Analysis of the impact of vertical deep hole blasting at the bottom of the hole on the lower ore body based on LS-dyna numerical simulation

Abstract

With the depletion of shallow resources, the transition from open-pit to underground mining has become an inevitable trend in the mining industry. Although the vertical longhole stage fill mining method is efficient and safe, its second-step stoping blasting is prone to damaging the underlying strategic rare orebody. To quantify the protective effect of the protective layer, this study established a three-dimensional fluid–structure interaction (FSI) numerical model for explosives-rock-backfill interactions using the ANSYS/LS-DYNA platform, based on the case of a large polymetallic mine. Systematic simulations were performed for six protective layer thicknesses ranging from 0.5 to 3.0 m, analyzing the cross-media propagation and attenuation characteristics of blasting stress waves and their dynamic damage mechanism to the underlying orebody.The results indicate that the protective layer thickness is a core parameter controlling damage, showing a significant negative correlation with the peak stress and displacement of the orebody. When the thickness is less than 1.5 m, the orebody response exceeds its damage threshold, leading to irreversible failure. When the thickness is ≥ 1.5 m, the peak stress can be reduced below the orebody’s ultimate compressive strength (74.871 MPa), and the displacement response is confined within the slight influence range (0.1–0.3 mm), achieving effective protection. The study innovatively applied the "Post Line Contour Mode" post-processing technique in LS-PrePost to achieve precise quantification of stress gradients and accurate localization of damage boundaries, validating the critical protective thickness of 1.5 m. This research clarifies the buffering mechanism and protection standards of the protective layer, providing a theoretical basis and design reference for safe and efficient coordinated mining of mineral resources under similar conditions.

Introduction

As the depletion of easily accessible shallow mineral resources intensifies and green mining practices and environmental protection regulations become increasingly stringent, the global mining industry is undergoing a strategic transition from open-pit to deep underground mining. Against this backdrop, the "large-diameter vertical deep-hole staged backfill mining method" has emerged as one of the dominant mining techniques, balancing operational efficiency with safety. However, the two-step extraction sequence inherent to this method introduces a critical technical challenge: during blasting operations in the second-step stope, explosive energy directly acts on adjacent backfilled goafs. The intense blast stress waves not only risk damaging the surrounding backfill structures and compromising their stability but may also penetrate protective rock layers, causing irreversible damage and dilution to underlying ore bodies yet to be mined. This issue becomes particularly acute when mining polymetallic deposits rich in strategically critical rare metals such as tantalum, niobium, and indium, directly affecting the comprehensive recovery of precious mineral resources and national resource security^1,2.

To address this challenge, scholars worldwide have extensively investigated blasting damage mechanisms through theoretical analyses, field monitoring, and physical model experiments. In recent years, numerical simulation has emerged as a vital supplementary approach for studying blast effects due to its cost-effectiveness, reproducibility, and ability to capture full-field dynamic responses. Researchers commonly employ software such as FLAC3D and ABAQUS to analyze stress distribution and failure patterns under blast loading^3–7. Notably, LS-DYNA, a leading explicit dynamics analysis code, offers unique advantages in simulating extreme nonlinear phenomena like explosive detonation, stress wave propagation, and fluid–structure interaction(FSI), and has been widely applied in blasting rock fragmentation and penetration protection studies.

Nevertheless, a review of existing literature reveals that most studies focus on direct damage to surrounding rock or backfill, while systematic quantitative research on the propagation patterns and protective standards of blast-induced damage from vertical deep-hole bottom blasting to underlying different ore types—especially rare ore bodies requiring prioritized protection—remains insufficient in open-pit to underground mining transitions^8–10. Current numerical simulations, when characterizing cross-media blast wave propagation and progressive damage evolution, predominantly rely on qualitative observations of stress nephograms, exhibiting significant limitations in precisely quantifying local stress gradients and spatially locating damage thresholds. Furthermore, translating simulation results into key engineering design parameters, such as the minimum safe protective layer thickness, necessitates deeper case validation and support^11,12.

