# In-situ deformation and fracturing characteristics of geomaterials under dynamic loading: Insights from ultra-high-speed X-ray phase contrast imaging and DEM modelling

H.C. Wang, K. Liu, B. Lukic, W.R. Hu, C.H. Braithwaite, J. Zhao, A. Rack, Q.B. Zhang

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## ► To cite this version:

H.C. Wang, K. Liu, B. Lukic, W.R. Hu, C.H. Braithwaite, et al. In-situ deformation and fracturing characteristics of geomaterials under dynamic loading: Insights from ultra-high-speed X-ray phase contrast imaging and DEM modelling. International Journal of Rock Mechanics and Mining Sciences, 2024, 175, pp.105656. 10.1016/j.ijrmms.2024.105656. hal-05128574

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# In-situ deformation and fracturing characteristics of geomaterials under dynamic loading: Insights from ultra-high-speed X-ray phase contrast imaging and DEM modelling

H.C. Wang<sup>a</sup>, K. Liu<sup>b</sup>, B. Lukic<sup>c</sup>, W.R. Hu<sup>a, *</sup>, C.H. Braithwaite<sup>d</sup>, J. Zhao<sup>a</sup>, A. Rack<sup>c</sup>, Q.B. Zhang<sup>a</sup>

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## ARTICLE INFO

### Keywords:

X-ray phase contrast imaging (XPCI)

X-ray digital image correlation (XDIC)

Dynamic fracturing

In-situ deformation

Discrete element method (DEM)

## ABSTRACT

Dynamic loadings, such as earthquakes, blasts, and impacts, are commonly encountered in mining and underground infrastructures, and therefore predicting the failure of geomaterials, including cement, concrete and rock at high strain rates holds significant importance. The exploration of fracturing and deformation properties in materials under dynamic loadings is essential for comprehending the failure process and mechanisms. In this study, a made-to-order split-Hopkinson-pressure bar (SHPB) is integrated with ultra-high-speed X-ray phase-contrast-imaging (XPCI) and X-ray digital image correlation (XDIC) analysis. This combination allows for the observation and quantification of in-situ through-volume fracturing process and deformation fields of materials such as cement, concrete and basalt under dynamic compression tests featuring various impact velocities. Furthermore, a coupled continuum-discrete element modelling is undertaken to validate the experimental findings and offer insights into the damage processes and failure mechanisms at various levels. Scanning electron microscopy (SEM) is also employed to characterise fracture surface morphologies, unveiling distinct failure mechanisms influenced by crack patterns originating from a microscale. The outcomes indicate that the XDIC technique is applicable when the material microstructure provides sufficient texture. The deformation of geomaterials under high loading rates can also be validated through numerical models utilising the discrete element method (DEM). Both experimental and numerical results consistently demonstrate that as the impact velocity increases, fracturing patterns transfer from interfacial cracks to transgranular cracks. Additionally, fracture initiation positions transition from the specimen's edge towards the middle. In case of higher heterogeneity, crack patterns evolve from tensile-dominant cracks to mixed (tensile-shear) cracks due to the generation of interfacial cracks, further enhancing plastic deformation. SEM results reveal that distinct fracture morphologies, such as roughness and flatness, are influenced by heterogeneous microstructures like microcracks, pores, grain boundaries, and minerals.

## 1. Introduction

Worldwide population growth, infrastructures development, and climate change raise new challenges in the extraction and use of earth resources and spaces.¹ In Australia, mining and construction are two major bases for economic growth while being traditional heavy industries, e.g., 13% of national energy is consumed each year by the mining sector.² However, both earth resources and subsurface infrastructures face unique challenges and huge uncertainties, and are

frequently exposed to natural disasters (e.g., earthquakes, landslides and rockfalls) and human-induced events (e.g., accidental explosions, induced earthquakes and rock blasting).³⁻⁵ These issues reveal a demand for dynamic fracturing prediction and energy-efficient resource extraction of geomaterials to reinforce safety, efficiency and sustainability in their life cycles, contributing towards UN Sustainable Development Goals (9, 11 and 13).⁶ The ability to predict the dynamic fracturing behaviour of geomaterials (e.g. rock, cement and concrete) is vital for warning of and protection from problems during mining and

<footnote><sup>a</sup> Department of Civil Engineering, Monash University, VIC, 3800, Australia</footnote>

<footnote><sup>b</sup> Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ, United Kingdom</footnote>

<footnote><sup>c</sup> ESRF - The European Synchrotron, CS40220, Grenoble, 38043, France</footnote>

<footnote><sup>d</sup> Cavendish Laboratory, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: Wanrui.Hu@monash.edu (W.R. Hu).</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 1. Prepared geomaterial specimens: cement (a), concrete (b), and basalt (c).</figcaption></figure>

infrastructure constructions.⁷⁻⁹ Energy-efficient blasting and commi-
nution methods are key to optimising fragmentation and achieving an
energy-saving extraction process,¹⁰ which is crucial for safe and sus-
tainable resource extraction and civil construction. All of these require a
scientific understanding of the dynamic behaviour of geomaterials,
including the dynamic deformation and fracturing processes, interaction
between microstructures and microcracks, and failure mechanisms at
high strain rates.

To replicate dynamic loadings found in industry, different facilities have been adopted in the literature, e.g. servo-hydraulic machine,¹¹,¹² drop weight machine,¹³,¹⁴ split-Hopkinson pressure bar (SHPB)¹⁵⁻¹⁷ and plate impact techniques¹⁸,¹⁹ for strain rates from 10⁻⁴ to 10⁶. SHPB facilities have been widely used as it has accurate measurement of mechanical response, a wide range of high strain rates (10¹⁻¹⁰⁴), and flexible switching of loading modes (compression, spalling, bending and shear tests).²⁰⁻²⁶ However, in addition to the mechanical properties, dynamic deformation and fracturing are also important to describe the failure process, verify numerical simulation results, and understand dynamic failure mechanisms of geomaterials.²⁷⁻³⁰ By combining SHPB with high-speed photography, the real-time fracturing process of geomaterials can be captured at the lab-scale.³¹,³² In addition, digital optical measurement techniques like digital image correlation (DIC) and 3D-DIC, have gained wide-spread popularity owning to its high accuracy, flexibility and easy operability.²⁰,³³⁻³⁵ The combination of SHPB, high-speed photography and DIC techniques can quantify the full-field dynamic deformation, and also offer detailed insights into phenomena like crack initiation, fracture evolution and rock ejection.³⁶⁻³⁸ Based on the binocular stereovision principle, the 3D deformation fields of the specimen surface can be measured by 3D-DIC technique with the help of two high-speed cameras. However, the high-speed photography and DIC techniques can only capture the surface deformation and fracturing. The internal deformation and fracturing properties are still obscure.

Non-destructive measurement techniques like micro computed tomography (micro-CT) are powerful tools to reconstruct microstructures, identify microcracks, and quantify 3D fractures with micron-level resolution.³⁹⁻⁴² With the aid of high-photon flux, Synchrotron-based micro-CT can significantly improve the image quality and achieve the reconstruction of microstructures and microcracks with a larger size.⁴³⁻⁴⁶ By combining synchrotron-based micro-CT and digital volume correlation (DVC) techniques, the internal 3D deformation fields of geomaterials under dynamic loading conditions were first quantified in recent study.⁴⁷ Considering the fact that the deformed 3D image data are acquired by CT scanning after each impact test, the deformation fields can only represent the post-test plastic deformation properties. However, the in-test interior fracturing and deformation process of geomaterials under dynamic loadings still present a challenge to be captured and quantified with these techniques.

