Structural response of all-concrete LNG storage tanks under coupled blast loading and cryogenic conditions

Abstract

All-concrete liquefied natural gas (ACLNG) storage tanks have emerged as an innovative and cost-effective alternative to conventional LNG containment systems. However, their structural behaviour under the simultaneous action of blast loading and cryogenic temperature conditions remains largely unexplored, despite the critical implications for structural safety and operational reliability. This study investigates the dynamic response and blast-induced damage of ACLNG storage tanks constructed with both normal strength concrete (NSC) and ultra-high performance concrete (UHPC). Temperature-dependent constitutive models incorporating cryogenic strength enhancement, reduced ductility, and strain rate effects were developed to accurately represent material behaviour at low temperatures. The adopted models were validated against experimental data, confirming their ability to capture concrete response under combined cryogenic and dynamic loading conditions. A full-scale finite element model of the ACLNG storage tank was established in LS-DYNA to simulate the structural response to blast loading with explicit consideration of cryogenic temperature effects. The results demonstrate that low-temperature exposure significantly increases concrete brittleness and markedly alters the damage patterns of the inner containment vessel during blast events, emphasising the necessity of incorporating temperature-dependent material behaviour in structural design. The findings provide new insights into the blast resistance of ACLNG storage tanks and offer practical guidance for enhancing structural safety and resilience under extreme service conditions.

Keywords

ACLNG storage tank ultra-high performance concrete blast load cryogenic temperature KCC model numerical investigation

Introduction

The growing worldwide demand for liquefied natural gas (LNG) as a low-emission energy source has accelerated the development of advanced LNG storage systems. Traditional full-containment LNG storage tanks, which rely heavily on 9% nickel steel for their inner containment, present challenges such as high construction costs, long project timelines, and reliance on imported raw materials. In response to these limitations, all-concrete LNG (ACLNG) storage tanks have emerged as a viable alternative storage solution (Kogbara et al., 2013). The inner tank of an ACLNG storage tank is exposed to extreme cryogenic temperatures, specifically −161.5°C, during its operational lifetime, while the outer tank is typically subjected to thermal shock only under accident scenarios, such as spillage, leakage, or rupture of the inner tank (Rostasy and Wiedemann, 1983). In the present study, the term ‘cryogenic’ refers specifically to temperatures at or below −160°C, consistent with the operational storage temperature of LNG. Additionally, potential exposure to dynamic loading events, such as accidental blasts or terrorist attacks, poses critical safety challenges for ACLNG tanks. However, the unique structural and material characteristics of ACLNG tanks when exposed to severe environmental, such as cryogenic temperatures as well as dynamic loading events, remain underexplored. The combined effects of cryogenic temperatures as well as dynamic loading on the performance of ACLNG storage tanks are complex and necessitate a thorough understanding to ensure structural integrity and reliability in demanding operational environments.

Exposure to cryogenic temperatures markedly affects the mechanical characteristics of normal strength concrete (NSC), introducing changes in strength (Rostasy et al., 1979; Xie et al., 2014), brittleness (Jiang et al., 2020; Lin et al., 2022), fracture (Maturana et al., 1990; Rocco et al., 2001) and dynamic behaviour (Chi et al., 2024a; Qiao et al., 2016). The enhanced mechanical performances of NSC under low temperatures were attributed to the frozen pore water. However, NSC demonstrated noticeable brittleness under such conditions (Chi et al., 2024d; Lin et al., 2022).

Ultra-high-performance concrete (UHPC) adopted as an innovative substitute for NSC in many applications (Bani et al., 2025; Stefaniuk et al., 2024; Wu et al., 2023). This advanced material demonstrates exceptional promise for low-temperature applications, offering remarkable mechanical properties such as elevated strength, enhanced toughness and higher performance under dynamic loadings that effectively address the traditional limitations of NSC (Chi et al., 2024b; Kim et al., 2017). Jin et al. (Jin et al., 2024a) investigated the mechanical properties of modified UHPC with coarse aggregate incorporation and varying steel fibre contents across a temperature range from 20°C to −90°C. It showed that the specimens with 2% steel fibre content have an increase of 46.3% for compressive strength at −90°C compared to room temperature and the 38.6% of improvement for splitting tensile strength at −90°C relative to 20°C. Liu et al. (Liu et al., 2023) performed both three-point as well as four-point bending experiments to examine the flexural behaviour as well as fracture properties of UHPC over a wide temperature range, from ambient temperature to cryogenic conditions as low as −160°C. The tests were conducted using beam specimens with dimensions of 515 × 100 × 100 mm (length × height × width). The results demonstrated a significant improvement in flexural performance at lower temperatures. In particular, the fracture energy at −160°C was approximately 1.87 times higher than that measured at 20°C, indicating enhanced resistance to crack propagation under cryogenic conditions.

Recent research has explored the flexural bending behaviour of reinforced concrete structures at ultra-low temperatures. Liu et al. (Liu et al., 2010; Xiang-Lin et al., 2025) conducted four-point bending tests on 6 reinforced NSC beams with dimensions of 40 × 40 × 300 mm to evaluate their flexural behaviour over a temperature range from 20°C to −180°C. The experimental findings indicated that decreasing temperature led to a clear enhancement in both structural stiffness and load-carrying capacity. In particular, the ultimate load capacity increased substantially at lower temperatures, reaching approximately 1.3, 1.4, 1.9, 2.1, and 2.6 times the ambient temperature capacity at −40, −80, −120, −160, and −180°C, respectively. These results demonstrate the significant influence of cryogenic conditions on the flexural performance of reinforced NSC members. To further explore the performance of reinforced concrete beams at cryogenic temperatures, Yan and Xie (Yan and Xie, 2017a) conducted larger-scale experiments. A total of twelve sets of four-point bending tests were conducted on 65 mm × 120 mm × 1600 mm reinforced concrete beams. The experimental findings demonstrated that the load-carrying capacity of reinforced NSC beams increased under reduced temperature conditions. Specifically, the ultimate strength of the beams increased by factors of 1.0, 1.1, and 1.3 at −40°C, −70°C, and −100°C, respectively, compared to the corresponding beam tested at room temperature. Xie et al. (Xie et al., 2017) also investigated the ultimate strength behaviour of unbonded prestressed NSC beams with dimension of 65 × 120 × 1600 mm at 20, -40, −70 as well as −100°C with prestress levels: 0.4, 0.6 and 0.75 of the characteristic tensile strength of prestressed strands via four-point bending test. It was found that prestressing effectively delayed cracking even in low temperatures, and the crack initiation resistance increased by13.8% at −40°C, 20.42% at −70°C and 35.83% at −100°C, compared to the room temperature. Jin et al. (Jin et al., 2024b) investigated the shear behaviour of reinforced concrete beams at low temperatures through a two-stage thermo-mechanical coupled mesoscale simulation method. The researchers conducted numerical analyses considering variations in temperature (20°C to −90°C), structural size (300–1200 mm height), and shear span-to-depth ratio (1.0–2.3). Their findings revealed that compared to room temperature, RC beams at low temperatures exhibited more rapid shear failure with increased brittleness, enhanced nominal shear strength (up to 57.0% increase at −90°C), reduced mid-span displacement (up to 46.8% decrease), and more significant influences of size effects on nominal shear strength (increasing from 21.1% to 41.5% reduction when scaling from 300 mm to 1200 mm height).

The structural safety of LNG storage tanks under the action of extreme loading scenarios (e.g. impact (Liu et al., 2025) and blast loadings) is of great importance. A number of studies have explored the impact performance of LNG storage tanks (Peng et al., 2021; Zou et al., 2021, 2022). Zou et al. (2022) carried out large-scale impact tests as well as validated numerical simulations on all-steel LNG storage tanks subjected to wind-borne missile impacts with velocities up to 50 m/s and missile masses of approximately 36.5 kg. Their results revealed that, despite significant plastic deformation in the outer tank, the inner tank remained undamaged, primarily owing to the energy dissipation provided by the tank structure and the resistance of the internal liquid. Peng et al. (2019) explored numerical simulations to assess the response of large LNG storage tanks to aircraft impact scenarios. The study simulated the complete impact process of an A320 aircraft striking the LNG tank at 150 m/s, analysing impact forces, deflections, and plastic strains in both the outer concrete tank and 9% Nickel inner tank. Parametric analyses examined the effects of impact angle (0°–45°), position (three different heights), and velocity (100–150 m/s) on the tank’s dynamic response. The results indicated that although the outer tank experiences significant damage with the maximum deflections reaching 306 mm and plastic strains exceeding failure limits, the 9% Nickel inner tank where LNG is stored maintains its integrity.