In light of this, this study takes the open-pit to underground mining transition of a typical rare metal-enriched polymetallic deposit as its engineering background¹³, aiming to systematically resolve the following key scientific issues through high-fidelity numerical simulations¹⁴: (1) Revealing the propagation and attenuation laws of blast stress waves from vertical deep-hole bottoms in the underlying rare earth ore body after penetrating backfill and protective layers; (2) Quantifying the controlling effects of protective layer thickness on peak stress, displacement response, and damage degree of the ore body, and determining its critical protective thickness; (3) Innovating post-processing analysis methods to achieve precise quantitative identification of damage boundaries. The study employs the ANSYS/LS-DYNA platform to establish a 3D FSI dynamic model accounting for the interactions among explosives, rock, and backfill, systematically simulating blasting processes under six protective layer thickness conditions ranging from 0.5 to 3.0 m. By comparing stress and displacement fields and innovatively applying "Post Line Contour Mode" for path-based quantitative extraction and failure criterion determination, the damage status of the ore body is comprehensively evaluated.

This study not only provides a direct basis for the scientific design of protective layer thickness in this mine, but the established analytical methods and findings can also offer theoretical references and technical insights for achieving safe and efficient synergistic mining of strategic mineral resources under similar complex geological conditions.

Model and parameter determination

This study employs the explicit dynamic analysis module LS-Dyna to simulate the dynamic response process of a rock mass under blasting loads using the finite element method. The modeling process primarily involves material definition, geometric modeling, mesh generation, material parameter assignment, and boundary condition setup.

Model establishment

To accurately simulate the damage effects of blasting loads on the backfill, this study employs a FSI coupling algorithm. The explosives are modeled using an arbitrary Lagrangian–Eulerian (ALE) approach, while the ore body and backfill are modeled using a Lagrangian approach.

The geometric configuration and mesh division of the model are shown in Fig. 1. The dark green area in the upper left represents the magnetite ore body, the highlight in green columns denote drill holes, and the light blue area in the lower right indicates the rare earth ore body requiring protection. Specific blasting parameters are as follows: borehole packing length of 2 m, charge roll diameter of 90 mm, row spacing of 3 m, and charge density of 0.645 g/cm³. A mapping mesh was generated for the model using SOLID164 three-dimensional solid elements. Non-reflective boundary conditions were applied to the left, top, and rear faces of the model to simulate an infinite domain. To investigate the impact of the distance between the bottom of vertical deep holes and the ore body boundary (i.e., the reserved protective layer thickness) on ore body stability during blasting, this study established six protective layer thickness scenarios: 0.5 m, 1.0 m, 1.5 m, 2.0 m, 2.5 m, and 3.0 m. These conditions simulate the dynamic response and damage characteristics of the ore body under high-charge blasting impacts.

Fig. 1.

Numerical model of ore body disruption under blasting impact and mesh partitioning.

The overall dimensions of the model are X × Y = 18 m × 68 m, with approximately 145,687 SOLID164 elements. To verify mesh independence, a mesh sensitivity analysis was conducted, comparing coarse mesh (about 75,570 elements), medium mesh (140,909 elements), and fine mesh (327,567 elements) under the same blast load in terms of peak stress and displacement. The results show that the difference between the medium and fine mesh is less than 5%, so the medium mesh is used to balance computational efficiency and accuracy.

Model-material interactions and algorithm selection

In rock blasting simulations, the interaction between different media such as explosives, air, and rock is a critical factor. Selecting an appropriate interaction model is essential for ensuring the reliability and accuracy of simulation results. During numerical modeling, interactions between different materials can typically be implemented through three methods: the co-node method, the contact method, and the fluid–solid coupling method, as shown in Fig. 2.

Fig. 2.

Schematic diagram of interaction mechanisms between different materials.

When addressing problems involving significant material deformation, such as blasting, the common node method and contact method may cause severe mesh distortion in materials like explosives and air, leading to computational difficulties or even termination. Consequently, fluid–solid coupling methods often become the preferred approach for rock blasting simulations. In this approach, solid rock materials are modeled using the Lagrange algorithm, while fluid materials employ Eulerian or ALE algorithms. By overlapping meshes of materials with different properties, fluid–solid coupling effectively handles interactions between materials. Explosive elements and blasted rock elements in the model share identical element nodes. These shared nodes establish connections between explosives and rock masses, with contact surfaces between rock masses and backfill defined as contact surface relationships. During rock blasting, the deformation of explosives and their coupled media (e.g., air) exhibits fluid characteristics. Consequently, ALE meshes are employed for explosives and coupled media in the numerical model. This approach allows materials to flow within the mesh, preventing severe mesh distortion. Solid materials (rock) are described using Lagrangian meshes.

