR100-3, to validate the repeatability of failure modes measurements.
<figure><img src="image_25.png" /><figcaption>Figure 21: DVC residual ρ(x) showing the cracks in the specimen without ASR (ASR0-1) (a) and with ASR (ASR100-1) (b). The edge of the foundation is represented by the gray voxels. The small residual levels have been made transparent to reveal the presence of cracks.</figcaption></figure>

The interfacial jumps [$u_z$] and [$u_n$] are calculated, along the reinforcement, for the two pull-out tests at loading stage corresponding to Scans 2 and 4 acquired before failure. Figure 22 displays moving vertical averages over 50 voxels to highlight the main trends. The opacities around the curves represent measurement uncertainties.

At Scan 2, the displacement jump [$u_z$] is smaller for the affected specimen ASR100 than the sound sample ASR0 (Figure 22(a)). For the aged specimen, [$u_z$] is very small along the interface. For the sound specimen, [$u_z$] is slightly higher in the slabs than in the chimney. Figure 22(b) shows the normal debonding at the interfacial nodes [$u_n$] at Scan 2. The trend exhibits no normal debonding, except for ASR0, where an interface opening begins to occur between the chimney and the first slab.

At Scan 4, Figures 22(c) and 22(d) show different behaviors between the affected and the sound sample. For ASR0, [$u_z$] displays an abrupt transition
from negative to positive, indicating the presence of a crack at the interface dur-
ing loading, with a vertical crack opening of about 80 µm. This crack is visible
in the CT scans of Figures 20(a) and 20(c). An increase of $[u_z]$ is observed for
ASR100, particularly in the slabs Figure 22(c). Regarding $[u_n]$ in Figure 22(d),
interface opens in the crack zone for the sound sample.

ASR seems to impact the interface behavior since the debonding are much lower for the structure affected by the reaction than the sound structure. For the affected sample, debonding appears in the slabs, whether they are open of in frictional conditions. For the sound sample, debonding is driven by the mortar cracks that propagate to the interface.

In addition, no crack is detected at the interface with ASR for the considered
Scan 2 and Scan 4, the structure affected by the ASR has better load resistance.
<figure><img src="image_26.png" /><figcaption>Figure 22: Displacement jumps $\llbracket u_z \rrbracket$ (a,c) and $\llbracket u_n \rrbracket$ (b,d) along the height of the reinforcement for the sound mortar ASR0-1 and 100% affected mortar ASR100-1 at Scan 2 (c,d) and Scan 4 (g,h). In details, at Scan 2, $F_{\text{ASR0-1}}=537$ N and $F_{\text{ASR100-1}}=542$ N, and at Scan 4, $F_{\text{ASR0-1}}=1,102$ N and $F_{\text{ASR100-1}}=1,288$ N.</figcaption></figure>

Figures 23 and 24 show nodal displacement jumps drawn onto the interface of the GFRP reinforcement. Debonding fields appear to be measurable and significant.

At Scan 2, displacement jumps $\llbracket u_z \rrbracket$ have higher amplitude for the sound specimen (Figure 23(a)) than for the affected sample (Figures 23(b)), the latter having a relatively uniform amplitude along the interface, as seen previously on average in Figure 22(a). Interface closure (negative value of $\llbracket u_n \rrbracket$) appears above the reinforcement ribs, and interface opening (negative value of $\llbracket u_n \rrbracket$) below the ribs (Figure 24), revealing that the increase in pull-out force is con-
trolled by the interaction between the ribs and the mortar [65]. At Scan 4, Figure 23(c) displays a strong displacement gradient, associated with crack, on the sound specimen. The crack partially follows the reinforcement ribs in Figure 24(c). In the ASR-affected structure, the reported debonding field shows no presence of displacement gradient associated with interfacial cracks, whether in opening or frictional conditions.

