An improved mapping adaptation method from three-dimensional non-solid geological information models to numerical computational models

Three-dimensional (3D) geological information models and numerical computational models differ substantially in their representation objectives, geometric organization, parameter systems, and spatial scales, which makes direct conversion between the two difficult. This study proposes a mapping-adaptation framework for transforming surface- or interface-based non-solid geological information models into geomechanical numerical computational models. Four principal mismatch types are identified, including geometric representation, structural discretization, parameter and solution-condition inheritance, and spatial extent. Correspondingly, geometric solidification, local structural adaptation, parameter and solution-condition mapping, and engineering-oriented computational-domain adaptation are integrated into a continuous mapping procedure linking the geological information model, geometric solid model, volumetric mesh model, and numerical computational model. In the case study, Delaunay triangulation was used to subdivide the original borehole distribution and introduce 50 virtual boreholes as supplementary geological constraints. The mean stratigraphic-sequence similarity increased from 0.483 to 0.553, while the mean depth-discretized stratigraphic consistency rate increased from 0.233 to 0.440 after virtual-borehole augmentation. The reconstructed stratigraphic surfaces were subsequently converted into closed geometric solids, discretized into volumetric meshes, and assigned corresponding material parameters, constitutive relationships, boundary conditions, and loading conditions. The resulting model was then used to complete the numerical calculation workflow. The case study demonstrates the continuity and numerical executability of the proposed geological-to-numerical mapping framework. In the present case, the computational-domain adaptation component is included as a framework capability rather than quantitatively evaluated through domain-size sensitivity analysis. The numerical results are used to verify workflow feasibility rather than the predictive accuracy of a specific engineering response.

Three-dimensional (3D) non-solid geological information models and 3D numerical computational models perform distinct functions in geotechnical engineering (Wellmann and Caumon, 2018; de la Varga et al., 2019; Wang et al., 2016). The former is primarily intended to organize and represent stratigraphic structures, spatial relationships, and object attributes, with core capabilities in describing complex geological bodies through stratigraphic interfaces, surface patches, and associated attribute relationships. The latter, by contrast, focuses on engineering computation and analysis, prioritizing computational domain organization, volumetric mesh discretization, material parameter assignment, boundary condition specification, and loading scenario definition. In underground engineering, both geological information models and numerical computational models are capable of representing geological structures. However, they differ fundamentally in their modeling objectives and data organization. Geological information models are primarily designed to preserve stratigraphic geometry, spatial topology, and geological semantics, whereas numerical computational models are established to support engineering analyses through computational meshes, constitutive models, material properties, boundary conditions, and loading scenarios. Therefore, the primary challenge is not whether numerical models can represent geological structures, but how geological information can be accurately, completely, and consistently transferred from information-oriented representations into computation-oriented numerical models while preserving essential geological characteristics and satisfying numerical analysis requirements. Consequently, establishing an effective mapping relationship between geological information models and numerical computational models has become a key prerequisite for reliable geotechnical numerical simulation.

Extensive research has been conducted on the construction of three-dimensional geological models and their integration with numerical simulation environments. Existing studies can generally be classified into three related but distinct research directions. The first direction focuses on geological structure reconstruction and representation. Various approaches, including interpolation-based methods, geostatistical techniques, implicit geological modeling, and surface reconstruction algorithms, have been developed to improve the representation of subsurface structures (Hillier et al., 2014; Hillier et al., 2021; Li et al., 2022; Lyu et al., 2021; Xu et al., 2011; Zhu et al., 2013; Jørgensen et al., 2015; Zhang and Zhu, 2018). These methods provide effective solutions for reconstructing stratigraphic interfaces, faults, discontinuities, and complex geological boundaries from sparse geological observations. In particular, interpolation and geostatistical approaches improve the spatial estimation of geological surfaces, whereas implicit modeling and reconstruction methods enhance the representation of complex geological geometries. However, these methods primarily focus on improving the fidelity of geological representation and generally do not directly address the subsequent requirements of numerical computation, such as volumetric discretization, mesh quality control, and computational parameter organization. The second direction concerns the generation of numerical models from geometric representations. Research in this field has mainly concentrated on geometric solidification, mesh generation, topology optimization, and computational preprocessing (Watson et al., 2015; Zehner et al., 2016; Schneeberger et al., 2017; Thornton et al., 2018; Madsen et al., 2022). Surface-based geological representations can be transformed into volumetric domains through solid reconstruction techniques, followed by mesh generation methods such as tetrahedral or hexahedral discretization. These approaches provide essential foundations for numerical simulation. Nevertheless, geological models often contain complex features, including thin layers, pinch-outs, irregular interfaces, and discontinuous structures, which may introduce difficulties during mesh generation. Therefore, geometric conversion alone cannot guarantee that the resulting numerical model maintains both geological consistency and computational reliability. The third direction involves the integration between geological information systems and engineering numerical analysis platforms. Existing studies have explored data exchange frameworks, multi-platform workflows, and model conversion strategies to improve interoperability between geological modeling software and numerical simulation tools (Ouyang et al., 2023; Shang et al., 2023; Zhuang et al., 2023; Zhou et al., 2022; Wu et al., 2024). These developments have promoted the application of digital geological models in engineering analysis. However, most existing workflows still rely on sequential operations, where geological reconstruction, geometric processing, mesh generation, parameter assignment, and computational domain definition are treated as relatively independent procedures. Consequently, the systematic adaptation mechanism required to ensure consistency between geological information representation and numerical computation remains insufficiently investigated. Based on these observations, the transition from a three-dimensional geological information model to a numerical computational model should not be considered as a simple geometric conversion process. Instead, it represents a multi-level adaptation problem involving geometric representation, structural discretization, parameter inheritance, and computational domain selection. Although existing studies have made significant contributions to individual aspects of geological reconstruction, numerical preprocessing, and model integration (Hao et al., 2024; Ji et al., 2024; Zhu et al., 2024; Wang et al., 2024), a comprehensive framework that identifies conversion mismatches and provides coordinated adaptation strategies remains lacking (Chen et al., 2024; Huang et al., 2024; Fonsati et al., 2023; Arroyo Ohori et al., 2018).