Common algorithms in LS-Dyna include the Lagrange method and the ALE method. The Lagrange method is prone to mesh distortion when handling large deformations, whereas the ALE method effectively overcomes this issue by allowing materials to flow within the mesh. Therefore, the ALE FSI algorithm is selected for this study.

Material models and failure criteria

The numerical model consists of three components: explosives, ore body, and backfill, with the ore body serving as the explosive target. During detonation, the rock near the center of the explosive charge undergoes yielding and fragmentation. The loading strain rate within the blast fragmentation zone exceeds that outside the zone. The dynamic compressive strength of the rock increases with rising loading strain rate, exhibiting a pronounced strain rate effect. Therefore, the ore body employs a nonlinear plastic material model (PLASTIC-KINEMATIC material model). The expressions for the yield stress and strain rate of the ore body are as follows:

1

Ep denotes the plastic hardening modulus, whose expression is:

2

In the equation: σ_y - dynamic ultimate stress, Pa;

σ₀ - initial yield stress, Pa;.

C, P - constants related to material properties;

ɛ - strain rate;

β - adjustable parameter;

t - cumulative time for plastic strain occurrence, s;

- plastic strain rate.

The ore body near the explosives employs a plastic kinematic strengthening model, implemented by establishing the model, meshing the domain, generating the K file, modifying the K file, and defining the MAT_PLASTIC_KINEMATIC keyword. The backfill similarly utilizes a nonlinear plastic material model (PLASTIC_KINEMATIC material model). The relevant mechanical parameters of the ore body required for numerical simulation are shown in Tables 1 & 2.

Table 1.

Key parameters of emulsion blasting material model for Rock 2#

Explosive density (g/cm3)	Detonation velocity (m/s)	Self-detonation distance (cm)	Sharpness (mm)	Work capacity (ml)	Cordarage diameter (mm)
1.20	3200	3	12	260	70

Table 2.

Main parameters of the rock emulsion explosive material model.

A (GPa)	B(GPa)	R1	R2		E (GPa)
611.3	10.65	4.4	1.2	0.32	7.127

In engineering blasting, the HIGE_EXPLOSIVE_BURN model and JWL equation of state describe the explosive process. Key parameters of the explosive material model are listed in Tables 2, while the JWL equation of state is as follows:

3

In the equation: P - Detonation pressure, Pa;

V - Relative volume;

E - Specific internal energy per unit volume, J;

Ω, A, B, R1, R2 - Parameters related to the explosive material.

Simulation results

Analysis of blasting stress effects

After running the post-processing software LS-PREPOST, open the simulation result files obtained from the four scenarios and read the d3plot numerical calculation result files. Extract the detonation propagation stress contour plots for the 1.0m protective layer at 1ms, 3ms, 7ms, and 14ms, as shown in Fig. 3. The propagation of stress waves within the rare earth ore is depicted in Fig. 4.

Fig. 3.

Contour plot of overall effective stress when the protective layer is 1.0 m.

Fig. 4.

Stress distribution map within the ore body at a protective layer of 1.0 m.

Figures 3 and 4 show that between 1 and 3 ms, the explosive stress wave begins to propagate outward from the borehole. By approximately 3 ms, the stress wave has reached the interface between the iron ore body and the rare earth ore body. At 7 ms, a distinct concentration of the blast stress wave becomes evident at the boundary interface. The peak of the blast stress wave has fully propagated to the boundary between the iron ore body and the rare earth ore body, where it undergoes diffusion, forming a compressional stress wave. As time progresses beyond 14 ms, the stress wave continues to diffuse deeper into the ore body, with the stress gradually diminishing and dissipating.