Regarding the blast resistance of LNG storage systems, several studies have investigated the structural performance of concrete containment structures under explosive loading. Lee et al. (2016) explored the explosive resistant capabilities of prestressed concrete exterior walls in a 2.7 $\times 10^{5}$ m³ LNG storage facility when exposed to severe loading conditions. Full-scale computational modelling was employed to examine structural performance against TNT charges varying between 45.36 kg and 68.04 kg positioned at 1 m standoff distance. The findings indicated that the exterior wall maintained structural integrity without catastrophic failure when subjected to charges up to 68.04 kg TNT. However, the mid-height region was identified as the most critical location due to its relatively lower reinforcement ratio, making it more susceptible to blast-induced damage. A computational analysis was performed by Zhang et al. (2018) to investigate the blast response characteristics of a large-scale LNG containment structure, specifically examining a 1.6 $\times 10^{5}$ m³ facility located in Qingdao, China. Their findings showed that the structure was capable of resisting blast loads equivalent to approximately 2 t TNT at a standoff distance of 10 m without experiencing critical structural failure. Sun et al. (2023) performed a detailed fluid-structure interaction modelling to evaluate the damage behaviour of a scaled ACLNG storage tank with an outer diameter of 2.7 m and a height of 1 m under combined penetration and explosion scenarios. The study considered different explosive materials, including TNT, 8701, and Comp B, as well as multiple detonation locations such as external surface explosions and penetration-induced internal detonations. The results revealed that the junction regions between the tank wall and the top and rear plates were particularly vulnerable to damage because of stress concentration and the amplification of shock wave effects in these areas.

The present study focuses on analysing the structural behaviour of ACLNG storage tanks under blast loading, taking into accounting for the impacts of cryogenic temperatures on the concrete. Through comprehensive numerical simulations and systematic parametric analyses, this research evaluates both impacts of blast loading and cryogenic temperatures on the structural behaviour, damage mechanisms, and failure characteristics of ACLNG storage tanks, providing valuable understanding for improving their safety and design performance in extreme operational environments.

Structural configuration and components of the ACLNG storage tank

In this study, a full-scale ACLNG storage tank with a total storage capacity of 8 $\times 10^{4}$ m³ was considered. The structural configuration and main components of the tank are presented in Figure 1. The tank has an outer diameter of 59.7 m as well as an inner diameter of 55.5 m, and the LNG filling height was assumed to be 35 m. The wall thicknesses of the outer tank, inner tank, and base slab were all specified as 0.6 m (Arup). The detailed geometric parameters of the ACLNG storage tank are summarised in Table 1. The exterior and interior tank walls were constructed as cast-in-place prestressed reinforced concrete structures to enhance load-carrying capacity and structural reliability. The outer tank was further protected by a reinforced concrete dome, providing additional resistance against extreme loading conditions. Prestressing was applied using seven-wire steel tendons with a strand diameter of 15.2 mm, a nominal cross-sectional area of 15.7 mm². These tendons possess a yield strength of 1600 MPa and an ultimate tensile capacity of 1860 MPa, providing high load resistance. The prestressing system was configured with both vertical and circumferential tendons installed at intervals of 250 mm. In addition, the vertical prestressing tendon spacing was approximately 2500 mm, while the circumferential tendon spacing varied between 600 mm and 1200 mm depending on the structural requirements. Conventional reinforcement consisted of double-layer steel bars with a diameter of 20 mm, spaced at 200 mm intervals, and was provided in both the tank walls and base slab to ensure adequate structural stiffness and crack control. The inner tank was assumed to be fully exposed to cryogenic LNG and maintained at a uniform temperature of −160°C in this study, consistent with typical LNG storage conditions reported in the literature (Dahmani, 2011; Li et al., 2012). The outer tank was assumed to remain at an ambient temperature of 20°C due to the presence of insulation layers between the inner and outer tanks.

Figure 1.

Schematic diagram of ACLNG storage tank (a) Global structural layout of the ACLNG tank (Arup) (b) Arrangement of wall reinforcement and prestressing tendons (Standard, 2006).

Table 1.

Key geometric properties of ACLNG storage tank (in unit: m) (Arup).

A	B	C	D	E	Tank wall thickness	Tank base slab
55.5	35	60.9	55.5	8	0.6	0.6

Based on the ACLNG tank configuration and the assumed thermal boundary conditions, the numerical analysis must capture the coupled effects of cryogenic temperature and blast induced high strain rates. Cryogenic exposure changes the mechanical performance of concrete as well as steel, while blast loading introduces strong rate dependence and damage evolution. Therefore, a temperature and rate-sensitive constitutive description is required. Besides NSC, UHPC is introduced as an alternative tank material to enhance structural robustness under the multi-hazard scenarios. This is motivated by the expected benefits of UHPC, including substantially higher mechanical performances, which are critical for maintaining containment integrity during blast events. Therefore, the modelling strategy considers both NSC and UHPC, enabling a direct comparison of damage localisation and overall blast resistance under cryogenic exposure. The following section provides a description of the constitutive relationships and material properties applied to concrete and reinforcement in LS-DYNA.

Material constitutive relationships and parameters

Karagozian & case concrete model

LS-DYNA provides several advanced constitutive models for simulating concrete behaviour under dynamic loading (e.g. KCC (Malvar et al., 1997), RHT (Borrvall and Riedel, 2011) as well as CSCM (Wu et al., 2012)). These models have been extensively applied in the analysis of NSC structures under the action of blast effects. Among them, the KCC model is particularly advantageous because its material parameters can be estimated directly from the uniaxial compressive strength, allowing reliable numerical implementation even when detailed experimental data are limited. In contrast, UHPC exhibits significantly different mechanical characteristics compared to NSC, including enhanced tensile strength, improved fracture resistance, and greater load-carrying capacity. As a result, the default parameter generation approach is not sufficient, and appropriate calibration of the KCC model parameters is required to accurately represent UHPC behaviour (Lin, 2018). Furthermore, exposure to cryogenic temperatures alters key material properties, such as stiffness, strength, and failure mechanisms, while strain-rate effects under blast loading further influence the structural response. Therefore, these temperature-dependent and rate-sensitive characteristics must be incorporated into the constitutive modelling to ensure accurate simulation of both NSC and UHPC under combined cryogenic and blast loading scenarios.

Strength surface parameters

In the KCC model, the material parameters can be generated directly based on the unconfined compressive strength of concrete. For NSC, the strength surface parameters are determined using the empirical relationships provided in equations (1)–(3), which describe the failure envelope of concrete under different stress conditions (Malvar et al., 2000). In these equations, $f_{c}$ denotes the uniaxial compressive strength of NSC, expressed in MPa.

a_{0} = 0.2956 f_{c}; a_{1} = 0.4463; a_{2} = 0.0808 / f_{c}

(1)

a_{0 y} = 0.2232 f_{c}; a_{1 y} = 0.625; a_{2 y} = 0.2575 / f_{c}

(2)

a_{1 f} = 0.4417; a_{2 f} = 0.1183 / f_{c}

(3)

In present study, the uniaxial compressive strength of NSC was taken as 41.2 MPa at ambient temperature and 55.7 MPa under cryogenic conditions (−160°C), in accordance with the experimental findings reported by Yan and Xie (Xie et al., 2017). For UHPC, the corresponding compressive strengths were adopted as 161.2 MPa at 20°C and 211.6 MPa at −160°C, as documented in previous research (Chi et al., 2024b). Based on these values, the strength surface parameters required for the KCC model were calculated accordingly and are summarised in Tables 2 and 3.