To observe the in-situ internal fracturing of specimen under dynamic

loadings, a new approach involving the high-speed phase-contrast im-
aging of SHPB experiments was presented,⁴⁸,⁴⁹ which can achieve the
in-situ radiography of specimen with a high-resolution under dynamic
loading in a sufficiently short time period.⁵⁰⁻⁵³ Geomaterials like
cement, concrete and rocks have been studied in dynamic tests to
explore the crack initiation and propagation process.⁵⁴⁻⁵⁷ However,
their deformation processes have not been fully considered under dy-
namic compressive loading conditions. X-ray based digital image cor-
relation (XDIC) technique has been successfully applied to high-speed
radiography analysis of metallic materials (e.g. Al, Mg alloys, and Ti
alloys) by chemical etching which produces surface roughness and give
rise to X-ray speckles.⁵⁸⁻⁶⁰ However, the application of the XDIC tech-
nique to quantify the in-situ internal deformation fields of geomaterials
under high strain rates has not been thoroughly explored before. The
innate heterogeneous microstructure in geomaterials is promising for
potential exploitation during digital image correlation analysis.⁴⁷ Since
the microcrack characteristics and failure patterns of geomaterials under
dynamic loadings are different from those under static loading condi-
tions,⁴⁶,⁶¹,⁶² it is necessary to use SEM technique to observe the fracture
surface morphologies to identify the fracture characteristics of different
failure patterns, to help understand the failure mechanisms of geo-
materials and the role of heterogeneous microstructures under dynamic
loading conditions. Moreover, the heterogeneous microstructure of
geomaterials can be incorporated into numerical models to evaluate its
influence on the failure behaviour and mechanical response of geo-
materials under static⁶³,⁶⁴ and dynamic loads.⁶⁵,⁶⁶

In this study, three types of geomaterials (cement, concrete and basalt) with homogeneous and heterogeneous structures are adopted. The made-to-order SHPB facility available at the ID19 beamline of the European Synchrotron Radiation facility (ESRF) is combined with XPCI and XDIC analysis to explore the mechanical, fracturing and deformation properties of geomaterials. A continuum-discrete coupled numerical method is also utilised to help validate the dynamic deformation and fracturing properties of geomaterials and help explain the dynamic failure mechanisms under the influence of heterogeneity. SEM imaging was carried out to identify the fracture surface morphology of different crack patterns to help understand the dynamic fracturing mechanisms from the microscale.

## 2. Methodology

### 2.1. *Material preparation*

In this study, three types of geomaterials are used as summarised in Fig. 1, including cement, concrete, and basalt, representing homogeneous and heterogeneous, artificial and natural geomaterials, all of which are frequently encountered and used in infrastructure and mining engineering.³,⁶⁷ After considering the size of the polychromatic source
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Schematic diagrams (a) and images (b) of experimental setup at beamline ID19, ESRF.</figcaption></figure>

of the ID19 beamline and the large field of view, all the three types of specimens were manufactured to a size of 10 × 8 × 3 mm³.

Cement paste specimens were fabricated with deionized water and ordinary Portland cement (OPC) in a weight proportion of 0.4:1. After the preparation of cement paste, it is cast in made-to-order cuboid moulds with size of 12 × 9 × 4 mm³ (length × width × height). Plastic film was used to prevent moisture loss. 24 h later, cement paste specimens were demoulded and moist-cured in a curing chamber at 23 ± 2.0 °C for 28 days. After curing, the specimens were ground and polished to a size of 10 × 8 × 3 mm³ using a series of abrasives finishing with a

3000-grit SiC paper.

Concrete specimens were manufactured with water, cement, sand and aggregate mixed in proportions of 0.6:1:2:3 by weight, as was done in the previous research.⁴⁶ Since the minimum size of the aggregate (basalt) used is 5 mm, larger than the specimen thickness (3 mm), it is not workable to cast concrete in made-to-order cuboid moulds directly. As an alternative, concrete materials were first cast in cubic steel moulds with dimensions of 54 × 54 × 54 mm³, then sectioned into smaller specimens by diamond saw, and eventually polished to 10 × 8 × 3 mm³.

Pure basalt samples were also used, consistent with the aggregate
<figure><img src="image_7.png" /><figcaption>Fig. 3. Typical experimental results: stress waves in incident and transmission bars (a); dynamic stress equilibrium verification (b).</figcaption></figure>

materials in the concrete. To fabricate the basalt specimens (10 × 8 × 3 mm³), the basalt blocks were cut, sectioned, ground and polished by surface grinder, diamond saw, and abrasives.

## 2.2. Made-to-order SHPB and X-ray radiography system

### 2.2.1. Overview of experimental setup

Experiments were performed at beamline ID19 at the European Synchrotron Radiation Facility (ESRF).⁶⁸ The schematic diagram of experimental set-up are shown in Fig. 2, including the made-to-order split-Hopkinson pressure bar (SHPB) system⁶⁹ and a synchrotron X-ray radiography system in the hutch, and the corresponding control system for recording and synchronisation of strain signals and X-ray radiographs in the control room.

The SHPB system (Fig. 2a) consists of a gas gun, a cylindrical striker (length 150 mm), an incident bar (length 1300 mm), a transmission bar (length 1100 mm), and a damper. The striker and bars are 12.7 mm in diameter, and made of zinc-based aluminium (7075 T6 with heat treatment). Their physical and mechanical properties are as follows: density $ρ_b$ = 2810 kg/m³, Young's modulus $E_b$ = 73 GPa, longitudinal wave velocity $C_b$ = 5090 m/s, and yield strength $σ_b$ = 560 MPa. Two pairs of strain gauges (350 Ω) are attached on the incident bar and transmission bar (400 ± 2 mm from the specimen) to record strain signals.

During the experiment, the time delay and threshold for triggering will be firstly determined in the control room (Fig. 2b). The pressure of the gas charged from the gas cylinder (Fig. 2c) is set up by the pressure controller. A shooting signal from the launch controller (Fig. 2d) opens the fast shutter and launches the SHPB projectile, generating an incident strain signal which is transferred via a Wheatstone-bridge and strain meter, and digitised by an oscilloscope (Waverunner 8404 M) at a 5 GHz sampling rate. The strain signal is also sent to the timing unit, and after the desired time delay, triggers the high-speed camera. Simultaneously, X-ray photons penetrate through the specimen perpendicular to the impact direction, converted to visible light by the LYSO:Ce scintillator and captured by the high-speed camera. A safety chamber (Fig. 2e) is used to contain the post-experiment fragments and protect the surrounding instrumentation.