To further verify the validity of the proposed model, the blasting parameters for protective layer mining of a copper mine reported in Reference ¹¹ were selected for comparative simulation. Under the same protective layer thickness (1.0 m), the error of the peak stress predicted by the model in this paper is within 8%, and the displacement response trends are consistent, indicating that the model established in this paper has good reliability and applicability.

Comparing different protective layer thicknesses, Fig. 5 shows no significant difference in the propagation velocity of effective stress within the iron ore body, with nearly identical maximum blast wave velocities. However, the protective layer causes a noticeable delay in stress wave propagation to the rare earth ore body, and stress gradually decreases with increasing protective layer thickness. This indicates that the protective layer provides effective protection against blast impact for the rare earth ore body.

Fig. 5.

Explosion wave propagation velocity at different protective layer.

Detailed analysis and results verification

To further precisely quantify the influence range of detonation propagation stresses, validate the conclusions from the preceding stress cloud map analysis, and address the limitations of traditional stress cloud maps in local gradient changes and quantitative comparisons, this study additionally employs LS-PrePost’s Post Line Contour Mode for post-processing analysis.

While the stress cloud diagrams (Figs. 3 and 4) clearly established the overall propagation pattern of detonation stress waves, this method struggles to intuitively quantify the “stress attenuation gradient along specific directions” and the “precise locations of localized regions exceeding the threshold.” As a complementary tool, Post Line Contour Mode resolves these issues through custom path extraction and linear data distribution. This approach aligns perfectly with the study’s objective of “optimizing protective layer.” It enables the design of uniform paths for different protective layer scenarios, allowing quantitative comparison of stress attenuation along these paths and eliminating subjective interpretation errors from cloud maps. It directly locates the range of regions exceeding the stress threshold, providing more precise quantitative support for the “irreversible damage” conclusion, as shown in Fig. 6.

Fig. 6.

Stress post line contour mode diagram under blasting load.

To eliminate visual obstruction of path data by the main model, the magnetite body, backfill, and other primary models are displayed transparently, retaining only wireframe structures. This clearly highlights the spatial relationship between the paths and key model regions, preventing data reading bias.

Contour lines densely cluster within the iron ore body, indicating regions of intense physical parameter variation and stress concentration. This confirms the iron ore as the damage initiation zone. Stress concentration triggers “failure”—crack initiation, structural penetration, and overall yielding—with movement trends aligning with design expectations and blast wave propagation patterns.

Rare earth ore deposits reside in areas with sparse contour lines, exhibiting gradual physical parameter distribution and relatively uniform regional mechanical behavior.

Blasting impact analysis

Analysis of the degree of impact on ore bodies

1. Under different protective layer thicknesses, the trend of maximum effective stress in the ore body remains largely consistent. Following the initiation of blasting, stress waves generated by the blast vibrations require time to propagate, resulting in an initial period where effective stress values register as zero. Subsequently, effective stress exhibits a fluctuating increase, reaches a peak, then undergoes a fluctuating decrease before eventually stabilizing.

2. The effective stress peak within the ore body is inversely proportional to the protective layer. For example, when simulating protective layer of 0.5 m and 1.0 m, the effective stress (compressive stress) peak exceeds the ore body’s ultimate compressive strength (74.871 MPa). This indicates irreversible damage to the ore body unit and surrounding areas, with significant impact. When simulating protective layer of 1.5 m, 2.0 m, 2.5 m, and 3.0 m, the peak effective stress (compressive stress) falls below the ore body’s ultimate compressive strength (74.871 MPa). This indicates that the ore body unit and its surrounding areas have not suffered irreversible damage.

Analysis of stress variation trends

As shown in Fig. 5 (maximum propagation range of aggregate stress waves, i.e., the range exceeding the ore body’s ultimate tensile strength) and the corresponding propagation time in Table 3, the following trends can be observed:

1. The trend of maximum effective stress within the ore body remains largely consistent across different protective layer. Following the initiation of blasting, the stress wave generated by the blast vibration requires a certain propagation time. Consequently, the effective stress value initially registers as zero for a brief period. Subsequently, the effective stress value exhibits a fluctuating increase, reaches a peak, then undergoes a fluctuating decrease before eventually stabilizing.