Table 2.

Updated strength surface parameters for NSC.

	a ₀	a ₁	a ₂	a _1f	a _2f	a _0y	a _1y	a _2y
NSC 41.2 MPa at 20°C KCC default	1.22E + 7	0.446	2.0E-9	0.442	2.87E-9	9.20E + 6	0.625	6.25E-9
NSC at −160°C	1.65E + 7	0.479	1.45E-9	0.442	2.12E-9	1.24E + 7	0.625	4.62E-9

Table 3.

Updated strength surface parameters for UHPC.

	a ₀	a ₁	a ₂	a _1f	a _2f	a _0y	a _1y	a _2y
UHPC at 20°C (Liu et al., 2022)	5.48E + 7	0.446	1.15E-9	0.442	1.08E-9	3.5E + 7	0.625	3.37E-9
UHPC at −160°C	7.27E + 7	0.446	8.73E-10	0.442	8.21E-10	4.7E + 7	0.625	2.57E-9

Within the KCC constitutive framework, the tensile strength of concrete under cryogenic conditions is an essential parameter, as it governs the cracking behaviour and residual tensile capacity of concrete structures at cryogenic temperatures. For NSC, Shi et al. (Shi et al., 2016) proposed an empirical relationship describing the variation in tensile strength ( $f_{t}$ ) with temperature over the range from 20°C ∼ −196°C. This relationship is used to account for the temperature-dependent tensile response of concrete under cryogenic exposure.

f_{t} = 0.429 f_{c}^{0.509} - 196 ℃ \leq T \leq 20 ℃

(4)

where

f_{c}

is compressive strength under low temperature in MPa. Therefore, when

f_{c}

= 41.5 MPa,

f_{t}

= 2.85 MPa for NSC at 25°C, and

f_{t}

= 3.32 MPa for NSC at −160°C.

The UHPC tensile strength values adopted in this study were 7.20 MPa at 25°C and 11.25 MPa at −160°C, based on the experimental results reported by Chi et al. (2024b).

Relationship between λ and η

To describe the evolution of strength during both hardening and softening in the compressive and tensile meridians, the KCC model adopts a predefined relationship between the modified effective plastic strain (λ) and the corresponding strength scaling factor (η) for NSC (Wu and Crawford, 2015). However, due to the distinct mechanical characteristics of UHPC, the default formulation is not directly applicable. Therefore, a revised λ–η relationship was developed to accurately represent the strength evolution behaviour of UHPC in the present study (Xu et al., 2022). The adopted λ–η relationships for both NSC and UHPC are summarised in Table 4.

Table 4.

λ–η relationship of NSC and UHPC within KCC model.

NSC λ-η relationship (Chi, Li and Wu, 2024c)		UHPC λ-η relationship (Xu et al., 2022)
λ	η	λ	η
0.0	0.0	0.0	0.0
8 × 10⁻⁶	0.85	8 × 10⁻⁶	0.85
2.4 × 10⁻⁵	0.97	2.4 × 10⁻⁵	0.97
4 × 10⁻⁵	0.99	4 × 10⁻⁵	0.99
5.6 × 10⁻⁵	1	5.6 × 10⁻⁵	1
7.2 × 10⁻⁵	0.99	7.2 × 10⁻⁵	0.99
8.8 × 10⁻⁴	0.97	8.8 × 10⁻⁵	0.97
3.2 × 10⁻⁴	0.5	2.5 × 10⁻⁴	0.8
5.2 × 10⁻⁴	0.1	6.2 × 10⁻⁴	0.5
5.7 × 10⁻⁴	0.0	1.1 × 10⁻³	0.3
1.0	0.0	2 × 10⁻³	0.1
10	0	5 × 10⁻³	0.0
10¹⁰	0	10¹⁰	0.0

Strain rate sensitivity

Material behaviour under dynamic loading is strongly influenced by strain rate effects. The dynamic increase factor (DIF) is widely used to characterise this rate dependency and is defined as the ratio of material strength under dynamic loading to its corresponding static strength.

For NSC, the strain-rate sensitivity is obtained from previously reported dynamic test results in compression and splitting tension (Chi et al., 2024a). The corresponding compressive DIF (CDIF) and tensile DIF (TDIF) values at ambient temperature and cryogenic temperature (−160°C) are summarised in Table 5. It is noteworthy that the CDIF decreases at cryogenic temperature compared to ambient conditions, while the TDIF exhibits the opposite trend. This phenomenon can be attributed to the different failure mechanisms governing compressive as well as tensile behaviour at cryogenic temperatures. The diminished CDIF at cryogenic temperatures results from a combination of strength-related and microstructural factors. Research has established that concrete displaying elevated static compressive strength tends to show reduced sensitivity to loading rate (Guo et al., 2017; Ngo et al., 2013), a phenomenon consistent with the enhanced baseline strength observed at low temperatures. At −160°C, pore water within the concrete matrix is fully frozen, forming a rigid ice phase that significantly alters the internal microstructure (Zhengwu et al., 2018). The volumetric expansion of freezing water (approximately 9%) (Huang et al., 2024), combined with the mismatch in thermal contraction among concrete constituents, induces pronounced microcracking, particularly within the interfacial transition zone (ITZ) (Kogbara et al., 2013). These microcracks act as initial defects and weaken the load-bearing capacity of the matrix. Under impact loading, such defects rapidly coalesce into macrocracks, accelerating compressive failure and thereby reducing the relative strain-rate enhancement, leading to a lower CDIF at −160°C.

Table 5.

NSC DIF values under different temperature conditions (Chi et al., 2024a).

20°C		−160°C		20°C		−160°C
Strain rate	CDIF	Strain rate	CDIF	Strain rate	TDIF	Strain rate	TDIF
0	1	0	1	0	1	0	1
24.61	1.18	39.10	1.12	6.73	2.57	24.32	4.23
37.87	1.39	45.26	1.12	18.92	3.42	25.99	4.26
39.18	1.47	79.38	1.16	22.03	3.41	41.26	4.82
38.63	1.47	83.13	1.20	24.09	3.43	44.26	5.10
76.60	1.54	108.99	1.26	36.77	4.13	58.06	5.29
81.45	1.54	118.88	1.31	41.08	4.01	71.97	5.43
81.81	1.55	155.16	1.36	41.15	3.83	78.79	5.63
87.65	1.55	158.19	1.37	43.76	3.90	-	-
119.30	1.73	-	-	57.2	3.99	-	-
121.30	1.79	-	-	59.38	4.16	-	-
124.01	1.75	-	-	60.64	4.24	-	-
127.00	1.79	-	-	78.05	4.44	-	-
159.97	1.82	-	-	80.90	4.46	-	-
164.28	1.89	-	-	81.14	4.50	-	-
166.63	1.93	-	-	-	-	-	-
207.85	1.94	-	-	-	-	-	-

In contrast, the TDIF increases at −160°C. At this temperature, the frozen pore water forms a continuous ice skeleton within the concrete microstructure, which acts as a natural crack-bridging mechanism and enhances the resistance to crack initiation and propagation under dynamic tensile loading (Zhengwu et al., 2018). The ice-filled microcracks provide additional internal restraint and generate a prestressed effect that delays crack growth. These mechanisms collectively contribute to the enhanced tensile strain-rate sensitivity and the observed increase in TDIF at −160°C.

For UHPC, the DIF data at 20°C and −160°C are obtained from the experimental data reported by Chi et al. (Chi et al., 2024b), as listed in Table 6. The elevated TDIF values of UHPC at −160°C result from several interacting mechanisms. Ice crystals forming within micro-cracks act as natural bridges, strengthening aggregate-paste bonds and generating a pre-stressed state that retards crack growth (Zhengwu et al., 2018). Simultaneously, the fibre–matrix bond improves at cryogenic temperatures due to increased frictional resistance, as evidenced by deeper fibre surface scratches observed after cryogenic pull-out testing (Kim and Yoo, 2020).