### 2.2.2. Ultra-high-speed X-ray phase contrast imaging (XPCI)

Beamline ID19 at the ESRF is one of few places in the world where phase-contrast imaging is coupled with SHPB facility, and can provide

ultra-high-speed phase-contrast X-ray radiography with a high photon flux density, a high degree of spatial coherence, an outstanding spatial resolution (micrometre scale) and a large field of view (12.8 mm × 8 mm). Synchrotron X-ray pulses (with a pulse width of ~60 ps and an interval of ~176 ns) for the beamline are emitted from the ESRF storage ring (operated in a '16-bunch' mode) at a distance of about 145 m from the hutch. Two axially aligned U32 long period undulators act as a source of a polychromatic X-ray beam with a mean photon energy of about 30 keV focused on the specimen using a series of two in-vacuum slits. The transmitted signal from the experiment was converted into visible light by a LYSO:Ce (500 µm thickness) single-crystal scintillator (Hilger Crystals, UK) 9 m away from the specimen. This allows for capturing of an edge enhanced image with propagation-based phase contrast thanks to the coherence of the source.⁷⁰,⁷¹ The light was collected by an indirect X-ray detector assembly consisting of a Nikon AF-S NIKKOR 50 mm f/1.8 tandem lens optically coupled to an ultra-high-speed camera (Shimadzu HPV-X2, Kyoto, Japan).⁷² For each experiment, 128 frames (i.e. 112.64 µs) were recorded with an interval time of 880 ns (frame rate 1.14 Mfps) and an exposure time of 200 ns, capturing 1 in 5 X-ray pulses reaching the experimental hutch. The obtained 2D image sequences have the original size of 400 × 250 pixels (length × width) with a spatial resolution of 32 µm/pixel.

### 2.2.3. Data acquisition and processing

With the set-up described in the previous section it is possible to acquire raw data, which then needs further processing⁵⁷: Firstly, an image sequence was captured without a specimen for flat-field correction and identification of the background distribution. Then, the cuboidal specimen was sandwiched between the incident and transmission bars with lubricant to reduce frictional effects. The centre of the specimen was aligned horizontally with the bars and orientated 90° with respect to the beam. After placement of the specimen, a thin-wall polycarbonate box was placed over the experiment as a safety chamber for fragments collection and protection of equipment. After the alignment of specimen, the image sequence of the specimen before the dynamic test is captured as the reference. After that, the dynamic compression tests were conducted with synchronisation of SHPB and X-ray radiography systems, achieved by X-ray bunch clock and a digital delay generator which controls the needed time interval between the incident wave signal, the camera exposure time and the X-ray pulse train.

During the test, a “shooting” command is generated to open the X-ray fast shutter (~20 ms opening time over FoV) and fire the SHPB system
<figure><img src="image_8.png" /><figcaption>Fig. 4. X-ray based digital image correlation (XDIC) principle.</figcaption></figure>

by using a coincidence logic unit, a digital delay generator and a computer triggered signal; then the striker was fired against the incident bar at a prespecified velocity (measured by light sources and photodiodes connected to an oscilloscope) and generated an elastic compression wave recorded by the strain gauge mounted on the incident bar. When the value of the incident wave signal exceeded the pre-set threshold, a trigger signal was generated at a specific time delay Δt (calculated by distance between strain gauge and specimen divided by the elastic wave velocity) to trigger the high-speed camera. Finally, the dynamic X-ray single-bunch radiographs can be captured in good synchronisation with strain gauge signals.

By the assumption of elastic one-dimensional (1D) stress wave propagation, the dynamic stress $\sigma_d$, strain rate $\dot{\epsilon}$ and dynamic strain $\epsilon_d$ in the impact direction are calculated, using the following equations$^{73,74}$:

$$ \sigma_d(t) = \frac{E_b A_b}{2A_s} [\epsilon_{in}(t) + \epsilon_{re}(t) + \epsilon_{tr}(t)] = \frac{E_b A_b}{A_s} \epsilon_{tr}(t) \quad (1) $$

$$ \dot{\epsilon}(t) = \frac{C_b}{L} [\epsilon_{in}(t) - \epsilon_{re}(t) - \epsilon_{tr}(t)] = - \frac{2C_b}{L} \epsilon_{re}(t) \quad (2) $$

$$ \epsilon_d(t) = \frac{C_b}{L} \int_0^T [\epsilon_{in}(t) - \epsilon_{re}(t) - \epsilon_{tr}(t)] dt = - \frac{2C_b}{L} \int_0^T \epsilon_{re}(t) dt \quad (3) $$

where $E_b$, $A_b$ and $C_b$ are the Young's modulus, cross-sectional area and the longitudinal wave velocity of the bars, respectively; $A_s$ and $L$ are the cross-sectional area and the length of the specimen; $\epsilon_{in}(t)$, $\epsilon_{re}(t)$ and $\epsilon_{tr}(t)$ are the incident, reflected and transmission strain signals measured by the strain gauges on the incident and transmission bars in the X direction; $\sigma_d(t)$, $\epsilon_d(t)$ and $\dot{\epsilon}(t)$ are dynamic stress, dynamic strain and strain rate, respectively.

Typical experimental results are presented in Fig. 3, including the stress wave signals in the incident and transmission bar recorded by strain gauges, and dynamic stress equilibrium verification. Fig. 3 (a) shows the wave propagation in a period of 300 µs along the incident and transmission bars. The dynamic stress equilibrium is validated in Fig. 3

<figure><img src="image_9.png" /><figcaption>Fig. 5. XDIC uncertainty in displacement $u_y$ (a) and strain $\epsilon_{yy}$ (b) measurement of concrete static radiographs.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 6. Coupled continuum-discrete model for experimental configuration (a) and contact law and failure criterion for bonded contact (b).</figcaption></figure>

(b), where dynamic stress on both ends of the specimen are generally consistent before the failure of specimen.

## 2.3. Deformation and fracturing characterisation

### 2.3.1. X-ray based digital image correlation (XDIC)

After the experiments, the dynamic deformation and fracturing processes are determined by the combination of the recorded

radiographic images and the digital image correlation (DIC) technique.³⁵ The microstructures (e.g. aggregates, minerals, and pores) inside these specimens were used as typical features instead of the speckles adopted in ordinary DIC techniques. Contrast-enhancement was also conducted by ImageJ to accentuate the contrast between different microstructures. By tracking these different microstructures and correlating their reference and deformed images, the displacement fields can be estimated, and strain fields are obtained by further differential
analysis (Fig. 4). The parameters are as follows: area of interest (AOI): 10 × 8 mm²; subset: 35–40 pixels, interpolation: cubic B-spline; subset shape function: affine transformation; correlation criterion: normalised sum of squared differences (NSSD). Although the image correlation principle is essentially the same as that of ordinary DIC, the name of X-ray based DIC (i.e. XDIC) is adopted in this study to emphasise its difference in image processing, speckle selection, and deformation indication (e.g. XDIC can quantify the internal deformation fields).

Radiographs obtained by XPCI will not only change with the deformation and fracturing of the specimen, but also be affected by the photon flux per bunch variation during experiments. As a result, it is necessary to conduct uncertainty analysis to explore the effect of photon flux variation on XDIC results. To achieve this, the radiographs of static specimens were also captured. By correlating the static radiographs, we can generally obtain the uncertainty in displacement and strain measurements. Fig. 5 exhibits the uncertainty evolution of displacement $u_y$ and strain $\epsilon_{yy}$ of concrete radiographs over time. It can be found that the average values of displacement and strain fluctuate around zero, and the standard deviations of displacement and strain are about 1.5–3.3 µm and 0.0027–0.0057 respectively. Compared with this, the experimental maximum and minimum values of displacement and strain can reach 11.39 µm and –11.47 µm, and 0.028 and –0.036. The uncertainty results of basalt are similar to concrete (e.g. the maximum standard deviations of displacement $u_y$ and strain $\epsilon_{yy}$ are 3.07 µm and 0.005), but the uncertainty results of cement are obviously larger (e.g. the maximum standard deviations of displacement $u_y$ and strain $\epsilon_{yy}$ are 8.42 µm and 0.025), indicating that the uncertainty results will be affected by the microstructures of the geomaterials. Based on the uncertainty results, it should be noted that the XDIC results during dynamic tests will not only indicate the actual deformation, but also include the uncertainty effect of photon flux which should not be neglected.