2. The effective stress peak within the ore body is inversely proportional to the protective layer. For example, when the simulated protective layer are 0.5m and 1.0m, the effective stress (compressive stress) peak exceeds the ore body’s ultimate compressive strength (74.871 MPa). This indicates that the ore body unit and its surrounding areas have suffered irreversible damage and significant impact. When simulating protective layer of 1.5 m, 2.0 m, 2.5 m, and 3.0 m, the peak effective stress (compressive stress) falls below the ore body’s ultimate compressive strength (74.871 MPa), as shown in Table 2 and Fig. 7. This indicates that the ore body unit and its surrounding areas have not suffered irreversible damage.

Table 3.

Summary of Peak effective stresses at stress concentration points in ore bodies.

Serial No	Thickness of the protective layer (m)	Peak effective stress (MPa)	Peak time (ms)
1	0.5	107	7
2	1.0	88.2	4
3	1.5	66.4	9
4	2.0	53.0	5
5	2.5	43.5	5
6	3.0	35.7	10

Fig. 7.

Trend of maximum stress variation with different protective layer.

Analysis of displacement change trends

The calculated d3plot numerical results file was read into the post-processing software LS-PREPOST. To control the analysis variables, the maximum displacement of the lower plate was selected as the analysis object. The maximum displacement variation curve is shown in Fig. 6, and the effective displacement peaks are listed in the Table 4.

Table 4.

Summary of peak effective displacements at stress concentration points in ore bodies.

Serial No	Protective layer (m)	Effective peak displacement (mm)
1	0.5	0.453
2	1.0	0.376
3	1.5	0.199
4	2.0	0.175
5	2.5	0.158
6	3.0	0.123

1. The maximum effective displacement peak is inversely proportional to the thickness of the protective layer. That is, as the protective layer thickness increases, the effective displacement peak gradually decreases. For example, when the protective layer thickness is 0.5m, the effective displacement peak is 0.453 mm, whereas when the protective layer thickness is 1.5m, the effective displacement peak is 0.199mm;

2. Based on the equivalent damage principle for effective displacement:—Displacement values between 0.1 and 0.3 mm indicate significant impact or minor damage to units at that location;—Displacement values between 0.3 and 0.9 mm indicate major damage or failure to units at that location;—Displacement values exceeding 0.9 mm indicate irreversible failure to units at that location. It can be seen that when the protective layer is 0.5–1.0 m, the effective displacement ranges from 0.376 to 0.453 mm, indicating the ore body has sustained significant damage and is destroyed. When the protective layer increases to 1.5–3.0 m, the effective displacement ranges from 0.123 to 0.199 mm, indicating the ore body has sustained minor damage and remains intact.

As shown in Fig. 8, the overall deformation of the model indicates that the primary deformation occurs at the center of the blast hole, radiating outward. This deformation significantly weakens upon reaching the protective layer. Due to the protective layer’s presence, the deformation impact on the ore body outside the protective layer is negligible. This demonstrates that the protective layer provides significant protection for the ore body.

Fig. 8.

Total deformation of the model.

In summary, blasting operations exert a certain influence on ore body stability. Under current charge quantities and varying protective layer thicknesses, the ore body will not undergo large-scale destruction but may sustain damage leading to localized collapses. Compared to protective layer thicknesses of 1.5m, 2.0m, 2.5m, and 3.0m, the damage to the ore body is relatively more severe when the spacing is 0.5m and 1.0m. Therefore, it is recommended that the thickness of the protective layer between ore bodies be maintained at 1.5m or above to prevent internal damage and spalling of the ore body, which could result in the loss of valuable mineral resources and affect the grade of the mined ore.