Table 6.

UHPC DIF values under different temperature conditions (Chi et al., 2024b).

20°C		−160°C		20°C		−160°C
Strain rate	CDIF	Strain rate	CDIF	Strain rate	TDIF	Strain rate	TDIF
0	1	0	1	0	1	0	1
38.50	1.19	45.22	1.02	20.99	2.00	23.29	2.71
40.72	1.16	50.04	1.07	21.39	2.00	42.33	2.85
41.01	1.18	82.32	1.13	24.79	2.06	46.58	2.90
77.20	1.27	88.86	1.15	25.24	2.31	64.34	3.16
71.70	1.25	119.21	1.27	39.89	2.27	80.48	3.58
81.38	1.32	122.82	1.24	40.63	2.31	-	-
103.15	1.37	161.49	1.30	42.71	2.59	-	-
119.09	1.46	-	-	42.82	2.57	-	-
118.90	1.47	-	-	60.02	2.62	-	-
120.09	1.47	-	-	60.84	2.42	-	-
158.23	1.52	-	-	61.68	2.49	-	-
162.60	1.45	-	-	63.22	2.54	-	-
165.81	1.56	-	-	76.20	2.59	-	-
-	-	-	-	77.38	2.44	-	-
-	-	-	-	81.32	2.77	-	-

Equation of state (EOS)

The pressure–volumetric strain response in the KCC model is defined using the TABULATED_COMPACTION equation of state, allowing accurate representation of concrete behaviour under high confinement. For NSC, the EOS parameters can be automatically generated based on the uniaxial compressive strength, and the resulting values are provided in Table 7.

Table 7.

EOS for NSC at cryogenic temperature.

20°C (default)	$μ$	0	−0.0015	−0.0043	−0.01	−0.0305	−0.0513	−0.0726	−0.0943	−0.174	−0.208
	C (MPa)	0	21.70	47.31	75.96	144.32	217.68	308.83	472.47	2758	4219
	K (GPa)	14.47	14.47	14.67	15.41	18.33	21.27	24.19	26.40	59.41	72.34
−160°C	$μ$	0	−0.0015	−0.0043	−0.01	−0.0305	−0.0513	−0.0726	−0.0943	−0.174	−0.208
	C (MPa)	0	25.23	55.01	88.31	167.81	253.10	359.03	549.35	3207	4906
	K (GPa)	16.82	16.82	17.05	18.15	21.58	25.35	28.92	31.56	71.02	86.49

For UHPC, however, a customised EOS formulation is required due to its distinct mechanical response. Therefore, a piecewise-defined EOS was developed in the present study to accurately capture the pressure–volumetric strain relationship of UHPC, as described below.

{\begin{cases} p = K μ p < p_{c r u s h} \\ p = p_{c r u s h} + K_{l o c k} (μ - μ_{c r u s h}) p_{c r u s h} < p < p_{l o c k} \\ p = K_{1} \bar{μ} + K_{2} {\bar{μ}}^{2} + K_{3} {\bar{μ}}^{3} p > p_{l o c k} \end{cases}

(5)

where

p_{c r u s h}

represents the pressure corresponding to the initial change in slope of the EOS curve, while

p_{l o c k}

denotes the pressure at the second transition point. The elastic bulk modulus,

K

, is defined as the ratio of

p_{c r u s h}

to the corresponding volumetric strain

μ_{c r u s h}

, and can also be expressed as

K = \frac{E}{3 (1 - 2 ν)}

, where

E

is the modulus of elasticity, which is equal to 47 and 60 GPa at 20 and −160°C for NSC (Yan and Xie, 2017a) while for UHPC, it was 56 GPa at 20°C and rose to 74 GPa at −160°C (Chi et al., 2024b), respectively.

ν

is the Poisson’s ratio assumed to be 0.15 and 0.19 for NSC and UHPC, respectively. The developed EOS parameters for NSC and UHPC across different temperature levels are listed in Tables 7 and 8, respectively.

Table 8.

EOS for UHPC at cryogenic temperature.

20°C	$μ$	0	−0.0016	−0.0043	−0.01	−0.0305	−0.0513	−0.0726	−0.0943	−0.174	−0.2
	C (MPa)	0	29.18	83.66	194.6	503.2	801.5	1107	1418.2	3016.4	4930
	K (GPa)	22.71	22.71	23.39	24.07	30.66	33.38	37.93	41.56	93.57	114
−160°C	$μ$	0	−0.0016	−0.0043	−0.01	−0.0305	−0.0513	−0.0726	−0.0943	−0.174	−0.2
	C (MPa)	0	49.18	107.2	172.1	327.1	493.3	699.8	1070.7	6251	9561
	K (GPa)	27.15	27.15	27.96	28.78	36.65	39.91	45.35	49.69	112	136

Determination of damage accumulation parameters

Wu and Crawford (Wu and Crawford, 2015) reported that the parameter $b_{1}$ can be determined by calibrating the model against experimental stress–strain data obtained from uniaxial compression tests, whereas the parameter $b_{2}$ is evaluated through calibration with fracture energy derived from tensile test results. In the present single-element verification analyses, displacement-controlled loading was applied under both uniaxial compression and tension conditions utilising the *PRESCRIBED_MOTION, allowing accurate regulation of the imposed displacement, as shown in Figure 2. During the compression simulations, displacement was applied downward on the top surface at a constant rate of 2.5 mm/s, while in the tensile simulations, the same surface was displaced upward at a rate of 0.02 mm/s to represent uniaxial tension loading. The stress-strain curves clearly demonstrated that concrete became much more brittle at cryogenic temperatures, as reflected in the b₁ parameter values (see Figure 3). At −160°C, the b₁ values for both NSC and UHPC were significantly lower than at room temperature, indicating increased brittleness. For NSC at cryogenic temperature, it showed b₁ values ranging from 1.0 to 1.65, with even the highest value producing a steep post-peak drop in stress capacity. In terms of UHPC, referring to the revision of the damage evolution parameter by Su et al. (2022), in this study, b₁ was adjusted starting from 1.0. For UHPC at −160°C, the b₁ values decreased to as low as 0.1 (compared to 0.25 at room temperature), with lower b₁ values corresponding to more abrupt failures. The relationship between b₁ and brittleness was particularly evident when comparing the curves within each graph as b₁ decreased, the post-peak portions of the curves became steeper.

Figure 2.

Single element test configuration (Xu et al., 2020).

Figure 3.

Single model stress-strain curve under uniaxial compression.

In the present investigation, the parameter $b_{1}$ for NSC was assigned values of 1.65 at ambient temperature and 1.0 at −160°C. For UHPC, the corresponding $b_{1}$ values were taken as 0.25 at ambient temperature and 0.1 at −160°C. Owing to the absence of uniaxial tensile test data for NSC, and without loss of generality, the parameter $b_{2}$ is considered to be 1.35 for NSC at all temperatures. For UHPC, $b_{2}$ is taken as 1.35 at room temperature, whereas $b_{2} = 4.0$ is adopted at −160°C based on a series of trial simulations (see Figure 4). Because of the limited amount of triaxial tension test data, this study adopted the auto-generated value of 1.15 for b₃.

Figure 4.

Single model stress-strain curve under uniaxial tension.

The KCC model includes a damage parameter, $ω$ , which controls volumetric expansion associated with shear dilatancy. Its value depends on material type and confinement conditions. Recommended values range from 0.80 to 0.90 for well-confined NSC and below 0.50 for high-strength or UHPC (Wu and Crawford, 2015). In this study, $ω$ was taken as 0.8 for NSC and 0.5 for UHPC.