### 2.3.2. Scanning electron microscopy (SEM)

SEM was also carried out to explore the morphologies of the fracture surfaces of the collected post-test fragments, and help qualify fracture characteristics and understand failure mechanisms. The specimens were firstly sputter coated with platinum, and then observed by a Nova NanoSEM 450 (FEI, Hillsboro, MA), operating at high vacuum with a beam accelerating voltage of 15 kV and spot size of 3.0 $^{75}$. An Everhard-Thornley detector (ETD) and a Concentric Backscattered Retractable detector (CBS) were used to capture the secondary electrons (SE) and back scattered electrons (BSE) photographs respectively. The photographs were further analysed to characterise the fracture surface morphologies, and reveal the failure mechanisms. The fracture surfaces of different crack patterns (including matrix crack, interfacial crack and transgranular crack) of concrete were investigated as the typical representatives. The cement and basalt were not analysed in this study as here were difficulties relating to fragment collection and the existence of a magnetic component disturbance.

## 2.4. Numerical modelling

Numerical modelling of dynamic compression behaviour of geomaterials was also conducted to validate the experimental findings and to provide insights into the damage process and failure mechanisms at multiple levels. A two-dimensional (2D) coupled continuum-discrete model is established to simulate the full-scale SHPB system including both metal bars and the specimen as shown in Fig. 6 (a). The capability of this model for replicating the dynamic responses of geomaterials under various strain rate and confinement conditions has been demonstrated in previous studies.$^{30,66}$

In the model, the metal bars and geomaterials are simulated by continuous zones implemented in FLAC$^{76}$ and discontinuous media are implemented in PFC2D,$^{77}$ respectively, due to their distinct mechanical properties. The metal bars possess high yield strength and Young's modulus and therefore can be regarded as a continuous medium, in

<table><caption>**Table 1**
Calibrated micro-parameters of cement and concrete.</caption><thead><tr><th>Micro-parameters</th><th>Cement</th><th>Aggregate</th><th>Interface</th></tr></thead><tbody><tr><td>Particle size range (mm)</td><td></td><td>[0.06, 0.0996]</td><td></td></tr><tr><td>Particle density ρ (kg/m³)</td><td>2150</td><td>3090</td><td>NA</td></tr><tr><td>Particle contact modulus E<sub>c</sub> (GPa)</td><td>8.0</td><td>61.0</td><td>4.0</td></tr><tr><td>Particle friction coefficient μ</td><td>0.4</td><td>0.5</td><td>0.4</td></tr><tr><td>PB modulus E&#773;<sub>c</sub> (GPa)</td><td>8.0</td><td>61.0</td><td>4.0</td></tr><tr><td>PB normal/shear stiffness ratio k&#773;<sub>n</sub>/k&#773;<sub>s</sub></td><td>2.0</td><td>2.2</td><td>2.0</td></tr><tr><td>PB tensile strength σ<sub>t</sub> (MPa)</td><td>13 ± 3.25</td><td>78 ± 19.5</td><td>7.8 ± 1.95</td></tr><tr><td>PB cohesion c&#773; (MPa)</td><td>13 ± 3.25</td><td>78 ± 19.5</td><td>7.8 ± 1.95</td></tr><tr><td>PB friction angle φ&#773;</td><td>30.0°</td><td>45°</td><td>30.0°</td></tr></tbody></table>

which elastic stress waves can be generated, propagated and transmitted without attenuation. Geomaterials may undergo both elastic deformation and irreversible fracturing under dynamic loadings. Therefore, geomaterials are simulated by a discrete bonded particle assembly using the discrete element method (DEM).$^{78}$ As shown in Fig. 6 (a), the interaction between the continuous medium and discontinuous medium is achieved by a coupling scheme$^{76,79}$ in which FLAC determines the velocities of the first layer of boundary particles while PFC2D returns the unbalanced forces of the same set of particles to the FLAC boundary grid. Coupling occurs during cycling such that each cycle in PFC2D corresponds with a cycle in FLAC.

Geomaterials including cement and concrete are simulated using the particle-based DEM model as shown in Fig. 6 (a). In the DEM model, geomaterials are represented by an assembly of rigid particles cemented by parallel bond at their contacts. The movements of the particles follow Newton's second law and the contact force is determined by the relative motion of adjacent particles. The contact law and failure criterion for the parallel bonded contact are shown in Fig. 6 (b). When the tensile stress exceeds the tensile strength or the shear stress exceeds the shear strength, bond breakage occurs and the bond is removed from the contact along with its accompanying force, moment, and stiffness. For the bonded contact, the tensile strength can be directly assigned while the shear strength is determined by the Mohr-Coulomb criterion. After bond breakage, the frictional resistance limit is dependent on the normal force multiplied by the friction coefficient.

Cement is regarded as a homogeneous medium such that cement specimens can be represented by a single set of particles and contacts. Concrete is a heterogeneous medium with aggregates embedded into cement matrix. The geometries of aggregates are generated following the typical aggregate contour in concrete specimens from the radiography images. Therefore, the concrete model consists of two sets of particles, cement and aggregate as well as correspondingly, two contact types. In addition, a third contact type is needed along the interfaces between cement and aggregate. The micro-parameters of cement and concrete are calibrated by a trial-and-error process against experiment results. The calibration method and procedures can be found in our previous studies.$^{30,66}$ The first step is to calibrate the mechanical properties of the cement and aggregate (basalt), respectively. Then, the calibrated micro-parameters are applied to the concrete model in which the interfacial micro-parameters still need to be selected to match the mechanical properties of concrete. The interfacial micro-parameters including stiffness and strength are determined by the average value of the contacting materials, multiplied by a reduction coefficient. The mechanical behavior of the bar-specimen interfaces follows a linear

<table><caption>**Table 2**
Calibrated macro-parameters of cement and concrete.</caption><thead><tr><th rowspan="2">Macro-parameters</th><th colspan="2">Cement</th><th colspan="2">Concrete</th></tr><tr><th>Experiment</th><th>Simulation</th><th>Experiment</th><th>Simulation</th></tr></thead><tbody><tr><td>Young's modulus (GPa)</td><td>8.3</td><td>8.5</td><td>34.3</td><td>34.6</td></tr><tr><td>Poisson's ratio</td><td>0.23</td><td>0.25</td><td>0.25</td><td>0.25</td></tr><tr><td>UCS (MPa)</td><td>11.5</td><td>13.7</td><td>54.7</td><td>51.5</td></tr></tbody></table>
<figure><img src="image_11.png" /><figcaption>Fig. 7. Dynamic stress-time curves of cement under impact velocity (a) $v_i$ = 6.4 m/s and (b) $v_i$ = 8.4 m/s.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 8. Fracturing radiographs of cement under impact velocity $v_i$ = 6.4 m/s by XPCI.</figcaption></figure>

elastic law in the normal direction and a frictional law in the shear direction. The micro contact parameters of the bar-specimen interface are assumed to be the minimum value of the bar and the specimen. The contact modulus and stiffness of the interface is equal to that of the specimen. The friction coefficient of the interface is selected to be 0.1 which represents the frictional property of the metal bar ends. The calibrated micro-parameters and macro-properties are shown in Table 1 and Table 2, respectively. A good agreement of the numerical and experimental results can be reached.