<figure><img src="image_27.png" /><figcaption>Figure 23: Displacement jumps $\ll u_z \gg$ along the height of the reinforcement for the sound mortar ASR0-1 (a,c) and the 100% affected mortar ASR100-1 (b,d) at Scan 2 (a,b) and Scan 4 (c,d)</figcaption></figure>
<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /><figcaption>Figure 24: Displacement jumps $\ll u_n \gg$ along the height of the reinforcement for the sound mortar ASR0-1 (a,c) and the 100% affected mortar ASR100-1 (b,d) at Scan 2 (a,b) and Scan 4 (c,d)</figcaption></figure>

**4. Conclusion**

To study the response of structures affected by alkali-silica reaction (ASR) under pull-out stress, an extensive experimental campaign was conducted, focusing on both material properties and foundations model at 1/50 scale. A mortar was manufactured and stored in autogenous curing conditions for 28 days before being submitted to an accelerated alkali-silica reaction, reaching 5500 µm/m swelling at 91 days of accelerated aging. Experiments were carried out at 0%, 35%, 65%, and 100% of final swelling.
In terms of mortar properties, the ASR-aging increases the compressive
strength from 28.9 MPa to 37.8 MPa due to filling of air voids and racks by the
gel together with further hydration. The Young's modulus shows a different
evolution. It reached its minimum value at 35% swelling, due to aggregates
dissolution and the numerous cracks appearing in the material, which sur-
passed positive effects raised to explain compressive strength increase. Then,
the Young's modulus increased slightly with the development of ASR swelling.
With regard to the ultimate flexural load, little change was measured during
ASR-aging, given the variability of measurements on the three tested speci-
mens. It is not straightforward to predict evolution of mechanical properties
due to antagonist effects occurring during ASR.

Concerning the models studied as mini-structures, in-situ pull-out tests of
a GFRP reinforcement embedded in a small-scale mortar foundation were car-
ried out in an X-ray tomograph. In addition to the pull-out force, the full 3D
displacement fields of the structure were quantified using a regularized FE-
DVC method. An image-based 3D mesh was developed to accurately repro-
duce the reinforcement and foundation geometries with twin nodes at the in-
terface. Debonding was measured from the discontinuous description of GFRP
and mortar displacements at the interface. The results showed that the pull-out
resistance of small-scale foundations increased by 44% with the development
of ASR. Failure modes are also modified. After swelling, failure of the structure
occurred through cracks at the slab junctions, whereas cracks appeared and
propagated in the chimney for the sound structure. These changes cannot be
explained by mortar properties alone, as only compressive strength increases
and was expected to have minimal influence on structural response during the
pull-out test. Digital Volume Correlation shows that the swelling of the mor-
tar foundation creates a positive radial debonding (i.e., an interface opening)
of the mortar from the reinforcement but no relative displacement in the axial
direction. The reinforcement then undergoes an extension of 2000 µm, which
pre-stresses the mortar foundation model, thereby improving its pull-out re-
sistance. During pull-out tests, interfacial displacement jump measurements
indicate that ASR affects the debonding and overall reduces the vertical com-
ponent in the direction of the pull-out loading. No cracks are detected at the
interface in the ASR-affected structure, as opposed to the sound structure.

In-situ tests combined with regularized FE-DVC proved effective in ana-
lyzing the mechanical behavior of small-scale foundations, providing insights
into the impact of ASR. Failure was analyzed through 3D gray-level residual
of the DVC procedure, and displacements measured with an uncertainty of
about 1 µm (for a CT scan resolution of 45 µm) for precise spatiotemporal mea-
surements of swelling and debonding at the interface between reinforcement
and foundation. Since the method relies on X-ray Computed Tomography, it
is currently limited to small structure sizes. Thus, the conclusions extracted
from the experimental study are subject to size effects, whether arising from
the chemical nature of ASR [57, 58] or from the quasi-brittle behavior of mor-
tar [59]. Thus, the experimental results reported herein should be extrapolated
with caution to full-scale structures. The three-dimensional kinematic fields
extracted from these imaging tools can be directly linked to mechanical mod-
els by comparing them to simulation results. One advantage of the method
is that the same finite-element mesh designed from 3D images for Digital Vol-
ume Correlation can be used for finite-element simulations. Such experimental
techniques make it possible to validate models at a reduced scale, which can
subsequently be applied to real-scale structures if the size effect is correctly
described from other experimental campaigns.

The kinematic results obtained offer valuable insights for testing constitu-
tive models of cement-based materials and interfaces with rebars, when such
materials are subjected to ASR and mechanical loading. Indeed, it can pro-
vide boundary conditions for numerical simulations and numerical results can
be compared to experimental ones globally (force vs displacement) but also lo-
cally: strain field due to swelling, crack openings and displacement jump at the
interface during mechanical loading. This approach is currently undertaken.
## Funding

This research was partly funded by the French National Research Agency (ANR) under the "HEAT COFFEE" project (grant "ANR-22-CHIN-0007-01") and the French Transmission System Operator (RTE).