Constitutive model for steel reinforcement

Effect of temperature on material

Steel reinforcement exhibits noticeable changes in mechanical behaviour when subjected to cryogenic temperatures. Chanda (2015) reported that X80 steel experienced moderate strength enhancement under cold conditions, with yield strength increasing by 4.8% at −30°C and 11.7% at −90°C relative to room temperature. Dahmani et al. (2007) further demonstrated that extremely low temperatures can significantly improve steel strength. Their study showed that reinforcing steel gained approximately 77.0% higher yield strength at −196°C, while prestressing steel showed a 17.9% increase at −165°C compared with ambient conditions. Additional investigations by Yan and Xie (2017b) on reinforced steel grades, including HRB335 and HRB400, revealed increases in stiffness and strength as temperature decreased. For HRB335 steel, reductions in temperature to −165°C resulted in increases of 9.5% in elastic modulus, 16.6% in yield strength, and 22.8% in ultimate strength. However, this strength improvement was accompanied by a decrease in ductility of approximately 30%. Similarly, Xie et al. (2023) examined mild steels such as Q235, Q355, and Q460 and found that cryogenic exposure led to considerable strength enhancement. In particular, Q235 steel showed increases of 61.1% in yield strength and 29.0% in ultimate strength at −165°C compared with room temperature. These findings demonstrate that while cryogenic temperatures improve the strength and stiffness of steel reinforcement, they may also reduce ductility, which is an important consideration for structural performance under extreme loading conditions.

Steel reinforcement exhibits distinct thermal behaviour compared to the surrounding concrete. Under cryogenic exposure, steel undergoes relatively small dimensional changes. This mismatch in thermal response between steel and concrete can help limit excessive deformation of the reinforcement, thereby contributing to the preservation of its structural function under low-temperature conditions. Some studies have indicated that the bond stiffness and bond strength are enhanced at low temperatures. Experimental pull-out tests by Vandewalle (1989) demonstrated that the ultimate bond strength between steel and concrete increased by 94.4% at −165°C, compared with ambient conditions. Similarly, Jin et al. (2023) and Zhang et al. (2023) evaluated the bond performance at cryogenic temperatures through combined pull-out tests and numerical simulations, reporting an approximately linear increase of 11.8% in ultimate bond strength as the temperature decreased from 20°C ∼ −120°C.

Yan and Xie (2017b) and Xie et al. (2023) investigated the mechanical behaviour of reinforcing steel under cryogenic temperature conditions. Their findings indicated that reductions in temperature resulted in increases in Young’s modulus, yield strength, as well as ultimate strength. However, a transition from ductile to brittle behaviour was observed for HRB335 and HRB400 reinforcing steels when the temperature decreased below approximately −80°C. The experimental trends of the normalised elastic modulus as well as tensile strength, respectively, in accordance with the results reported by Yan and Xie and Xie presented in Figure 5(a) and 5(b).

Figure 5.

Variation in elastic modulus and yield strength with temperature for different steels.

Based on the experimental observations, regression analysis was performed to establish temperature-dependent relationships for steel reinforcement properties. In this study, the variation in elastic modulus and yield strength with temperature was defined using empirical expressions derived from the HRB335 steel data, as given below:

I_{E} = \frac{E_{T}}{E_{a}} = - 0.0003 T + 1.006 - 165 ℃ \leq T \leq 20 ℃

(6)

I_{y} = \frac{f_{T}}{f_{a}} = - 0.0013 T + 1.026 - 165 ℃ \leq T \leq 20 ℃

(7)

where T is in °C,

I_{E}

and

I_{y}

denote the normalised elastic modulus and yield strength, respectively.

E_{a}

and

f_{a}

refer to the respective values at ambient temperature in GPa and MPa, while

E_{T}

and

f_{T}

represent the elastic modulus and yield strength at the corresponding low temperature in GPa and MPa.

Strain rate effect

The strain rate sensitivity of steel reinforcement is incorporated using the dynamic increase factors for yield and ultimate tensile strengths, as proposed in the CEB model (Béton, 1988), are expressed as follows:

YDIF = \frac{f_{y}}{f_{y 0}} = 1.0 + (\frac{6.0}{f_{y 0}}) \ln (\frac{\dot{ε_{s}}}{\dot{ε_{s 0}}})

(8)

UDIF = \frac{f_{u}}{f_{u 0}} = 1.0 + (\frac{7.0}{f_{u 0}}) \ln (\frac{\dot{ε_{s}}}{\dot{ε_{s 0}}})

(9)

where YDIF and UDIF represent the dynamic increase factors for yield strength and ultimate tensile strength, respectively, which quantify the enhancement in steel strength under dynamic loading compared to quasi-static conditions.

f_{y}

and

f_{u}

denote the dynamic yield strength as well as dynamic ultimate tensile strength, respectively, while

f_{y 0}

and

f_{u 0}

are the corresponding static strengths in MPa.

{\dot{ε}}_{s}

is the applied strain rate, and

{\dot{ε}}_{s 0}

is the reference quasi-static strain rate, taken as

5.0 \times 10^{- 4} s^{- 1}

. These factors account for the strain rate sensitivity of steel reinforcement, which leads to increased strength under high-rate loading conditions such as blast events.

Model validation for a reinforced concrete beam subjected to static loading under cryogenic conditions

To validate the reliability of the reinforced concrete model under cryogenic conditions, the quasi-static bending test conducted by Liu et al. (2010) and Xiang-Lin et al. (2025) was used as a reference. According to the experimental data, the concrete compressive strength was approximately 20 MPa. The reinforced concrete beam specimens had dimensions of 40 mm × 40 mm × 300 mm. The longitudinal and secondary reinforcement bars had a diameter of 4 mm, while the stirrups were formed using steel wires with a diameter of 1.6 mm, as illustrated in Figure 6. Additional geometric and reinforcement details are available in Liu et al. (Liu et al., 2010; Xiang-Lin et al., 2025). A corresponding finite element model was developed in LS-DYNA to replicate the quasi-static test conditions, using the implicit solver to ensure numerical stability and accuracy. As shown in Figure 7, the numerical model consisted of three main components: the reinforced concrete beam, the loading platen, and the support system, which together simulated the experimental setup. A mesh sensitivity study was conducted to evaluate the influence of element size on numerical accuracy and computational efficiency. Three mesh schemes were examined. In Group 1, the element sizes assigned to the concrete, reinforcement, loading platen as well as support were 5 mm, 2.5 mm, 5 mm, as well as 5 mm, respectively. For Group 2, the mesh sizes were increased to 10 mm for the concrete, loading platen, and support, while a mesh size of 5 mm was used for the reinforcement. In Group 3, a coarser discretisation was adopted, with element sizes of 20 mm for the concrete, loading platen, and support, and 10 mm for the reinforcement. The results showed that further mesh refinement from group 2 to group 1 led to only minor changes in the predicted response while significantly increasing computational cost, whereas the coarser mesh in group 3 resulted in noticeable deviations in the numerical results. Therefore, the mesh configuration in group 2 was selected as a reasonable compromise between computational efficiency and numerical accuracy for subsequent analyses.

Figure 6.

Dimensions of reinforced concrete beam (Liu et al., 2010).

Figure 7.

Details of the reinforced concrete beam configuration.

The concrete was modelled using the KCC model, while the steel reinforcement was represented using the MAT_PIECEWISE_LINEAR_PLASTICITY material model to capture its nonlinear behaviour. The loading platen and support were defined as rigid bodies using the MAT_RIGID material model. The material parameters adopted in the simulation are listed in Table 9. The numerical analysis was performed using the implicit solver in LS-DYNA to ensure stable convergence under quasi-static loading conditions. The load was applied through the upper loading platen, with a spacing of 80 mm between the two loading points, consistent with the experimental configuration. Displacement-controlled loading was imposed on the platen to replicate the quasi-static test conditions. The numerical results obtained in this study were subsequently compared with the experimental data at both 20°C and −160°C for validation purposes.

Table 9.

Material properties of concrete and steel reinforcement used in the quasi-static validation.