### 3. Experimental results

In this section, the dynamic stress-strain curves of three rock-like materials (i.e. cement, concrete and basalt) under different impact

velocities are presented, and the corresponding fracturing radiographs and strain fields by XPCI and XDIC techniques are also exhibited to explore the initiation and propagation of microcracks and failure process. The fracture morphologies of post-test concrete specimens are also characterised by SEM to validate experimental observations and reveal the failure mechanisms.

#### 3.1. Cement

The typical dynamic stress-time results of cement under impact velocities $v_i$ = 6.4 m/s and $v_i$ = 8.4 m/s are presented in Fig. 7. The stress-time curves exhibit different characteristics under different impact velocities. Under the lower impact velocity (i.e. $v_i$ = 6.4 m/s), the stress-time curve shows a lower peak stress (33.27 MPa) and corresponding
<figure><img src="image_13.png" /><figcaption>Fig. 9. Fracturing radiographs and strain fields of cement under impact velocity $v_i = 8.4$ m/s by XPCI and XDIC.</figcaption></figure>

longer load time (54.9 µs). This can be compared to the higher impact velocity (i.e. $v_i = 8.4$ m/s), where the peak stress is 41.84 MPa and the load time is 19.2 µs. The increase of peak stress can be explained by the strain rate effect.²⁴,⁸⁰ In addition, the post-peak stages of two stress time curves are also different. The post-peak stage under impact velocity $v_i = 6.4$ m/s exhibits an obvious decline, indicative of sample fracture and a loss of load bearing capacity. However, the post-peak stage under impact velocity $v_i = 8.4$ m/s shows a plateau and a slower decrease after the peak stress, indicating a slower and more progressive fracturing evolution process, which could be relevant to the microstructural property and microcrack evolution of the specific specimen.

The fracturing process of cement under impact velocity $v_i = 6.4$ m/s is captured by XPCI as shown in Fig. 8. It can be seen that there is no obvious microcrack initiation before 30.2 µs. At around 46.1 µs, a few independent microcracks initiate around the pore (with brighter grey-scale) and near the transmission bar on the top part of the specimen. At about 54.9 µs (i.e. the peak stress point), these microcracks propagate

and coalesce along the impact direction, and form two main fractures. At about 61.9 µs, microcracks can be also observed at the bottom part of the specimen. After that, fractures develop at both the top and the bottom parts of the specimen, with propagation and coalescence along the impact direction and obvious increase of crack width, as can be seen at 69.8 µs and 93.6 µs. The specimen not only is compressed along the impact direction, but also dilates towards the top and the bottom due to the Poisson's effect and the crack opening. The deformation results are not presented for this case since there are less obvious microstructures for contrast inside the specimen, and as a result, this set of image data can hardly be analysed by the XDIC technique.

The fracturing radiographs and strain fields of cement under impact velocity $v_i = 8.4$ m/s by XPCI and XDIC are presented in Fig. 9. It shows that no obvious microcracks and tensile strain concentration can be observed before 11.3 µs. At around 19.2 µs (i.e. the stress time curve reaches the peak point), no obvious microcracks can be observed from the fracturing radiographs but tensile strain ($e_{yy} > 0.03$) appears to
<figure><img src="image_14.png" /><figcaption>Fig. 10. Dynamic stress-time curves of concrete under impact velocity (a) $v_i = 6.2$ m/s and (b) $v_i = 8.8$ m/s.</figcaption></figure>

concentrate at both the top and the bottom of the specimen. At 25.3 µs, more obvious tensile strain concentration ($e_{yy} > 0.05$) can be observed at both top and bottom parts of specimen indicating the positions where microcrack may initiate. After 33.3 µs, several microcracks can be observed at the top of the specimen near the transmission bar and bottom parts of the specimen close to the incident bar. From 42.1 µs to 51.7 µs, more microcracks initiate from the transmission end, propagate along the impact direction, and coalesce with other microcracks. At about 64.9 µs, the middle part of specimen also exhibits cracks along with crack branching, as indicated by the two yellow arrows, i.e. one horizontal crack branches into two oblique cracks at the central part of the specimen. By analysing the images around 62.3–64.9 µs, it can be found that at least 1 mm length microcrack appears in a 880 ns period, corresponding to the crack velocity about 1136 m/s, which is larger than the 60% of the Rayleigh velocity (~1840 m/s) of the cement paste material. It could be regarded as a necessary condition reflecting a redistribution of the stress tensor after branching and help explain why the crack branching appears in the cement paste under a higher impact velocity.⁷,⁸,¹² At 74.6 µs, more microcracks appear in the middle part of the specimen, and another pair of branching cracks can be observed near the pore. The crack branching phenomenon indicates that the stress concentration may be higher in the middle part of the specimen with the increase in loading rate, and the microstructures like pores could influence the propagation of cracks and contribute to the appearance of crack branching. At about 93.1 µs, in addition to the further development of existing fractures with propagation and coalescence, two vertical microcracks can be observed near the middle part of the specimen, which may be induced by reflected tensile stress waves, and may eventually form spalling cracks. After 25.3 µs, the XDIC results are not shown as the deformation fields cannot be accurately calculated and analysed due to the large deformation and low image contrast.

## 3.2. Concrete

The dynamic stress-time curves of concrete under impact velocities $v_i = 6.2$ m/s and $v_i = 8.8$ m/s present different characteristics as presented in Fig. 10. Under the impact velocity $v_i = 6.2$ m/s, the stress-time curve exhibits a lower peak stress (87.35 MPa) and a stress platform (from 17.7 µs to 50.5 µs). Under the impact velocity $v_i = 8.8$ m/s, the peak stress reaches 168.33 MPa at around 18.4 µs. The stress platform under the lower impact velocity (i.e. $v_i = 6.2$ m/s) manifests that the specimen undergoes obvious plastic deformation, which should be

identified and clarified by the fracturing results.

The fracturing radiographs and strain fields of concrete under impact velocity $v_i = 6.2$ m/s by XPCI and XDIC are shown in Fig. 11. It should be noted that there are different greyscale distributions in the fracturing radiographs, which are due to the various densities of matrix and aggregate inside the concrete specimen. The darker areas in the upper left and lower left regions of the specimen indicate the locations of two elongated aggregates, which will affect the fracturing behaviours of the specimen. At 8.9 µs, no obvious microcracks and tensile strain concentration areas can be observed, indicating an elastic deformation. From 17.7 µs to 24.7 µs, a few tensile strain concentration areas appear especially in the upper left region of the specimen and near the edges of the aggregate, indicating a potential microcrack initiation around the aggregate interface. At about 35.3 µs, obvious microcracks can be seen in the lower right of the specimen near the transmission bar, which is also demonstrated by the strain fields. From 44.1 µs to 53.8 µs, both microcracks and tensile strain concentration areas appear in the upper left region of the specimen especially around the aggregate, which indicates that the plastic deformation stage shown in Fig. 10 (a) is related to interfacial cracking. At about 61.7 µs, microcracks in the upper left region of the specimen further propagate along the aggregate interface and coalesce with each other as can be seen from the fracturing radiographs and strain fields. In addition, tensile cracks in the lower right part of the specimen also appear, accompanying the obvious strength shown in Fig. 10 (a). From 70.5 µs to 77.5 µs, tensile cracks in the lower part of the specimen propagate from the transmission end to the incident end along the impact direction. When these cracks reach the aggregate, they just propagate around the aggregate and form interfacial cracks, as displayed in the fracturing radiographs. After 77.5 µs, two main fractures can be observed at both top and bottom parts of the specimen with interfacial cracks dominate. In addition, a few tensile strain concentration areas can be found in the central part specimen, indicating the formation of tensile cracks in that region.