## CRediT authorship contribution statement

**Sylvain Langlois:** Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing - original draft, Writing - review & editing. **Farid Benboudjema:** Conceptualization, Formal analysis, Funding acquisition, Project administration, Supervision, Validation, Writing - review & editing. **Maroua Maaroufi:** Conceptualization, Supervision, Writing - review & editing. **Benjamin Smaniotto:** Data curation, Methodology, Resources, Software. **Fikri Hafid:** Funding acquisition, Project administration. **Amélie Fau:** Conceptualization, Data curation, Formal analysis, Methodology, Supervision, Validation, Visualization, Writing - review & editing.

## Declarations of competing interests

The authors have no competing interests to declare that are relevant to the content of this article.

## Data availability

Data will be made available on request.

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Glossary

<table><caption>Table 4: The Digital Volume Correlation and mechanical notations used in this study.</caption><thead><tr><th>Digital Volume Correlation notation</th><th>Mechanical notation</th></tr></thead><tbody><tr><td><b>x</b> Discrete voxel position</td><td>ε Strain tensor</td></tr><tr><td><b>f</b>(<b>x</b>) Gray level of the reference volume</td><td>ε<sub>l</sub> Longitudinal strain</td></tr><tr><td><b>g</b>(<b>x</b>) Gray level of the deformed volume</td><td>ε<sub>t</sub> Transverse strain</td></tr><tr><td><b>ρ</b>(<b>x</b>) Difference in gray level between two volumes</td><td>κ<sub>0</sub> Failure strain of the mortar</td></tr><tr><td>Φ<sub>c</sub> Image residual</td><td>E Young's modulus</td></tr><tr><td><b>u</b> Three dimensional displacement field</td><td>ν Poisson ratio</td></tr><tr><td><b>u</b><sub>RBM</sub> Rigid Body Motion</td><td>R<sub>f</sub> Flexural strength</td></tr><tr><td><b>t</b> Rigid Body Translation</td><td>f<sub>c</sub> Compressive strength</td></tr><tr><td><b>w</b> Rigid Body Rotation</td><td>F Pull-out force</td></tr><tr><td><b>X</b> Position of the node in the mesh</td><td>d Distance between a pair of nodes</td></tr><tr><td>ℓ<sub>reg</sub> Regularization length</td><td></td></tr><tr><td>l̃<sub>reg</sub> Effective regularization length</td><td></td></tr><tr><td>[[<b>u</b>]] Three dimensional displacement jump</td><td></td></tr></tbody></table>
# Appendix A. Tomograph hardware and Digital Volume Correlation parameters

The tomograph hardware parameters used to scan the specimens during the *in-situ* pull-out test and ASR-aging are listed in Table A.5.

<table><caption>Table A.5: CT hardware parameters</caption><tr><td>Tomograph</td><td>North Star Imaging X50+</td></tr><tr><td>X-ray source</td><td>XRayWorX XWT-240-CT</td></tr><tr><td>Target / Anode</td><td>32.5 W (reflection mode)</td></tr><tr><td>Filter</td><td>none</td></tr><tr><td>Voltage</td><td>210 kV</td></tr><tr><td>Current</td><td>150 µA</td></tr><tr><td>Focal spot size</td><td>5 µm</td></tr><tr><td>Tube to detector</td><td>615 mm</td></tr><tr><td>Tube to object</td><td>105 mm</td></tr><tr><td>Detector</td><td>Dexela 2923</td></tr><tr><td>Definition</td><td>1536 × 1944 pixels (2 × 2 binning)</td></tr><tr><td>Number of projections</td><td>1200</td></tr><tr><td>Angular amplitude</td><td>360°</td></tr><tr><td>Frame average</td><td>15 per projection</td></tr><tr><td>Frame rate</td><td>15 fps</td></tr><tr><td>Acquisition duration</td><td>Around 30 min</td></tr><tr><td>Reconstruction algorithm</td><td>Filtered back-projection</td></tr><tr><td>Gray Levels amplitude</td><td>16 bits</td></tr><tr><td>Resolution</td><td>45 µm/vx</td></tr></table>