Building upon the aforementioned limitations, this study investigates the mapping adaptation problem between three-dimensional geological information models and numerical computational models. Here, the term “non-solid geological information model” refers to a surface-based geological representation composed mainly of stratigraphic interfaces, surface meshes, and associated geological attributes, which describes geological structures and spatial relationships but lacks the volumetric discretization and solution-oriented information required for numerical analysis. The numerical computational model considered in this study primarily refers to geomechanical models based on finite element or finite difference methods, which require a computational domain, volumetric mesh, material parameters, constitutive relationships, boundary conditions, and loading conditions. Therefore, the challenge addressed in this study is not the inability of numerical models to represent geological structures, but the effective transfer and adaptation of geological information into a computationally valid numerical representation. To address this issue, an improved mapping-adaptation framework is proposed, consisting of geometric solidification, local structural adaptation, parameter and solution-condition mapping, and engineering-oriented computational-domain adaptation. The proposed framework aims to establish a systematic linkage between geological information representation and numerical simulation requirements by coordinating the adaptation of geometry, structure, computational attributes, and spatial extent.

This study considers the transition from a three-dimensional geological information model to a numerical computational model as a multi-stage adaptation process rather than a direct model conversion operation. Four model representations are distinguished throughout this study: (1) the three-dimensional geological information model, which describes geological structures through stratigraphic interfaces, surface meshes, topology relationships, and geological attributes; (2) the geometric solid model, which represents closed volumetric geological entities reconstructed from geological information and provides explicit spatial domains for subsequent discretization; (3) the volumetric mesh model, which discretizes geometric solids into computational elements while preserving essential geological structures; and (4) the numerical computational model, which further integrates material parameters, constitutive relationships, boundary conditions, and loading conditions for engineering analysis.

The objective of this study is not to replace geological modeling methods or numerical simulation techniques, but to establish an adaptation framework that improves the consistency between geological information representation and numerical computation requirements. Based on the differences between these model representations, the mapping process is analyzed from four aspects: geometric representation, structural discretization, parameter and solution-condition inheritance, and computational-domain selection. Accordingly, the research contents include: (1) identifying the main mismatch types occurring during the transition from geological information models to numerical computational models; (2) developing corresponding adaptation strategies involving geometric solidification, local structural adaptation, parameter and solution-condition mapping, and engineering-oriented computational-domain adaptation; and (3) evaluating the effectiveness of the proposed framework through geometric integrity, parameter consistency, and numerical modeling feasibility assessments.

Mismatch categories in mapping from 3D non-solid geological information models to numerical computational models

The transition from a three-dimensional geological information model to a numerical computational model involves multiple intermediate adaptations because the two models are established for different purposes. A geological information model mainly describes geological structures, spatial relationships, and semantic attributes, whereas a numerical computational model requires explicit volumetric domains, discretized elements, material properties, and solution conditions. Therefore, the mapping process should be regarded as a transformation between different representation systems rather than a direct exchange of geometric data.

In this study, the mismatch between the two models is categorized into four aspects: (1) geometric representation mismatch, caused by the difference between surface/interface-based geological representations and volumetric computational domains; (2) structural discretization mismatch, resulting from inconsistencies between geological complexity and mesh-generation requirements; (3) parameter and solution-condition mismatch, caused by differences between descriptive geological attributes and computational variables; and (4) spatial-extent mismatch, resulting from differences between regional geological representation and local engineering analysis requirements. These four mismatch categories provide the basis for developing the corresponding adaptation strategies described in Section 2.2.

The geological information model can be conceptually represented as:

Where G e m o represents geometric information such as stratigraphic interfaces and geological surfaces; T o p o represents spatial relationships among geological entities; A t t r represents geological attributes including lithology and stratigraphic classification; and S e m represents geological meanings associated with these entities.

In contrast, the numerical computational model can be represented as: where Ω represents the computational domain, M represents the volumetric mesh, P represents material parameters, B represents boundary conditions, and L represents loading or analysis conditions. The mapping process therefore requires establishing relationships between these two representation systems rather than directly transferring individual model components.

Mismatch between 3D non-solid geological information models and numerical solid models

A three-dimensional geological information model is commonly represented by stratigraphic interfaces, surface meshes, and boundary relationships. Although such representations are sufficient for geological visualization and spatial interpretation, they do not directly provide the closed volumetric domains required for numerical computation. Therefore, an intermediate geometric solid reconstruction step is necessary before mesh generation.

In this study, the geometric mismatch is defined as the inconsistency between geological boundary representation and computational domain representation. Let the geological surface representation be denoted as: where S i represents the i-th geological interface or surface. Through surface reconstruction and closure operations, the corresponding solid domain can be obtained: where Φ represents the solidification operation. A successful solidification process requires that adjacent geological interfaces maintain topological consistency and form closed volumetric regions suitable for subsequent mesh generation.