Material	LS-DYNA model	Input parameters	20°C	−160°C
Concrete	MAT_CONCRETE_ DAMAGE_REL3 MAT_ADD_ EROSION	Density Strength parameters λ-η relationship EOS Maximum principal strain	2400 $kg / m^{3}$ Refer to Table 2 Refer to Table 4 Refer to Table 7 0.9	2400 $kg / m^{3}$ Refer to Table 3 Refer to Table 4 Refer to Table 8 0.9
Steel reinforcement	MAT_PIECEWISE_ LINEAR_PLASTICITY	Density Yield strength Poisson’s ratio Young’s modulus	7800 $kg / m^{3}$ 329 MPa 0.3 198 GPa	7800 $kg / m^{3}$ 368 MPa 0.3 204 GPa
Loading platen & support	MAT_RIGID	Density Poisson’s ratio Young’s modulus	7800 $kg / m^{3}$ 0.3 210 GPa	7800 $kg / m^{3}$ 0.3 210 GPa

Figure 8 illustrates the damage pattern of the reinforced concrete beam subjected to displacement-controlled loading. The accuracy of the numerical model was assessed by comparing its predictions with the quasi-static four-point bending experimental results (Liu et al., 2010). As shown in Figure 9, the simulated load–deflection relationship at 20°C closely follows the experimental trend, with a discrepancy of nearly 11.43%. At −160°C, the numerical predictions show strong agreement with the corresponding test observations. The model effectively captured the influence of low temperature on both the material behaviour and the overall structural response. Notably, the beam exhibited greater stiffness and an increased load-bearing capacity at −160°C compared to ambient conditions, which is consistent with the expected strengthening effect of cryogenic exposure. The difference in the maximum deflection between the simulation and experiment at −160°C was approximately 12.51%, confirming the reliability and accuracy of the developed finite element model in reproducing the structural response under cryogenic conditions.

Figure 8.

Comparison of reinforced concrete beam failure patterns at (a) 20°C and (b) −160°C (Xiang-Lin et al., 2025).

Figure 9.

Load–deflection curves from experimental and simulation results.

Model validation of reinforced concrete slab subjected to blast loading

Experimental programme

Validation of the numerical model was performed using blast experimental results obtained by Choi et al. (2018) on a prestressed reinforced concrete slab. The tested slab had dimensions of 1.0 m × 1.4 m × 0.3 m (width × length × thickness), and the reinforcement layout and rebars details are shown in Figure 10. The slab was reinforced with both prestressing tendons and reinforcing bars. Steel bars with a nominal diameter of 13 mm were arranged in two orthogonal directions to form a reinforcing mesh. The reinforcing bars were placed near both the top and bottom faces of the slab, with a concrete cover of 50 mm. The bar spacing in both primary and secondary direction was 100 mm. The slab was prestressed using 7-strand steel tendons with a nominal diameter of 15.2 mm and an ultimate tensile strength of 1860 MPa. Each tendon was applied with an initial prestressing force of approximately 510 kN.

Figure 10.

Geometric and reinforcement details of the prestressed concrete slab in the blast experiment (Choi et al., 2018) (unit: mm).

The blast loading was generated by a spherical explosive charge of 25 kg ANFO, detonated at a standoff distance of 1.0 m from the slab surface. The structural response of the slab was monitored during the test. In particular, the midspan deflection was measured using a linear variable differential transformer (LVDT) installed at the centre of the rear surface of the slab. After the blast event, the rear-surface crack patterns and damage distribution were recorded and used as key indicators for model validation.

Finite element model

A finite element model was established in LS-DYNA to replicate the experimental setup. The numerical model included the explosive, surrounding air domain, and the prestressed reinforced concrete slab, as illustrated in Figure 11.

Figure 11.

Numerical simulation model of the prestressed reinforced concrete slab.

The air as well as explosive was represented utilising the Arbitrary Lagrangian–Eulerian (ALE) multi-material formulation, whereas the concrete slab was modelled using solid Lagrangian elements. Based on the mesh sensitivity analysis discussed in Section 4, a uniform element size of 10 mm was adopted throughout the model. Fluid-structure interaction (FSI) between the ALE domain and the concrete slab was implemented using the CONSTRAINED_LAGRANGE_IN_SOLID coupling algorithm to ensure accurate transmission of blast loads. The reinforcement was embedded within the concrete using the CONSTRAINED_BEAM_IN_SOLID approach.

The explosive charge was defined as a spherical ANFO charge with a mass of 25 kg, implemented utilising the INITIAL_VOLUME_FRACTION_GEOMETRY method. The concrete material behaviour was described utilising the KCC constitutive model, with parameters corresponding to C40 concrete at ambient temperature.

Material properties and constitutive models

In LS-DYNA, air behaviour is commonly defined using the MAT_NULL material model in combination with the EOS_LINEAR_POLYNOMIAL (Hallquist, 2013). The general expression for pressure is given by:

p = C_{0} + C_{1} µ + C_{2} µ^{2} + C_{3} µ^{3} + (C_{4} + C_{5} µ + C_{6} µ^{2}) E

(10)

where

p

represents the pressure,

C_{0}

C_{6}

are material constants, and

μ = \frac{ρ}{ρ_{0}} - 1

, with

ρ

and

ρ_{0}

denoting the current and reference densities, respectively.

E

is the internal energy per unit reference volume. When modelling air as an ideal gas, the constants are assigned as

C_{0} = C_{1} = C_{2} = C_{3} = C_{6} = 0

and

C_{4} = C_{5} = γ - 1

, resulting in the simplified pressure–energy relationship:

p = (γ - 1) \frac{ρ}{ρ_{0}} E

(11)

where γ is the ratio of specific heats, and

ρ_{0}

is the initial air density. In this study, γ = 1.4,

ρ_{0}

= 1.225 kg/

m^{3}

and

E

is 2.5

\times 10^{5}

m^{3}

(Chi et al., 2023).

The explosive material was modelled using the MAT_HIGH_EXPLOSIVE_BURN formulation coupled with the Jones–Wilkins–Lee (JWL) equation of state to describe the pressure generated during detonation. The JWL EOS can be expressed as (Qian et al., 2021):

P = A (1 - \frac{ω}{R_{1} V}) e^{- R_{1} V} + B (1 - \frac{ω}{R_{2} V}) e^{- R_{2} V} + \frac{ω E}{V}

(12)

where

P

is the hydrostatic pressure,

A

B

R_{1}

R_{2}

, and

ω

are explosive-specific constants,

V

is the relative volume, and

E

represents the internal energy per unit volume. The material properties and JWL parameters adopted for ammonium nitrate fuel oil (ANFO) and TNT are summarised in Table 10.

Table 10.

Explosive material properties and corresponding EOS parameters.

Parameter	ANFO (Sanchidrian et al., 2015)	TNT (Dobratz, 1981)
$ρ_{0}$ (kg/ $m^{3}$ )	830	1603
$v_{0}$ (m/s)	3879	6930
$P_{C J}$ (GPa)	3.25	21
$A$ (GPa)	231.8	371.2
$B$ (GPa)	3.414	3.231
$R_{1}$	6.76	4.5
$R_{2}$	1.07	0.95
ω	0.36	0.3
$E_{0}$ (J/ $m^{3})$	$1.58 \times 10^{9}$	$7 \times 10^{9}$

The strain response of the prestressing tendon and concrete beam follows the condition of compatible condition (Do et al., 2018),

ε_{T} = ε_{C} + ε_{T e}

(13)

where

ε_{C}

represents the strain associated with concrete shrinkage,

ε_{T e}

is the tensile strain in the prestressed tendon caused by interaction forces, and

ε_{T}

corresponds to the thermal strain in the tendon induced by temperature reduction in the absence of external restraint.

In the numerical model, prestressing was introduced by simulating thermal contraction of the tendons. Based on the compatibility of deformation between the concrete and prestressed tendon, the required temperature variation ( $Δ T$ ) can be determined from the equilibrium relationship:

Δ T \times α = \frac{f}{A_{C} E_{C}} + \frac{f}{A_{s} E_{s}}

(14a)

which can be rearranged as:

Δ T = \frac{f}{α} \times (\frac{1}{A_{C} E_{C}} + \frac{1}{A_{s} E_{s}})

(14b)

where

f

is the prestressing force (kN),

A_{s}

and

E_{s}

are the cross-sectional area and elastic modulus of the prestressing tendon, respectively, and

A_{C}

and

E_{C}

represent the corresponding properties of the concrete.