The DVC parameters for computing the displacement fields are given in Table A.6.
<table><caption>Table A.6: DVC analysis parameters</caption><thead><tr><th>DVC software</th><th>Correli 3.2 [66]</th></tr></thead><tbody><tr><td>Image filtering</td><td>none</td></tr><tr><td>Element length (mean)</td><td>16 vx</td></tr><tr><td>Shape functions</td><td>linear (T4 elements)</td></tr><tr><td>Mesh</td><td>see Table B.7 and Figure 7(a)</td></tr><tr><td>Matching criterion</td><td>penalized sum of squared differences</td></tr><tr><td>Interpolant</td><td>linear</td></tr><tr><td>Regularization length l<sub>reg</sub> for analyzing ASR swelling</td><td>64 voxels</td></tr><tr><td>Regularization length in damaged elements l&#771;<sub>reg</sub> for analyzing ASR swelling</td><td>No detection</td></tr><tr><td>Regularization length l<sub>reg</sub> for analyzing the pull-out tests</td><td>64 voxels</td></tr><tr><td>Regularization length in damaged elements l&#771;<sub>reg</sub> for analyzing the pull-out tests</td><td>16 voxels</td></tr></tbody></table>

## Appendix B. Meshing and debonding quantification via Digital Volume Correlation

The properties of the meshes used to compute displacement fields for the ASR0 pull-out and ASR100 pull-out tests are given in Table B.7.

<table><caption>Table B.7: Mesh properties for the ASR0 pull-out test and the ASR100 aging and pull-out tests</caption><thead><tr><th>Mesh for pull-out test</th><th>Elements</th><th>Nodes</th><th>Element size</th><th>Aspect ratio</th></tr></thead><tbody><tr><td>ASR0</td><td>69,854</td><td>14,625</td><td>18±3 vx</td><td>&lt; 20</td></tr><tr><td>ASR100</td><td>71,674</td><td>14,961</td><td>18±3 vx</td><td>&lt; 20</td></tr></tbody></table>

The interface between the reinforcement and the mortar foundation is made
of split nodes, allowing for the estimation of the interfacial displacement jumps

$$ \llbracket \mathbf{u} \rrbracket = \mathbf{u}_{\text{mortar}}^{\text{interface}} - \mathbf{u}_{\text{GFRP}}^{\text{interface}}, \qquad (B.1) $$

where $\mathbf{u}_{\text{GFRP}}^{\text{interface}}$ and $\mathbf{u}_{\text{mortar}}^{\text{interface}}$ denote the displacement of interfacial nodes be- longing to the GFRP and mortar, respectively [67]. The displacement jumps are then decomposed into opening $\llbracket u_n \rrbracket$ and tangential slip $\llbracket u_t \rrbracket$ as shown in Figure 7(b)

$$ \llbracket \mathbf{u} \rrbracket = \llbracket u_n \rrbracket \mathbf{e}_n + \llbracket u_t \rrbracket \mathbf{e}_t, \qquad (B.2) $$

where $\mathbf{e}_n$ is the normal to the GFRP reinforcement. The jump can also be ana- lyzed from its three components in cylindrical coordinates

$$ \llbracket \mathbf{u} \rrbracket = \llbracket u_r \rrbracket \mathbf{e}_r + \llbracket u_{\theta} \rrbracket \mathbf{e}_{\theta} + \llbracket u_z \rrbracket \mathbf{e}_z. \qquad (B.3) $$

## Appendix C. Rigid body motions formulation

Rigid body motions are included in the measured displacement fields. The mechanical displacement of the sample $\mathbf{u}$ is computed from the measured dis- placement $\mathbf{u}_{\text{DVC}}$ by subtracting the rigid body motions $\mathbf{u}_{\text{RBM}}$

$$ \mathbf{u} = \mathbf{u}_{\text{DVC}} - \mathbf{u}_{\text{RBM}}. \qquad (C.1) $$