Stratigraphic unit mismatch

Geological information models are usually constructed to preserve geological authenticity as completely as possible. Consequently, they often contain thin layers, pinch-outs, rapidly varying interfaces, and locally irregular geological boundaries. These features are important for accurately representing geological structures but may significantly reduce the quality of volumetric meshes during numerical discretization. In practice, excessively thin geological bodies may generate highly distorted elements, whereas locally irregular boundaries may cause abrupt changes in element geometry, thereby reducing computational stability.

Therefore, the structural mismatch considered in this study refers to the inconsistency between geological representation accuracy and numerical discretization requirements. Instead of preserving every geometric detail, the objective is to retain the dominant geological structures while locally adapting features that are incompatible with mesh generation. Such adaptation includes the treatment of extremely thin layers, locally complex boundaries, and rapidly varying interface geometries whenever these features would otherwise lead to poor-quality mesh elements.

Let l g denote the characteristic geometric scale of a local geological feature and h denote the target mesh size. Structural adaptation becomes necessary when

Because the characteristic geological feature cannot be adequately resolved by the selected mesh resolution. Under this condition, local geometric simplification or structural adjustment is performed while preserving the continuity of the principal stratigraphic framework. Consequently, the objective of structural adaptation is not to simplify the geological model indiscriminately, but to improve compatibility between geological complexity and numerical discretization while minimizing the loss of essential geological information.

Parameter mismatch

The attributes stored in a three-dimensional geological information model are mainly used for geological identification and information management, and commonly include lithological type, stratigraphic code, interface elevation, burial depth, and spatial relationships. In contrast, the geomechanical numerical model considered in this study requires solution-oriented information, including material parameters, constitutive models, boundary conditions, and loading conditions. Therefore, descriptive geological attributes cannot be directly treated as numerical parameters, and explicit mapping relationships must be established between geological units and computational zones.

For the k -th stratigraphic unit, let P k a v a i l denote the set of material-parameter fields available after mapping, and let P r e q denote the set of material parameters required by the selected constitutive model. The material-parameter completeness of the k th unit is defined as:

Where · denotes the number of parameter fields contained in a set. When C k P = 1, all material parameters required by the constitutive model have been assigned to the corresponding computational zone; when C k P < 1, supplementary parameter determination is required before numerical calculation. Boundary conditions and loading conditions are defined and examined separately at the model level because they depend on the engineering problem and analysis scenario rather than solely on individual stratigraphic units. Accordingly, the parameter mismatch arises from the difference between descriptive geological attributes and the complete solution-oriented information required by the numerical model.

Mismatch in spatial extent

A three-dimensional geological information model is generally constructed to represent the geological environment over a regional spatial extent, whereas a numerical computational model usually focuses on a specific engineering object and its surrounding zone of influence. Consequently, directly converting the complete geological information model may introduce unnecessary geometric entities, mesh elements, and parameter assignments, thereby increasing preprocessing and computational costs. Conversely, extracting a computational domain that is too narrow may place model boundaries within the principal response zone and may omit relevant geological, mechanical, or hydrogeological constraints.

Let Ω G denote the spatial domain of the geological information model, Ω A the engineering action zone, and Ω C the extracted computational domain. Their relationship should satisfy:

The extent of Ω C cannot be determined solely from the geometric boundary of the engineering object. It must also account for the expected deformation or stress-influence zone, the sensitivity of calculated responses to boundary locations, the distribution of major geological interfaces and discontinuities, groundwater boundaries where relevant, and the type of numerical analysis being conducted. Therefore, the spatial-extent mismatch includes two opposing conditions: an excessively large domain that reduces computational efficiency and an excessively small domain that introduces boundary effects or excludes essential environmental constraints. The purpose of computational-domain adaptation is therefore to define an analysis domain that retains the geological and boundary information required by the intended engineering problem while avoiding unnecessary inclusion of regions unrelated to the numerical analysis.

Improved mapping adaptation from 3D non-solid geological information models to numerical computational models

Based on the four mismatch categories identified in Section 2.1, this study establishes a corresponding mapping-adaptation framework comprising geometric solidification, local structural adaptation, parameter and solution-condition mapping, and engineering-oriented computational-domain adaptation. These operations are not treated as independent preprocessing steps; instead, they are organized according to the successive requirements of geometric closure, mesh compatibility, parameter completeness, and analysis-domain validity. The output of each stage provides the input and acceptance conditions for the subsequent stage, thereby forming a continuous transition from the geological information model to the geometric solid model, volumetric mesh model, and fully specified geomechanical numerical model.

Solidification improvement for addressing the solid/non-solid model mismatch

The objective of geometric solidification is to transform the surface- or interface-based geological representation into a set of closed and topologically consistent stratigraphic solids. The reconstruction is conducted according to stratigraphic sequence, interface identity, and structural continuity rather than by directly connecting all borehole points without geological classification. Borehole control points are first grouped according to the stratigraphic interface to which they belong, and the corresponding interface is reconstructed from the control points associated with the same geological horizon. The interpolation or surface-fitting method used in the case study, together with its parameter settings, is specified in Section 3.

For a continuous stratigraphic interface, its elevation may be represented as: where f k x, y denotes the reconstructed elevation of the k -th interface at the horizontal position x, y. The reconstructed surface is constrained to pass through, or approximate within a prescribed tolerance, the borehole control points assigned to that interface. Stratigraphic ordering is subsequently checked to prevent unintended intersections or reversals between adjacent interfaces.