α

is the coefficient of thermal expansion of the prestressing tendon, taken as

1.0 \times 10^{- 4} {° C}^{- 1}

in this study (Do et al., 2018), and

Δ T

is the equivalent temperature reduction applied to generate the desired prestressing force.

The temperature-dependent behaviour of the prestressing tendons was defined using MAT_ADD_THERMAL_EXPANSION, which enables the introduction of thermal strain through a prescribed temperature history. A LOAD_THERMAL_LOAD_CURVE was employed to specify the relationship between temperature and time for the tendons. In combination with this thermal loading, the CONTROL_DYNAMIC_RELAXATION option was adopted to establish the prestressing force by allowing the model to reach a stable equilibrium state prior to the blast analysis.

Model validation

Figure 12 compares the experimentally observed rear-surface crack pattern with the numerically predicted failure pattern. It showed good agreement in damage distribution and crack orientation. Figure 13 presents the midspan displacement time-history curves obtained from both the experimental measurements and the numerical simulations. The deflection response was recorded using a LVDT positioned at the mid-point of the rear surface of the concrete slab. A close correlation between the experimental and numerical results is observed according to both the overall deformation trend and peak displacement response. The predicted response from the finite element model closely follows the experimentally measured behaviour. In addition, the maximum deflection values obtained from the simulation and the experiment differ by approximately 10.12%, demonstrating that the numerical model provides an accurate representation of the structural response of the prestressed concrete slab subjected to blast loading.

Figure 12.

Experimental and numerical failure pattern comparison of the RC slab.

Figure 13.

Midspan response time histories.

Structural performance of the ACLNG storage tank to blast loading at cryogenic temperature

To evaluate the dynamic behaviour of the ACLNG storage tank subjected to blast loading, a full-scale numerical model was developed. The computational domain included an air region covering a domain of 70 m × 70 m × 65 m along the X, Y, and Z directions, as illustrated in Figure 14.

Figure 14.

Finite element model of ACLNG storage tank.

The LNG was modelled using MAT_NULL, consistent with the formulation adopted for air, while the pressure–volume relationship of LNG was defined using the Grüneisen equation of state. Under compressive conditions, the pressure is expressed as:

P = \frac{ρ_{0} C^{2} μ [1 + (1 - \frac{γ_{0}}{2}) μ - \frac{a}{2} u^{2}}{{[1 - (S_{1} - 1) μ - S_{2} \frac{μ^{2}}{μ + 1} - S_{3} \frac{μ^{2}}{{(μ + 1)}^{2}}]}^{2}} + (γ_{0} + a μ) E

(15)

For expansion, the pressure is given by:

P = ρ_{0} C^{2} μ + (γ_{0} + α μ) E

(16)

where

C

represents the intercept of the shock velocity–particle velocity (

u_{s}

–

u_{p}

) relationship;

S_{1}

S_{2}

, and

S_{3}

are material constants defining the slope of this relationship;

γ_{0}

is the Grüneisen parameter;

E

denotes the internal energy per unit volume; and

μ

represents the volumetric strain, defined as

μ = ρ / ρ_{0} - 1

, where

ρ

and

ρ_{0}

correspond to the present as well as reference densities, respectively. The EOS parameters for LNG were adopted as

C = 2200

m/s,

S_{1} = 0

S_{2} = 0

S_{3} = 0

γ_{0} = 0

, and

ρ = 480

kg/m³ (Zou et al., 2022).

The surrounding air, explosive charge as well as LNG were represented utilising the ALE multi-material method, while the concrete tank was modelled with a Lagrangian formulation. FSI was incorporated using the CONSTRAINED_LAGRANGE_IN_SOLID coupling, allowing effective transfer of pressure and interaction forces. The material model and properties of the ACLNG storage tank are summarised in Table 11.

Table 11.

Key design and material values of the ACLNG storage tank.

Element	LS-DYNA model	Input parameters	NSC	UHPC
Concrete (including outer & inner wall, dome and base slab)	MAT_CONCRETE_ DAMAGE_REL3 MAT_ADD_ EROSION	Density Strength parameters λ-η relationship DIF EOS Maximum principal strain	2400 $kg / m^{3}$ Refer to Table 2 Refer to Table 4 Refer to Table 5 Refer to Table 7 0.9	2400 $kg / m^{3}$ Refer to Table 3 Refer to Table 4 Refer to Table 6 Refer to Table 8 0.9
Steel reinforcement & Prestressed tendon	MAT_PIECEWISE_ LINEAR_ PLASTICITY	Density Yield strength Poisson’s ratio Young’s modulus Strain rate	7800 $kg / m^{3}$ Refer to equation (7) 0.3 Refer to equation (6) Refer to equations (8) & (9)	7800 $kg / m^{3}$ Refer to equation (7) 0.3 Refer to equation (6) Refer to equations (8) & (9)
Perlite insulation (Peng et al., 2019)	MAT_PLASTIC_ KINEMATIC	Mass density Yield strength Poisson’s ratio Young’s modulus	66 $kg / m^{3}$ 0.5 MPa 0.4 13.3 GPa	66 $kg / m^{3}$ 0.5 MPa 0.4 13.3 GPa

In accordance with AS 3961: 2017 (Standard, 2017), safety regulations require a minimum separation distance of 1.5 m between the tank and the surrounding protective barrier. Accordingly, a standoff distance of 1.5 m was adopted between the TNT and the outer tank wall in the present analysis.

The explosive charge was implemented using the INITIAL_VOLUME_FRACTION_GEOMETRY approach as a rectangular TNT-equivalent load of 1800 kg, simulating a small delivery vehicle scenario (Chipley et al., 2012).

Figure 15 shows the von Mises stress field in the ACLNG storage tank after prestressing was applied and before the blast load was introduced, representing the initial stress condition of the structure. The structural response under blast loading is presented in Figure 16. The outer and inner tanks exhibit different deformation characteristics, which are strongly influenced by the cryogenic temperature at −160°C. The exterior tank demonstrates a relatively uniform effective plastic strain distribution, demonstrating that the structural response is governed by overall bending behaviour (see Figure 16(a)). In contrast, the interior tank exhibits pronounced strain localisation, indicating a higher tendency for concentrated damage and potential local failure under blast loading (see Figure 16(b)).

Figure 15.

Stress distribution of the ACLNG storage tank after prestressing.

Figure 16.

Comparison of blast responses between the exterior and interior ACLNG storage tanks.

Cryogenic temperature exposure significantly affects the mechanical behaviour of concrete. Extremely low temperatures increase material brittleness and reduce deformation capacity, making the structure more prone to cracking and spalling when subjected to dynamic loading. The displacement time-history curves shown in Figure 17 further illustrate the transient response of the exterior tank, characterised by a rapid initial increase in displacement followed by a gradual reduction in deformation rate as the structural motion stabilises. The presence of cryogenic conditions may further amplify the peak deformation response, thereby increasing the structural demand on the tank.

Figure 17.

Time histories of displacement and total energy under blast loading.

These results demonstrate the importance of evaluating the combined effects of prestressing, blast loading as well as cryogenic temperature on the structural response of ACLNG storage tanks. In particular, the interaction between the inner and outer tank components plays a critical role in determining the overall structural behaviour and damage resistance of the containment system under extreme loading conditions.

Parametric study

Impact of concrete material on structural response

The damage response of the inner tank was evaluated for two material configurations, namely NSC and UHPC, while the outer tank was constructed using NSC in both cases. The comparison, presented in Figures 16 and 18, corresponds to a blast scenario involving a 1.8 t TNT charge at a standoff distance of 1.5 m. For the NSC inner tank (Figure 16(b)), the damage zone is noticeably more extensive than that observed in the UHPC inner tank (Figure 18). Significant spalling and widespread material degradation are evident in the NSC case, indicating substantial structural damage and reduced load-carrying capacity.