The rigid body motions $\mathbf{u}_{\text{RBM}}$ consist of a translation vector $\mathbf{t}$ and a rotation vector $\omega$

$$ \mathbf{u}_{\text{RBM}} = \mathbf{t} + \omega \wedge \mathbf{X} \qquad (C.2) $$

computed using the finite-element mesh as underlying description, with $\mathbf{X}$ the positions of the nodes. $\mathbf{u}_{\text{RBM}}$ is written as linear combination of six indepen- dent modes $\alpha$

$$ \mathbf{u}_{\text{RBM}} = \mathbf{N}\alpha \qquad (C.3) $$

describing the three components of translation $\mathbf{t}$ and the three components of rotation $\omega$

$$ \alpha = (t_x, t_y, t_z, \omega_x, \omega_y, \omega_z). \qquad (C.4) $$
If one considers a mesh node of index *i* with coordinates **X**<sub>*i*</sub> = (X<sub>*i*</sub>, Y<sub>*i*</sub>, Z<sub>*i*</sub>), the shape function describing rigid body motions denoted **N**<sub>*i*</sub> writes

$$
\mathbf{N}_i = \begin{pmatrix} 1 & 0 & 0 & 0 & Z_i & -Y_i \\ 0 & 1 & 0 & -Z_i & 0 & X_i \\ 0 & 0 & 1 & Y_i & -X_i & 0 \end{pmatrix}. \qquad (C.5)
$$

By writting **u**<sub>RBM</sub> in a single column vector, **N** will be a matrix of size [3 × N<sub>nodes</sub>, 6], where N<sub>nodes</sub> denotes the number of mesh nodes. α is obtained by minimizing the least-squares residual such that

$$
\alpha_{\text{opt}} = \operatorname{argmin} (\| \mathbf{u}_{\text{DVC}} - \mathbf{N}\alpha \|^2). \qquad (C.6)
$$

**Appendix D. Failure modes for other unaffected (ASR0) and 100% affected (ASR100) specimens**

Sagittal sections of the scan before the peak force, i.e., pre-failure, and post-
peak, i.e., post-mortem, are shown in Figures D.25 and D.26 for other ASR0 and
ASR100 specimens, respectively. Without ASR (Figure D.25), cracks appear
and propagate first at the junction between the chimney and the first slab. In
samples affected by ASR (Figure D.26), cracks are non-existent in this area. In
post-mortem specimen, cracks are visible at the junction between slabs for all
specimens. These images validate the repeatability of the analysis of the failure
modes outlined in Section 3.2.2.

It can be seen that the quality of the ASR0-2 CT scans is poorer than that of
the others, due to technical problems with the tomograph. This poorer qual-
ity would increase uncertainties on DVC measurements, as observable in Fig-
ure 19(a) compared with ASR0-1 and ASR0-3.
<figure><img src="image_32.png" /><figcaption>(a) ASR0-2 - Scan 4 (F=880 N) - Pre-failure</figcaption></figure>

<figure><img src="image_33.png" /><figcaption>(b) ASR0-2 - Scan 7 (F=209 N) - Post-mortem</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>(c) ASR0-3 - Scan 4 (F=954 N) - Pre-failure</figcaption></figure>

<figure><img src="image_35.png" /><figcaption>(d) ASR0-3 - Scan 5 (F=274 N) - Post-mortem</figcaption></figure>

Figure D.25: ASR and pull-out cracks for sound specimens ASR0-2 and ASR0-3. Forces are measured at the beginning of the scan acquisition.
<figure><img src="image_36.png" /><figcaption>Figure D.26: ASR and pull-out cracks for 100% affected specimens ASR100-2 and ASR100-3. Forces are measured at the beginning of the scan acquisition.</figcaption></figure>

Crack location of the four post-mortem samples using DVC is illustrated in Figure D.27. In sound mortars (Figures D.27(a,b)), cracks appear between the first slab and the bottom of the chimney. In 100% affected mortar (Figures D.27(c,d)), cracks are below the chimney. These observations confirm the previous analyses.
<figure><img src="image_37.png" /><figcaption>(a) ASR0-2 - Scan 7 (F=209 N) - Post-mortem</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>(b) ASR0-3 - Scan 5 (F=274 N) - Post-mortem</figcaption></figure>

<figure><img src="image_39.png" /><figcaption>(c) ASR100-2 - Scan 5 (F=141 N) - Post-mortem</figcaption></figure>

<figure><img src="image_40.png" /><figcaption>(d) ASR100-3 - Scan 5 (F=102 N) - Post-mortem</figcaption></figure>

Figure D.27: DVC residuals ρ(x) of the post-mortem specimens showing the cracks in the sound mortars ASR0-2 (a) and ASR0-3 (b), and 100%ASR affected mortars ASR100-2 (c) and ASR100-3 (d). The edges of the foundation are represented by the gray voxels. The small residual levels have been made transparent to render the large values visible and reveal the cracks.