Conclusion

This study employs ANSYS/LS-DYNA numerical simulation technology to investigate the impact of vertical deep-hole bottom blasting on rare earth ore bodies. Through simulation analysis of scenarios with varying protective layer (0.5 m, 1.0 m, 1.5 m, 2.0 m, 2.5 m, 3.0 m) and LS-PrePost post-processing, the following core conclusions are drawn:

1. Critical relationship between protective layer and rare earth ore damage: protective layer exhibits a significant inverse relationship with peak effective stress and maximum displacement within the ore body: When the protective layer is 0.5m and 1.0m, the peak effective stress of the rare earth ore body (107MPa and 88.2MPa) exceeds its ultimate compressive strength (74.871 MPa), while the effective displacement (0.453mm and 0.376mm) falls within the 0.3–0.9mm range, leading to irreversible failure of the ore body. When the protective layer thickness was ≥ 1.5m, the peak effective stress (66.4MPa–35.7MPa) was lower than the ultimate compressive strength, and the effective displacement (0.199mm–0.123mm) remained within the 0.1–0.3mm range. resulting in only minor damage to the ore body. Therefore, 1.5m is the critical protective thickness for the lining layer, preventing internal damage and spalling of rare earth ore caused by blasting impacts.Through systematic comparison of six groups of working conditions with different thicknesses, the fitting relationship between the protective layer thickness and the peak stress is obtained as

   4

   which further verifies the significant inhibitory effect of thickness on damage from a statistical perspective.

2. Propagation Patterns of Blasting Stress Waves and the Buffering Effect of the Protective Layer The propagation of blasting stress waves exhibits distinct temporal characteristics:—1–3 ms: Diffusion from the blast hole to the surrounding area—3 ms: Arrival at the boundary between the rare earth ore and magnetite—7 ms: Aggregation at the boundary to form a compressional stress wave—After 14 ms: Diffusion into the depths of the rare earth ore and gradual dissipation Under different protective layer thicknesses, the propagation velocity of stress waves within the rare earth ore shows no significant difference. However, the protective layer significantly delays the arrival time of stress waves at the rare earth ore and attenuates stress peaks, effectively mitigating the impact of blasting on the ore.

3. Value of Post Line Contour Mode for Detailed Analysis LS-PrePost’s Post Line Contour Mode enables quantitative data extraction via custom paths (radial, boundary, longitudinal), overcoming limitations of traditional stress contour plots:—Precisely quantifies stress attenuation gradients along the “drill hole-rare earth ore” path (e.g., under a 1.5m protective layer, stress at the drill hole drops to only 66.4MPa at the ore boundary)—Identifies regions where localized stresses exceed thresholds (74.871 MPa)—Corrects stress wave propagation depth where stress at the borehole drops to only 66.4 MPa at the ore boundary), identifies regions exceeding the stress threshold (74.871 MPa), and corrects stress wave propagation depth (longitudinal propagation of 2.8 m at 14 ms under a 0.5 m protective layer, only 1.2m under a 3.0m protective layer), and generated numerical tables for subsequent processing. This further validated the consistency between simulation results and blasting theory.

4. Engineering Recommendations for Rare Earth Ore Protection. Based on current blasting parameters (2m borehole filling, 90mm charge roll diameter, 3m row spacing, 0.645 g/cm³ packing density), to balance the in-situ preservation of rare earth minerals with efficient magnetite recovery, it is recommended to maintain a protective layer thickness of at least 1.5m between rare earth and magnetite deposits. This approach prevents the loss of scarce rare earth resources due to damage while ensuring ore grade quality.

Future work can be carried out in the following aspects: (a) conduct on-site microseismic monitoring to obtain real blasting vibration data for calibrating and validating the numerical model; (b) consider rock mass anisotropy and joint networks to establish a more complex geomechanical model; (c) extend the research to dynamic charging structure optimization, seeking a comprehensive optimal solution between protective layer thickness and blasting efficiency.

Author contributions

A: Conceptualization; Data Curation; Formal Analysis; Investigation; Writing—Original Draft; Writing—Review & Editing; Visualization. B: Conceptualization; Data Curation; Formal Analysis; Investigation; Visualization. C: Conceptualization; Data Curation; Formal Analysis; Investigation; Writing—Original Draft; Software; Visualization. D: Visualization; Investigation. E: Resources; Funding Acquisition. F: Funding Acquisition; Supervision; Writing—Review & Editing.

Funding

This research was funded by the Deep Earth Probe and Mineral Resources Exploration—National Science and Technology Major Project (Nos. 2024ZD1003703, 2024ZD1003702).

Data availability

The data that support the findings of this study are available on request from the corresponding author, [Qinli Zhang], upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.