The fracturing radiographs and strain fields of concrete under impact velocity $v_i = 8.8$ m/s by XPCI and XDIC are displayed in Fig. 12. The front and rear views of the specimen are also presented to provide the locations of aggregates. By comparing the front and rear views with the radiographs, three regions with darker greyscales in the radiographs can be matched with the two largest aggregates in the front view and the largest aggregate in the rear view, which can help identify the crack patterns. At 12.2 µs, the specimen is under elastic deformation without obvious microcrack initiation and tensile strain concentration. When the
<figure><img src="image_15.png" /><figcaption>Fig. 11. Fracturing radiographs and strain fields of concrete under impact velocity $v_i$ = 6.2 m/s by XPCI and XDIC.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. 12. Fracturing radiographs and strain fields of concrete under impact velocity $v_i$ = 8.8 m/s by XPCI and XDICs.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Fig. 13. Dynamic stress-time curves of basalt under impact velocity (a) $v_i$ = 6.0 m/s and (b) $v_i$ = 8.7 m/s.</figcaption></figure>

peak stress is reached at 18.4 µs, several tensile strain concentration areas can be observed but microcracks have not visible. From 24.6 µs to 28.1 µs, more and more tensile strain concentration areas appear in the lower left region of the specimen and mainly near the aggregate shown in the front view of the specimen. However, no obvious microcrack initiation can be observed during this period. At around 30.7 µs, several microcracks initiate in the middle part of the specimen and propagate through the aggregate with the formation of transgranular cracks along the impact direction as indicated by the red arrows, which are also verified by the tensile strain fields. In addition, tensile strain concentration areas in the lower left coalesce with each other, forming an oblique tensile strain concentration region, which is considered to be related to the interfacial crack along the profile of the aggregate. At 33.4 µs, more microcracks initiate and propagate along the impact direction, which can be also identified by the strain fields. At 41.3 µs, microcracks further propagate along the impact direction and coalesce with each other, with obvious crack opening in the middle part of the specimen. The tensile strain results also demonstrate the positions of obvious crack openings. After 59.8 µs, the main fractures have coalesced in the middle of the specimen. In addition, as pointed out by the blue arrows, shear sliding can be also observed along the interface of the aggregate in the lower left, indicating the formation of shear cracks. Strain fields are not provided at 59.8 µs since the large deformation precludes accurate calculation.

### 3.3. Basalt

The dynamic stress-time curves of basalt under impact velocities $v_i$ = 6.0 m/s and $v_i$ = 8.7 m/s are exhibited in Fig. 13. Compared with cement and concrete, basalt materials show obviously higher dynamic strength. Under the impact velocity $v_i$ = 6.0 m/s, the stress-time curve exhibits a lower peak stress (103.3 MPa) with a longer loading time (55.4 µs). However, under the higher impact velocity i.e. $v_i$ = 8.7 m/s, the peak stress reaches 193.8 MPa at around 18.7 µs. The peak stress enhancement is relevant to the strain rate effect, and the shorter post-peak stage (around 14.9 µs) under the higher impact velocity $v_i$ = 8.7 m/s indicates that the specimen may reach a brittle failure without obvious plastic deformation.

The fracturing radiographs and strain fields of basalt under impact velocity $v_i$ = 6.0 m/s by XPCI and XDIC are shown in Fig. 14. Compared with the radiographs of cement and concrete, the basalt radiographs exhibit higher contrast owing to the obvious density difference of

minerals (i.e. darker regions represent the higher density), which can help with the XDIC analysis. From 17.7 µs to 49.4 µs (i.e. pre-peak stage), no obvious microcracks can be observed in the fracturing radiographs. The tensile strain fields do not show obvious strain concentration areas before 17.7 µs, indicating that the specimen is undergoing an elastic deformation stage. However, from 33.5 µs to 49.4 µs, tensile strain concentration areas can be identified in the middle left of the specimen near the incident bar, which means that microcracks may have initiated inside the specimen. After the time at which the peak stress is reached, the microcracks can be obviously observed. For example, at 65.2 µs, a short crack appears in the middle left of the specimen. Considering the obvious density difference of the minerals above and below the crack, it can be speculated that this microcrack is highly likely to be an intergranular crack. From 71.4 µs to 103.9 µs, there are only a few microcracks generated in the specimen without obvious fractures and failure as shown in the tensile strain concentration areas, which means the specimen still retains a load bearing capacity.

The fracturing radiographs and strain fields of basalt under impact velocity $v_i$ = 8.7 m/s by XPCI and XDIC are presented in Fig. 15. Different from the limited crack development under lower impact velocity, the specimen reaches failure with obvious fracture initiation and propagation processes under the impact velocity $v_i$ = 8.7 m/s. Specifically, at 12.5 µs before the peak stress, no obvious microcracks and tensile strain concentration areas can be identified. At 18.7 µs, a few tensile strain concentration areas can be observed at the middle right of the specimen near the transmission end, but no obvious cracks can be viewed. At 24.8 µs, tensile strain concentration areas in the middle part of the specimen develop from the transmission end to the incident end along the impact direction. Simultaneously, microcracks can be observed in the central part of the specimen as indicated by the red arrows. From 29.2 µs to 33.6 µs, more microcracks appear in the middle of the specimen, coalesce with each other, and propagate along the impact direction, all of which can also be seen in the strain fields. At 33.6 µs, in addition to the crack coalescence in the middle part of the specimen, another few cracks also appear in the lower part of the specimen as indicated by the tensile strain concentration areas. After 42.4 µs, middle cracks further develop along the impact direction with obvious crack opening. From the crack characteristics, it can be speculated that the middle cracks are generally pure tensile cracks potentially including the pattern of transgranular cracks. Cracks in the lower part of the specimen can be also observed accompanying by the curved propagation, indicating the potential intergranular cracking.
<figure><img src="image_18.png" /><figcaption>Fig. 14. Fracturing radiographs and strain fields of basalt under impact velocity $v_i = 6.0$ m/s by XPCI and XDICs.</figcaption></figure>

# 4. Numerical results

The advantage of numerical simulation in designing and controlling specimen structures and material parameters, is that the influence of a single factor can be investigated without being disturbed by other factors. In order to clarify the influence of heterogeneity on dynamic behaviour of geomaterials, the cement, concrete with half-sized original aggregate, and original concrete are respectively simulated to reflect the gradually increased heterogeneity. The numerical results including the deformation fields, fracturing process and contact force chains are presented in the following section. Besides, fracturing properties, deformation fields, and strain/stress concentration of experimental and numerical results are also compared and discussed.