Geological discontinuities are treated as explicit structural boundaries rather than being smoothed by unrestricted interpolation. When a mapped fault or discontinuity intersects the modeling domain, the borehole and interface-control data are partitioned into separate structural blocks. Interface surfaces on opposite sides of the discontinuity are reconstructed independently, and the fault surface is introduced as a common boundary between the resulting blocks. This prevents data from different fault blocks from being combined into a single continuous surface and preserves the displacement relationship across the discontinuity.

After the upper and lower interfaces of the k -th stratum are obtained, its volumetric domain is defined as: where D k is the horizontal extent of the stratum, and z k u p p e r and z k l o w e r denote its upper and lower interfaces, respectively. The lateral surfaces are generated by connecting the corresponding boundary curves of the upper and lower interfaces along the boundary of D k. At the outer boundary of the modeling domain, these lateral surfaces coincide with the model boundary; at a fault, they coincide with the fault surface; and at a pinch-out, the upper and lower interfaces converge to a common termination boundary.

The upper interface, lower interface, and lateral surfaces are then joined to form a closed stratigraphic solid. Each reconstructed solid is examined for open edges, self-intersections, overlaps, gaps, and inconsistent contacts with adjacent solids. Only solids that satisfy geometric closure and interlayer-topology requirements are transferred to the subsequent mesh-generation stage. In the present implementation, Rhino is used to perform surface reconstruction, boundary connection, solid joining, and geometric inspection; however, these operations represent general geometric requirements and are not restricted to a specific software platform.

Local structural adaptation improvement for addressing stratigraphic unit mismatch

Local structural adaptation is performed to resolve geometric features that cannot be adequately represented by the selected mesh resolution while preserving geologically and mechanically important structures. The adaptation does not automatically remove all thin layers or irregular interfaces. Instead, each local feature is evaluated according to its geometric scale, geological significance, engineering relevance, and influence on mesh quality.

Let t j denote the local thickness or characteristic scale of the j th geological feature, h the target mesh size, and n min the minimum number of elements required to represent the feature across its characteristic dimension. A feature can be directly retained when:

When this condition is not satisfied, two alternative treatments are considered. If the feature represents an important weak layer, discontinuity, material boundary, water-bearing zone, or other structure that may materially affect the numerical response, the feature is preserved and the mesh is locally refined. If the feature is below the resolvable scale and has no significant influence on the intended analysis, controlled geometric adaptation may be applied, including local smoothing of abrupt interface fluctuations, removal of isolated geometric artifacts, or merging of an extremely thin unit with an adjacent geologically compatible unit.

Geometric adaptation is constrained by three requirements. First, the original stratigraphic order and major contact relationships must remain unchanged. Second, faults, engineering-critical weak layers, and principal pinch-out boundaries must not be removed solely to facilitate meshing. Third, when geometric adaptation is actually applied and quantitatively evaluated, the deviation introduced by adaptation should be assessed by comparing the adapted interfaces with the original geological interfaces and should remain within an application-specific tolerance.

The target mesh size is selected according to the smallest engineering-relevant geological feature, the dimensions of the engineering structure, the expected gradient of the numerical response, and the available computational resources. It is therefore not determined solely by the overall dimensions of the geological model. After an initial mesh is generated, mesh quality is evaluated, and local refinement or further structural adaptation is performed in regions containing distorted or poorly shaped elements.

Improvement of parameter and solution-condition mapping to address parameter mismatch

Parameter and solution-condition mapping is performed after the geometric solids have been discretized into a boundary-conforming volumetric mesh. Because the mesh conforms to the reconstructed stratigraphic boundaries, each mesh element inherits a unique stratigraphic unit identifier from the solid in which it is located. A mapping table is then established between the geological-unit identifier and the numerical information required for geomechanical analysis, including the constitutive model and its associated physical and mechanical parameters.

For the k-th stratigraphic unit, the parameter vector is defined as: where ρ k, E k, ν k, c k, φ k denote density, Young’s modulus, Poisson’s ratio, cohesion, and internal friction angle, respectively. For a mesh element e belonging to the solid domain Ω k, its material assignment is expressed as: where C k denotes the constitutive model assigned to the k-th stratigraphic unit. Before numerical calculation, the parameter-completeness criterion defined in Section 2.1.3 is examined. If any parameter required by the selected constitutive model is missing, the corresponding unit is not accepted for calculation until the missing information has been supplemented or justified.

Boundary conditions and loading conditions are mapped separately from material parameters because they are determined by the computational-domain geometry, engineering object, analysis stage, and intended simulation scenario rather than solely by lithological classification. Each boundary-condition record specifies the associated geometric boundary, constrained degree of freedom, constraint direction, and prescribed value or function. Each loading-condition record specifies the loading region, loading type, magnitude, direction, and application stage. The resulting numerical model is accepted only when every computational element has a unique material assignment and all required boundary and loading conditions have been explicitly defined.

Computational-domain adaptation for spatial-extent mismatch

To address the mismatch between the spatial extent of geological information models and the requirements of numerical analysis, the proposed framework introduces an engineering-oriented computational-domain adaptation strategy. Unlike geological information models, which are generally established to preserve comprehensive geological structures within a study area, numerical computational models usually focus on the region directly related to a specific engineering problem. Therefore, the computational domain should be determined according to the analysis objectives, engineering activity range, and relevant geological influence zone, while maintaining the essential geological structures and boundary information required for numerical simulation.