Figure 18.

Damage response of the UHPC inner tank.

This behaviour is primarily associated with the relatively lower strength and reduced deformation resistance of NSC compared to UHPC. In addition, the exposure to cryogenic temperature conditions further influences the material response. Low temperatures tend to increase the brittleness of concrete, thereby reducing its ability to dissipate energy under dynamic loading. As a result, the NSC inner tank becomes more susceptible to blast-induced cracking, spalling, and structural deterioration, leading to a larger damaged region.

In contrast, the UHPC inner tank exhibits a more confined damage distribution and significantly less spalling. The superior mechanical properties of UHPC, including its higher compressive strength, improved tensile resistance, and enhanced energy absorption capacity, contribute to its improved resistance against blast-induced damage. Furthermore, UHPC demonstrates greater stability under cryogenic conditions, maintaining its structural integrity more effectively than NSC. Consequently, the UHPC inner tank shows a more controlled damage pattern and improved overall structural performance.

The comparative results clearly demonstrate the improved performance of UHPC relative to NSC for interior tank applications in ACLNG storage systems. The use of UHPC substantially reduces damage severity and limits the spatial extent of structural degradation, thereby enhancing the blast resistance and structural reliability of the containment system under combined cryogenic and blast loading conditions.

The selection of UHPC for both the exterior and interior tanks was motivated by the objective of evaluating high-performance material solutions capable of improving structural resistance under severe cryogenic and blast loading conditions. UHPC possesses superior mechanical properties, including higher strength, enhanced fracture resistance, and improved energy absorption capacity, which are expected to enhance the structural resilience of ACLNG containment systems.

As shown in Figure 19, the ACLNG storage tank constructed entirely with UHPC demonstrates significantly improved damage resistance compared to the NSC configuration presented in Figure 16. The UHPC outer tank exhibits a more confined damage region, with reduced spatial extent of effective plastic strain. Likewise, the UHPC inner tank shows a more localised damage response and improved structural integrity, indicating its enhanced ability to withstand blast-induced loading. The improved performance of UHPC can be attributed to its superior strength and resistance to crack initiation and propagation, which limit the development and expansion of blast-induced damage.

Figure 19.

Structural damage distribution in the ACLNG storage tank with UHPC.

In contrast, the tanks constructed with NSC, as discussed in Section 6, show more extensive damage and greater susceptibility to cracking and spalling. This behaviour is associated with the comparatively lower strength and fracture resistance of NSC, particularly under the combined influence of cryogenic temperatures and high-intensity dynamic loading. These findings highlight the effectiveness of UHPC as a promising material for improving the blast resistance and structural safety of ACLNG storage tanks operating in extreme environments.

Impact of liquid level on structural response

The liquid filling level has a substantial influence on the blast behaviour of the inner tank in the ACLNG containment system. Figure 20 illustrates the damage distribution of the NSC inner tank subjected to a 1.8 t TNT blast under different liquid level conditions. At higher filling levels, such as the 75% case shown in Figure 20(a), the cryogenic LNG generates higher internal hydrostatic pressure on the tank wall, which provides additional confinement and limits structural deformation. When the filling level decreases to 50%, as presented in Figure 20(b), the reduction in internal pressure weakens this confinement effect, allowing larger deformation of the inner tank wall. Consequently, the damaged region observed in the 50% filling condition is noticeably larger than that in the fully filled and 75% filled scenarios. In the completely empty condition shown in Figure 20(c), the absence of internal LNG pressure results in the most severe damage extent among all cases.

Figure 20.

Effect of filling ratio on the damage distribution of the inner tank.

These findings demonstrate that the liquid level strongly affects the structural behaviour of the interior tank subjected to blast loading. Higher LNG filling levels improve the blast resistance and containment performance of the ACLNG storage system by providing internal restraint against deformation. The presence of cryogenic liquid enhances the structural stability of the tank and reduces the likelihood of large-scale structural failure when subjected to extreme dynamic loading.

Impact of charge weight on structural response

The damage characteristics of the ACLNG storage tank subjected to blast loading are strongly impacted by the TNT charge weight, as illustrated in Figures 21 and 22 for the outer and inner tanks, respectively. In this investigation, both the inner and outer tank structures were constructed using NSC. Four charge weights, namely 454 kg, 1800 kg, 4500 kg, and 27000 kg, were considered in this study. These charge magnitudes were selected based on equivalent TNT masses associated with potential vehicle-borne explosive threats, including SUV/van, water truck, and semitrailer scenarios (Chipley et al., 2012). Figure 21 illustrates the spatial distribution of damage in the outer tank under various TNT charge levels of 454 kg, 4500 kg as well as 27000 kg. As the explosive mass increases, both the intensity and extent of effective plastic strain in the outer tank increase noticeably. For the 454 kg charge (Figure 21(a)), deformation is primarily limited to localised areas, particularly near the base and upper sections of the tank wall. Conversely, when the charge weight is increased to 4500 kg (Figures 21(b) and 22(b)) and further to 27000 kg (Figures 21(c) and 22(c)), the affected regions become significantly larger, indicating more widespread structural damage across the tank. The elevated blast intensity induces severe material degradation, indicating that the concrete approaches its ultimate failure state, characterised by extensive cracking, spalling, and the formation of large openings in the tank wall.

Figure 21.

Outer tank damage patterns at different TNT charge levels.

Figure 22.

Inner tank damage patterns at different TNT charge levels.

As the TNT charge weight increases, the resulting blast pressure and impulse acting on the ACLNG storage tank become more severe, leading to amplified deformation and more extensive damage across the interior and exterior tank systems.

Conclusion and limitations

Conclusions

This study presents a comprehensive evaluation of the structural behaviour of All Concrete Liquefied Natural Gas (ACLNG) storage tanks subjected to combined blast loading as well as cryogenic temperature conditions.

• UHPC exhibited significantly improved performance compared with NSC when exposed to blast loading and cryogenic temperatures. UHPC showed enhanced resistance to damage and spalling, contributing to improved structural stability. The compressive strength of UHPC increased from 161.2 MPa at ambient temperature to 211.6 MPa at −160°C, representing a 31.5% enhancement.

• The enhanced Karagozian & Case Concrete (KCC) modelling approach efficiently simulates how materials behave under varying temperatures, creating a reliable computational analysis framework. The validated models showed agreement with experimental data within approximately 11.43% and 12.51% discrepancy in load-deflection response at 20°C and −160°C respectively.

• Exposure to cryogenic temperatures markedly alters the mechanical behaviour of concrete, resulting in increased brittleness and decreased ductility.

• The LNG filling level had a pronounced influence on the blast resistance of the inner tank. At 75% fill, internal LNG hydrostatic pressure provided confinement that limited wall deformation and reduced damage extent compared to the 50% fill and empty conditions. The empty tank exhibited the most severe and spatially extensive damage among all filling scenarios, demonstrating the critical role of maintaining sufficient liquid content for structural safety under blast events.

• As the TNT charge weight increased, damage to both tanks became more severe and widespread. At 454 kg, damage was limited to small localised areas, while at 4500 kg and 27000 kg, extensive cracking, spalling, and large openings developed across the tank walls.

Limitations

Despite the contributions of this study, several limitations should be noted. A uniform temperature distribution was assumed between −160°C (inner tank) and 20°C (outer tank), whereas actual conditions involve a thermal gradient through the insulation, which should be considered in future coupled thermal–structural analyses. Second, perfect bond between steel reinforcement and concrete was assumed throughout the analyses. Although experimental evidence supports enhanced bond strength at cryogenic temperatures, bond-slip behaviour under combined cryogenic and dynamic loading conditions warrants further investigation through dedicated pull-out test simulations. Finally, long-term effects such as prestress loss, freeze-thaw cycling, and material degradation under repeated cryogenic exposure were not considered and represent important directions for future experimental and numerical investigation.

Footnotes

ORCID iDs

Kaiyi Chi

Jun Li

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study is supported by Australian Research Council (FT240100222).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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