## 4.1. Deformation fields

The simulated deformation fields of three types of specimens under different impact velocities are displayed in different loading stages, as shown in Fig. 16. In order to better display the deformation properties in pre-peal and post-peak stages, two different legends are used for 0.5 pre-$\sigma_p$ stage and the other stages.

In the 0.5 pre-$\sigma_p$ stage, all the specimens are generally under the elastic deformation, as also observed in the experimental results. However, due to the difference in heterogeneity, the three types of specimens show distinct deformation properties. For example, cement specimens under impact velocities of 6.4 and 8.4 m/s both show uniform deformation along the impact direction. Concrete specimens with different aggregate sizes all exhibit non uniform deformation especially around
<figure><img src="image_19.png" /><figcaption>Fig. 15. Fracturing radiographs and strain fields of basalt under impact velocity $v_i = 8.7$ m/s by XPCI and XDICs.</figcaption></figure>

aggregates. With the increase of aggregate size, the heterogeneous deformation becomes more obvious. The main reason is the elastic mismatch between aggregate (i.e. basalt) and cement materials. Specifically, when the stress wave propagates through the specimen, the stiffness difference between basalt and cement will generate different deformation responses, which results in heterogeneous deformation fields.

From 0.9 pre-$\sigma_p$ stage to the final stage, it can be observed that the deformation magnitudes of all specimens are increased with the loading stage and impact velocity. Under the same deformation legend, there are generally no obvious large deformation areas before the peak stress, indicating that cracks have not developed much during this period. After the 0.8 post-$\sigma_p$ stage, uneven deformation can be observed in all specimens, especially more obvious in the specimens with larger

heterogeneity. For example, cement specimens exhibit a relatively higher magnitude deformation zone along the impact direction, indicating crack formation in this region. For concrete specimens, the deformation fields will be highly affected by aggregates, particularly in specimens with a larger aggregate size. Several areas with different deformation magnitudes are distinguished by the aggregate contour and separated by the aggregate interface. The modelling therefore indicates the role of heterogeneous structures in geomaterials on controlling the deformation development.

## 4.2. Fracturing properties

The simulated fracturing processes of three types of specimens under different impact velocities in different loading stages are shown in
<figure><img src="image_20.png" /><figcaption>**Fig. 16.** Simulated deformation fields of cement, concrete with a half original aggregate size, and original concrete under impact velocity of (6.2–6.4) m/s and (8.4–8.8) m/s.</figcaption></figure>

**Fig. 17.** Generally speaking, the fracturing properties of cement and concrete are consistent with the corresponding experimental observations. For example, fractures are aggravated with the increase of impact velocity, and crack types develop from matrix crack to interfacial and transgranular cracks with the increase of heterogeneity.

Specifically, for cement specimens, cracks first initiate near the top and bottom edges and then propagate along the impact direction, which can be also observed in Figs. 8 and 9. Under an impact velocity of 6.4 m/s, the simulated fractures seem more likely to concentrate at the top and bottom parts. However, under an impact velocity of 8.4 m/s, more

fractures appear in the central part, and vertical cracks can be also observed. Compared to cement, fractures in concrete will be highly dependent on the aggregates. Microcracks are more likely to first appear along the aggregate interfaces, and finally form shear bands. Additionally, with the increase in aggregate size, transgranular cracks can be also observed in the middle part of the specimen and are even more obvious under higher impact velocity. The simulated fracturing results validate that the dynamic fracturing patterns of geomaterials will be highly dependent on their meso- and microstructures.

In addition to the fracturing process, the contact force chains acting
<figure><img src="image_21.png" /><figcaption>**Fig. 17.** Simulated fracturing process of cement, concrete with a half original aggregate size, and original concrete under impact velocity of (6.2–6.4) m/s and (8.4–8.8) m/s.</figcaption></figure>

on adjacent particles can also show the contact force distribution and further explain the fracturing properties. As shown in Fig. 18, contact force distribution is generally consistent with the crack evolution exhibited in Fig. 17. With the increase of heterogeneity, the contact force chains exhibit a transformation from an uniform distribution to a non uniform distribution, and from a horizontal distribution to an interface-oriented dominant distribution. Specifically, in cement specimens, contact force chains with a higher magnitude appear near top and bottom edges in the 0.9 pre-$\sigma_p$ stage, further developing along the impact direction in $\sigma_p$ stage. With the formation of cracks on the top and bottom parts, particles debond from each other and force chains disappear in these regions but appear in the central part, as shown in 0.8 post-$\sigma_p$ and 0.5 post-$\sigma_p$ stages. For concrete specimens, higher magnitude contact forces are more concentrated along the interface of aggregates as indicated in the $\sigma_p$ and 0.8 post-$\sigma_p$ stages, promoting the formation of oblique shear cracks. Compared with the concrete with a half size original aggregate size, the original concrete exhibits a more obvious contact force concentration area in the central part, as seen in the $\sigma_p$ and 0.8 post-$\sigma_p$ stages, which results in the initiation and propagation of transgranular cracks.

### 4.3. Comparison between experimental and numerical results

In order to verify the reliability of the numerical modelling, the obtained numerical results are compared with those in experiments, as shown in Fig. 19.

When examining the fracturing fields, it can be found that both experimental and numerical results exhibit the transgranular cracks in the left and right aggregates, and the location of transgranular cracks are mainly located near the middle position. Additionally, interfacial cracks propagate along the contour of the aggregate in both results and also form an obvious shear band. The deformation field of the experiment is obtained by the XDIC technique. From the deformation fields it can be found that both simulation and experiment results share similar deformation patterns. For instance, the deformation magnitude in the right-side aggregate region is smaller than the left part, and the contour of this deformation region generally reflects the contour of the right-side aggregate. The deformation transition zone in the lower left region from both experimental and numerical results can both depict the interface contour of the lower left aggregate. Their consistency can also in turn verify the reliability of XDIC results and the rationality of designing three aggregates in the modelling. Moreover, the stress concentration areas reflected by tensile strain concentration areas in the XDIC results are also compared with the contact force concentration areas. It can be seen that both results exhibit the stress/force concentration along the interface of the lower left aggregate, and the stress/force concentration in the central region can also indicate the location of transgranular cracks in the lower left aggregate. These comparison results generally reflect the agreement between experiments and numerical simulation, and also indicate the importance of their mutual complementarity.
<figure><img src="image_22.png" /><figcaption>Fig. 18. Contact force chains of cement, concrete with a half original aggregate size, and original concrete under impact velocity of (6.2–6.4) m/s and (8.4–8.8) m/s.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 19. Comparison of experimental and simulated fracturing, deformation and stress/force concentration results of concrete under impact velocity of 8.8 m/s.</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>**Fig. 20.** Greyscale distribution (a) and dynamic increase factor (b) of cement, concrete and basalt, and failure pattern transformation under the effect of heterogeneity (c) and strain rate (d).</figcaption></figure>

**5. Discussion**

Due to the existence of heterogeneous microstructures like inclusions, minerals, interfaces, microcracks, and pores,⁸³⁻⁸⁵ different geomaterials generally exhibit a variety of dynamic behaviours. The influence of heterogeneity on the rate effect and failure patterns of geomaterials is further discussed in this section.