In this framework, local computational-domain adaptation does not represent a simple geometric truncation of the original geological information model. Instead, it establishes a relationship between the comprehensive geological representation and the solution-oriented requirements of numerical analysis. The geological information model provides the basis for selecting the required computational region, whereas the numerical model focuses only on the spatial extent necessary for the intended analysis. This strategy enables flexible adaptation of model scale according to engineering requirements and provides a foundation for reducing unnecessary computational redundancy in practical applications.

Overall mapping-adaptation procedure

The complete mapping-adaptation procedure is summarized in Algorithm 1. The procedure incorporates decision and feedback rules rather than treating solidification, meshing, parameter assignment, and domain extraction as independent software operations.

Algorithm 1 Overall mapping-adaptation procedure from a 3D non-solid geological information model to a numerical computational model. Classify borehole and surface-control data according to stratigraphic horizon and structural block.

Where faults or discontinuities occur, separate the data into individual structural blocks.

Reconstruct each stratigraphic interface and check continuity, stratigraphic order, and unintended intersection.

Generate lateral boundaries and join the upper, lower, and lateral surfaces into stratigraphic solids.

Check each solid for open edges, self-intersections, overlaps, gaps, and inconsistent contacts.

Evaluate each thin or locally complex feature using its characteristic scale, engineering significance, and target mesh size.

Retain and locally refine engineering-critical features; apply controlled adaptation only to noncritical sub-resolution features.

Define or adapt the computational domain according to the engineering analysis objective, expected influence range, and relevant geological boundaries.

Generate the volumetric mesh and evaluate the available mesh-quality indicators.

If the geometric or mesh criteria are not satisfied, return to Steps 5–8 for repair, adaptation, or local refinement.

Map each mesh element to a unique geological-unit identifier, constitutive model, and material-parameter vector.

Check parameter completeness and resolve missing or duplicate assignments.

Apply boundary and loading conditions according to the engineering scenario.

Evaluate mapping consistency, mesh validity, and numerical executability.

Export the model when all acceptance criteria are satisfied; otherwise return to the relevant adaptation stage.

After structural adaptation, the generated computational mesh is further examined to ensure geometric validity and numerical compatibility. The inspection focuses on mesh integrity, element connectivity, and the absence of invalid geometric configurations that may affect subsequent numerical calculations.

Evaluation of mapping adaptation performance from 3D non-solid geological information models to numerical computational models

Following the completion of geometric solidification, local structural adaptation, parameter and solution-condition mapping, and computational-domain definition, the mapping results are evaluated to determine whether the 3D non-solid geological information model has been successfully transformed into a computable 3D numerical model. The goal of adaptation improvement extends beyond merely executing geometric conversion and parameter organization during model construction; more importantly, it seeks to ensure that the improved model satisfies the stringent requirements of numerical analysis at the geometric, parametric, and solution-oriented levels. Accordingly, this study structures the evaluation of mapping adaptation performance across three levels: geometric and structural examination, parameter and condition examination, and numerical modeling feasibility examination. To ensure a logical evaluation sequence, the assessment proceeds in the order of “geometric and structural examination → parameter and condition examination → numerical modeling feasibility examination,” as shown in Figure 1.

Geometric and structural examination

Geometric and structural examination serves to determine whether, subsequent to solidification and local structural adaptation, the 3D non-solid geological information model yields geometric solids and mesh structures that conform to the requirements of numerical discretization. The examination focuses on critical geometric integrity criteria, including: continuity of stratigraphic interfaces, closure of stratigraphic solids, absence of overlaps or gaps between adjacent solids, appropriate treatment of locally complex structures, and the capacity to generate a stable mesh across the entire geometric domain. This examination directly corresponds to the geometric-representation and structural-discretization mismatches discussed in Section 2.1. Its purpose is to assess whether the surface-based representation of the information model has been successfully transformed into volumetric solids and mesh structures suitable for computation.

Parameter and condition examination

Parameter and condition examination primarily verifies whether the adapted model has successfully transitioned from informational attributes to solution-oriented attributes. Specifically, the examination includes: verification of material parameter assignment to each stratigraphic zone, consistency of parameter values with zoning relationships, correspondence between constitutive models and computational regions, completeness of boundary condition establishment, rationality of loading condition specification, and the integration of these solution conditions into a complete numerical-analysis input set. This examination directly corresponds to the parameters and solution-condition mismatch outlined in Section 2.1. It seeks to ascertain whether the representational attributes of the information model have been effectively converted into the solution attributes and solution conditions required by the numerical model.

Numerical modeling feasibility examination

Numerical modeling feasibility examination primarily verifies whether the adapted model can successfully proceed to the numerical analysis stage. This examination transcends isolated structural or attribute checks, adopting a holistic, workflow-oriented perspective. It assesses whether the model can successfully accomplish geometric solid generation, mesh discretization, parameter assignment, and boundary-condition specification; whether it can be imported into the numerical analysis platform without geometric mismatches, mesh errors, or interruptions during the solution process. This examination primarily addresses the practical viability of the proposed mapping adaptation improvements in an engineering implementation context; that is, it confirms whether the aforementioned improvements in geometry, structure, parameters, and analysis domain collectively support the reliable establishment of a numerical model. Through the three-level examination of “geometry and structure → parameters and conditions → numerical modeling feasibility,” the proposed mapping adaptation improvement methodology is subjected to systematic and rigorous evaluation.

Case overview

The engineering case examined in this study originates from a geological engineering project located in southwestern China. The surface geomorphology of this area is characterized by relatively subdued weathering and erosion, juxtaposed with comparatively complex geological conditions and predominantly hilly terrain. The strata in this region consist mainly of slightly weathered rock layers. Table 1 presents a sample of actual borehole data from the project site. The stratigraphic types and corresponding codes identified from the boreholes mainly include silty clay (1), angular gravel (2), crushed stone (3), rounded gravel (4–1), pebble (4–2), coarse sand (4–3), boulder-bearing layer (4–4), drift boulder layer (4–5), and slate (5–1). These borehole datasets contain key information such as borehole number, planar coordinates, collar elevation, stratigraphic classification, and the bottom elevation of each layer. These data not only constitute the direct constraints for building the 3D geological information model but also provide the fundamental geological basis for subsequent solid geometry generation, mesh discretization, and numerical model development. They therefore offer essential data support for the subsequent construction of a refined geological model and for multi-platform coupled simulation analyses.

Identification results of mismatches between 3D non-solid geological information models and numerical computational models

Before identifying the mismatches involved in the geological-to-numerical model conversion, a three-dimensional geological information model was first established using the 43 actual boreholes available within the study area. Because the actual boreholes were unevenly distributed and some areas lacked sufficient spatial constraints, Delaunay triangulation was performed based on their planar coordinates. The resulting triangular network was further subdivided, and 50 virtual boreholes were introduced within the study area to supplement the spatial distribution of the original borehole constraints, as shown in Figure 2.

The horizontal locations of the virtual boreholes were determined through subdivision of the Delaunay triangular network rather than by arbitrary placement. The stratigraphic sequence of each virtual borehole was generated according to the spatial neighborhood relationships and stratigraphic-transition characteristics of the surrounding actual boreholes. Specifically, local stratigraphic-transition probabilities were established from neighboring actual boreholes, and distance-based weights were introduced so that boreholes closer to the target virtual-borehole location exerted a greater influence on sequence generation. The stratigraphic sequence was then generated layer by layer using a spatially coupled Markov-chain procedure. Geological constraints, including the regional stratigraphic order, restrictions on repeated layers, and total borehole depth, were incorporated during the generation process to avoid geologically unreasonable sequence combinations.

The stratigraphic-interface elevations of the virtual boreholes were not obtained by independently interpolating individual interfaces. After the stratigraphic sequence of a virtual borehole had been determined, the predicted thicknesses of successive strata were accumulated to obtain the corresponding layer-bottom depths. The elevation of each stratigraphic interface was subsequently calculated by subtracting the cumulative depth from the collar elevation of the virtual borehole. Therefore, the vertical positions of the interfaces were jointly determined by the collar elevation and predicted stratum thicknesses, which ensured continuous and internally consistent vertical relationships among the strata within each virtual borehole.

The virtual boreholes were used only as supplementary geological constraints for subsequent stratigraphic reconstruction and did not replace the actual borehole observations. Their introduction increased the spatial coverage of geological constraints, particularly in areas with sparse actual borehole distribution.

Leveraging the spatial distribution constraints imposed by the borehole dataset, the major strata within the study area were further systematically indexed and organized according to the recorded top and bottom depths of each layer, their stratigraphic succession, and lithological classifications. Stratigraphic interfaces were subsequently constructed layer by layer. The resulting stratigraphic interface maps demonstrate that the major strata maintain relatively continuous spatial extension, exhibit clear superpositional and contact relationships among different strata, and preserve overall stratigraphic sequence stability. Compared with geometric connections derived solely from a limited set of actual boreholes, the introduction of virtual boreholes markedly improves the completeness of stratigraphic boundary representation in borehole-sparse areas and alleviates, to some extent, boundary distortions arising from insufficient local interface constraints. However, from a model representation standpoint, the currently established 3D geological information model remains predominantly constituted by stratigraphic interfaces, surface triangular patches, and their associated topological relationships, as shown in Figure 3. While this structure excels at delineating stratigraphic boundaries and spatial relationships, it lacks the internal volumetric mesh and node organization indispensable for numerical solution. In essence, although this model exhibits a robust capability for geological structure representation, it persists as a non-solid information model and cannot be directly deployed as a 3D numerical model.

Beyond differences in geometric representation, mismatches between the information model and the numerical model also manifest at the level of structural discretization. Analysis of the stratigraphic interfaces and 3D stratigraphic entity models indicates that some stratigraphic boundaries within the study area exhibit rapid spatial variation, and certain strata contain localized thinning regions or complex transitional boundaries. While such features are beneficial for realistically representing underground structures in an information model, they inherently increase the complexity of subsequent volumetric mesh generation. This can readily lead to local mesh distortion, over-refinement, or even meshing failure. Therefore, local geometric details that are favorable for geological representation do not necessarily satisfy the rigorous requirements of numerical discretization.

Meanwhile, the attribute information in the information model is mainly conveyed through lithological categories, stratigraphic codes, and spatial positional data. While sufficient for supporting stratigraphic identification and structural organization, these attributes remain insufficient to directly satisfy the requirements of numerical solution, which demand explicit material parameters, constitutive relationships, boundary conditions, and loading scenarios. In addition, the current 3D geological information model is intended to represent the geological environment of the entire study area, whereas numerical analysis is usually confined to a specific engineering action zone and its associated zone of influence. This discrepancy introduces an additional mismatch between the overall model scale and the requisite analysis-domain extent. Taken together, the mapping process from a 3D non-solid geological information model to a 3D numerical computational model in this case study is far from a simple data-export process. Instead, it is simultaneously constrained by multiple forms of mismatch, including those related to geometric representation, structural discretization, parameters and solution conditions, and analysis-domain extent. To further examine whether the introduction of virtual boreholes improves the consistency of the reconstructed geological information model and provides a sufficiently stable geological basis for subsequent mapping adaptation, a strict 43-fold leave-one-out validation procedure was adopted. In each validation fold, one of the 43 actual boreholes was completely withheld and used only as the independent reference borehole, while the remaining 42 actual boreholes were used for geological reconstruction. For the reconstruction incorporating virtual boreholes, the local stratigraphic-transition statistics, Delaunay triangular network, and the 50 virtual boreholes were regenerated using only the remaining 42 actual boreholes. Therefore, information from the withheld borehole was not used directly or indirectly during virtual-borehole generation or geological-model reconstruction, thereby avoiding information leakage during validation. This procedure was repeated until each of the 43 actual boreholes had served once as the independent validation borehole.