Firstly, the heterogeneity of geomaterials should be quantitatively analysed. However, how to quantify the degree of heterogeneity is still a matter for debate and definitive criterion has not yet been established. Considering the fact that microstructures with different densities often demonstrate obvious variety in strengths and stiffness,⁸⁶ density difference is adopted to describe the heterogeneity of different materials in this study. For cement and basalt, their density difference can be well characterised by the greyscale difference of their radiographs. The raw image of concrete surface is directly used considering its obvious density distinction between matrix and aggregates. By calculating the standard deviation of pixel grey values in different material images, their density dispersion degree can be estimated, which could further distinguish the

heterogeneity. As shown in Fig. 20 (a), the greyscale distribution maps of three materials are displayed. The greyscale of cement is mainly concentrated in the range of 40000–50000, with maximum counts of 5000 at about 45000. Basalt exhibits a broader distribution of grey values from 10000 to 50000, indicating that the minerals of basalt have different properties. For concrete, aggregates and matrix show two different greyscale concentrated ranges, i.e. 3000-15000 and 35000–60000. By further standard deviation calculation, the results show that concrete has the largest greyscale distribution dispersion, indicating that concrete is endowed with higher heterogeneity compared with basalt and cement.

The effect of strain rate on the dynamic increase factor (i.e. the ratio of dynamic strength to static strength) of different materials are also analysed. As can be seen in Fig. 20 (b), compared with basalt and concrete, cement specimens exhibit higher dynamic increase factor, which means the cement specimens exhibit more pronounced strength enhancement with increasing strain rate. However, although the concrete specimen is mainly composed of cement and basalt, it shows the lowest strain rate effect of the three materials examined in this study.
<figure><img src="image_25.png" /><figcaption>**Fig. 21.** SEM photographs (including BSE and SE images) of microscopic fracture characteristics in different crack patterns of concrete: matrix crack (a), interfacial crack (b), and transgranular crack (c).</figcaption></figure>

Similar phenomenon have also been observed in previous studies.⁸⁰,⁸⁷ One possible reason is that cement and basalt are relatively more homogeneous compared to the concrete, and their failure patterns are dominated by tensile cracks. Considering the fact that the tensile strength of geomaterials generally shows a higher rate effect than compressive strength, it can be speculated that specimens where tensile failure is dominant will exhibit a higher rate effect. On the contrary, due to the existence of aggregate and induced weak bond between aggregate and matrix, more shear cracks are likely to appear along the interfaces of concrete, as can be seen in Figs. 11 and 12, resulting in a more distributed stress transfer, larger ductile deformation, and less strength increment with the increasing strain rate.

Fig. 20 (c) presents the evolution of failure patterns of geomaterials with the increase of heterogeneity by taking cement and concrete as exemplars. Both experimental and numerical results show that the failure pattern transforms from a region of tensile dominant cracks (parallel to the impact direction) to tensile-shear mixed cracks with the increase of heterogeneity, helping to explain the rate effect difference shown in Fig. 20 (b). The influence of both strain rate and heterogeneity on the dynamic fracturing properties of geomaterials is further summarised in Fig. 20 (d). It shows that, as the strain rate increases, fracturing positions evolve from primarily being at the top and bottom of the specimen to the middle, and fracturing patterns transform from interfacial cracks to transgranular cracks. It should be noted that transgranular cracks are more likely to appear in the middle part of the specimen due to the high stress concentration in this region.⁴⁶,⁴⁷ When the heterogeneity of the specimen is increased, the crack patterns shift from pure tensile cracks to mixed (tensile-shear) cracks.

The surface morphologies of different fracture patterns can also be examined to further understand the failure mechanisms from the microscale.⁶²,⁸⁸ The microscopic fracture surface of concrete specimens (including matrix crack, interfacial crack and transgranular crack) were characterised by SEM and the obtained BSE and SE photographs are shown in Fig. 21. It is obvious that different crack patterns are endowed with distinct fracture characteristics. For example, the fracture surface of matrix is relatively rough compared with the interfacial and

transgranular cracks since small grains (e.g. sands) debond from matrix leaving obvious grain boundary pits. Meanwhile, microcracks and micropores can also be observed from the matrix fracture surface in the BSE image, where crack initiation and propagation are more likely to appear.⁸⁹ The fracture surfaces of interfacial cracks exhibit a ladder-like characteristic which is related to the inclination of the aggregate. It is also covered by interfacial transition zone (ITZ) with high porosity and cement powders which is deemed to be generated by the surface shear sliding. A few cleaved aggregate grains can also be viewed on the fracture surface of interfacial cracks, which are mainly induced by the tensile stress. Additionally, compared with matrix and interfacial cracks, the fracture surfaces of transgranular cracks are relatively even where grain cleavages are dominant, indicating that transgranular cracks are mainly generated by tensile stress.

## 6. Conclusion

The made-to-order SHPB facility, coupled with the ultra-high-speed X-ray phase contrast imaging (XPCI) technique at the European Synchrotron Radiation Facility (ESRF) and the X-ray based digital image correlation (XDIC) technique, provides a useful probe to investigate the mechanical properties, subsurface fracturing process and internal deformation fields of different geomaterials (including cement, concrete and basalt) under dynamic compression. DEM modelling was utilised to further investigate the influence of heterogeneity on the dynamic deformation and fracturing properties. SEM is also used to qualify the fracture surface morphology of different cracks patterns from a microscale. The following results were made:

1. The XDIC technique is a promising one to allow for quantification of the deformation fields of geomaterials especially with high density contrast, like concrete and basalt. DEM modelling can complement the experimental results and also help validate the reliability of deformation and fracturing fields obtained by XDIC.

2. Both experimental and numerical results indicate a failure pattern dependence on the strain rate and heterogeneity. With an
increase of strain rate, fracturing patterns transform from interfacial cracks to transgranular cracks, and fracturing positions change from the top and bottom parts of the specimen to the middle. With an increase of heterogeneity, the crack patterns shift from pure tensile cracks to mixed (tensile-shear) cracks, and crack types develop from matrix crack to interfacial and transgranular cracks.

(3) The dynamic increase factors of geomaterials increase with increasing strain rate, exhibiting an obvious rate effect. Moreover, the rate effect differs with different heterogeneity, indicating that the rate effect is also affected by the intrinsic properties of geomaterials.

(4) Fracture surface morphologies of matrix cracks, interfacial cracks and transgranular cracks are endowed with distinct characteristics, e.g. rough surface with grain debonding in matrix cracks, ladder-like surfaces with cement powders in interfacial cracks, and flat surfaces with grain cleavage dominant in transgranular cracks.

### CRediT authorship contribution statement

H.C. Wang: Conceptualization, Funding acquisition, Investigation, Methodology, Writing – original draft, Writing – review & editing. K. Liu: Investigation. B. Lukic: Methodology, Resources. W.R. Hu: Investigation, Validation. C.H. Braithwaite: Supervision. J. Zhao: Supervision. A. Rack: Supervision. Q.B. Zhang: Supervision.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data will be made available on request.

### Acknowledgement

This work was financially supported by the Australian Research Council (LE150100058, IH150100006 and DE200101293). The authors would like to acknowledge the opportunities provided by the European Synchrotron Radiation Facility (ESRF, France) for experiments within the project (ME-1604). The first author also gives special thanks to Dr. Xiyao Sun from University of Oxford for the support during experiments and Dr. Navid Tourani from ARC Nanocomm Hub for the help of SEM operation.

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