For each validation fold, the reconstruction based only on the retained actual boreholes was compared with that incorporating the regenerated virtual boreholes. Considering that the quality of a stratigraphic model is reflected not only by the order of stratigraphic units but also by their depth-wise distribution and thickness characteristics, three complementary indicators were adopted: Mean sequence similarity, Mean depth-discretized stratigraphic consistency rate, and Mean Absolute Error of Stratum Thickness, as shown in Figure 4. These indicators respectively evaluate the consistency of stratigraphic sequence, the agreement of stratigraphic categories along the depth direction, and the deviation in reconstructed stratum thickness. Their mathematical definitions are given as follows.

The consistency of the reconstructed stratigraphic framework was evaluated using the mean of sequence similarity. For each validation borehole, the reference stratigraphic sequence extracted from the withheld real borehole was compared with the modeled stratigraphic sequence generated from the remaining borehole constraints. Let S i r e f and S i mod represent the reference and modeled stratigraphic sequences of the i th validation borehole, respectively. The sequence similarity was calculated based on the normalized longest common subsequence (L C S):

Where L C S · denotes the length of the longest common subsequence between two stratigraphic sequences, and S represents the number of stratigraphic units contained in the sequence. The mean of sequence similarity was calculated as:

Where N represents the total number of validation boreholes. A higher value of S S m e a n indicates that the modeled boreholes preserve a more consistent stratigraphic ordering and geological framework compared with the observed boreholes.

The vertical consistency of stratigraphic classification was quantified using the mean value of depth-discrete stratigraphic consistency rate. For each validation borehole, both the reference and modeled boreholes were discretized at a vertical interval of 1 m, and the stratigraphic label at each discrete depth position was compared. Let T i, j r e f and T i, j mod denote the reference and modeled stratigraphic labels at the j -th depth interval of the i -th validation borehole, respectively. The depth-discrete stratigraphic consistency rate was calculated as:

Where I · is an indicator function, which equals one when the reference and modeled stratigraphic labels are identical and 0 otherwise, and M i represents the total number of discretized depth intervals of borehole i. The mean value of depth-discrete stratigraphic consistency rate was obtained as:

A higher D C R m e a n indicates better agreement between the modeled and observed stratigraphic distributions along the borehole depth direction.

The accuracy of stratigraphic thickness reproduction was evaluated using the mean absolute error of stratum thickness. For each validation borehole, the thicknesses of corresponding stratigraphic units between the reference and modeled boreholes were compared. Let h i, k r e f and h i, k mod denote the thicknesses of the k -th stratigraphic unit in the reference and modeled boreholes, respectively. The thickness error for each validation borehole was calculated as:

Where K i represents the number of matched stratigraphic units in validation borehole i. The mean absolute error of stratum thickness was calculated as:

Where N represents the total number of validation boreholes. A lower value of M A E h, i indicates that the modeled boreholes better reproduce the thickness variation characteristics of the observed stratigraphic units.

The statistical results of the 43-fold leave-one-out validation are summarized in Table 2. In addition to the mean values, the standard deviations are reported to characterize the variability among individual validation boreholes. These mean values indicate an overall improvement in stratigraphic sequence, depth-wise stratigraphic consistency, and stratum-thickness reproduction after the introduction of virtual boreholes. However, the relatively large standard deviations also indicate considerable variability among individual validation locations. Therefore, the observed improvement should be interpreted as an overall statistical tendency rather than as a uniform improvement at every borehole location.

Improvement results of mapping adaptation from 3D non-solid geological information models to numerical computational models

To address the aforementioned mismatches, this study first carried out solidification improvement of the 3D non-solid geological information model from a geometric representation perspective. Using stratigraphic interfaces as geometric constraints, the major interfaces were reconstructed on the Rhino platform, and the corresponding three-dimensional geometric solids were subsequently generated, as shown in Figure 5. The results demonstrate that, following interface reconstruction, the geometric solids representing different strata maintain well-defined superposition relationships and boundary correspondences in spatial configuration. This indicates that the stratigraphic structures from the original information model can be transmitted with relative stability to the geometric modeling stage. Through this process, the initial non-solid information model—wherein geological structures were represented primarily by surface interfaces and external boundaries—is transformed into a volumetric geometric solid model, thus completing the preliminary transition from surface-based to solid representation.

Building upon geometric solidification, this study further performed local structural adaptation to rectify structural-discretization mismatches. The purpose of this step is not to alter the basic spatial relationships of the strata, but rather to optimize the geometric model for volumetric mesh generation while preserving the primary structural characteristics of the strata. Following mesh discretization of the Rhino-generated geometric solids using the Griddle plug-in, it is evident that the stratigraphic solids can be successfully converted into a numerical mesh model. The resultant mesh exhibits clear overall zonation, and well-preserved interlayer boundaries at the mesh level, as shown in Figure 6. This confirms that the adapted geometric solids generally satisfy the requisite conditions for subsequent discretization and that the structural representation in the information model—originally intended primarily for visualization purposes—has been effectively reconfigured into a discretized structure suitable for numerical computation. Subsequently, to address mismatches between parameters and solution conditions, this study further performed parameter and condition mapping. Based on stratigraphic zonation, different physical and mechanical parameters were assigned to individual strata according to their lithological categories and engineering characteristics, thereby endowing each computational domain with explicit material attributes. Upon completion of these processes, the information model, which originally contained only representational attributes, was systematically reorganized into a computational model possessing solution-oriented attributes and solution conditions.

To address the mismatch between geological representation scale and numerical analysis requirements, the proposed framework allows the computational domain to be defined according to the engineering analysis objective and the corresponding geological influence range. In the present case study, the numerical computational model was generated from the adapted geological information model to demonstrate the complete transition process from geological representation to numerical computation. Therefore, the spatial extent of the computational model was maintained consistent with the adapted model to ensure the integrity of geological structures and to focus on verifying the continuity and executability of the mapping procedure.

The final 3D numerical computational model illustrates the complete transformation pathway: information model → geometric model → mesh model → numerical model. The results demonstrate that the proposed framework can effectively establish a continuous linkage between geological information representation and numerical computation.

Examination of mapping adaptation performance from 3D non-solid geological information models to numerical computational models

Results of geometric and structural examination

The geometric and structural examination primarily serves to verify whether, subsequent to solidification and local structural adaptation, the 3D non-solid geological information model yields geometric solids and mesh structures that satisfy the requirements for numerical discretization. The derived stratigraphic interfaces and the Rhino solid-model outputs demonstrate that the major stratigraphic interfaces maintain continuous spatial extension, that different stratigraphic solids preserve clear superposition relationships and boundary correspondences, and that no obvious anomalies—such as missing solids, boundary misalignment, or severe gross structural disorder—are observed. Furthermore, the Griddle mesh-model results indicate that all stratigraphic solids can be successfully discretized into volumetric meshes. The overall zonation remains distinct, and interlayer boundaries are faithfully maintained at the discretized level. These findings demonstrate that, following adaptation improvement, the surface-based representation inherent in the original information model has been successfully transformed into solid and mesh structures suitable for computational purposes.

To further characterize the generated computational mesh, additional statistics were extracted from the final FLAC3D model, as summarized in Table 3. The computational model consisted of 28,791 zones and 16,145 gridpoints. Four zone types, including Brick, Wedge, Pyramid, and Tetra, were incorporated to accommodate the complex stratigraphic interfaces and local geometric transitions. Together with the successful generation of the volumetric mesh, these statistics demonstrate that the converted model provides the discretization basis required for subsequent numerical analysis.

The above statistics confirm that the generated mesh provides the necessary geometric and computational basis for subsequent numerical analysis.

Results of parameter and condition examination

Following the generation of geometric solids and mesh discretization, material-parameter assignment, boundary-condition specification, and loading-case definition were further carried out to constitute a complete 3D numerical computational model. Parameter assignment was predicated on stratigraphic zonation, wherein different strata were assigned corresponding physical and mechanical parameters according to lithological classification and engineering characteristics, thereby ensuring that each computational region possesses explicit material attributes. The transfer from geological information to numerical solution parameters was achieved by establishing correspondences between lithological types in the 3D geological information model and predefined sets of physical-mechanical parameters, which were subsequently mapped onto the corresponding computational regions in the numerical model.

The complete physical and mechanical parameter sets for all nine geological units identified in the borehole data are provided in Table 4, including density, Young’s modulus, Poisson’s ratio, cohesion, and internal friction angle. In the FLAC3D implementation, the elastic properties were assigned in terms of bulk modulus K and shear modulus G. Therefore, Young’s modulus E and Poisson’s ratio ν were converted into the corresponding FLAC3D elastic parameters according to:

Regarding boundary condition specification, constraints were specified for the model base, side boundaries, and other necessary boundaries according to the spatial extent of the study area and specific analysis requirements. Regarding loading scenario definition, self-weight and other pertinent external actions were applied consistent with the engineering background of the investigation. The boundary conditions and loading conditions adopted in the numerical model are summarized in Table 5. Upon completion of parameter assignment, boundary condition setting, and load case establishment, the mesh model was further evolved into a 3D numerical computational model endowed with explicit material attributes and solution constraints, thereby satisfying the basic prerequisites for the subsequent numerical analysis stage.

Results of numerical modeling feasibility examination

The numerical modeling feasibility examination is intended to determine whether the geological information transferred through the preceding adaptation stages can be continuously incorporated into a complete numerical-analysis workflow. Therefore, the purpose of the numerical calculation in this study is not to validate the predictive accuracy of a specific engineering response, but to verify the continuity and executability of the mapping process from geological information representation to numerical computation.

After geometric solidification, volumetric mesh generation, and material-parameter assignment, the resulting computational model was imported into FLAC3D for numerical analysis. The Mohr–Coulomb constitutive model was adopted for the stratigraphic materials, with the corresponding physical and mechanical parameters assigned according to the stratigraphic zoning established in the geological information model. The bottom and lateral boundaries of the computational model were constrained according to the numerical-modeling requirements, and gravitational loading was applied to the entire model. Tensile strength and dilation angle were not assigned independently in the present case and therefore retained the default values used in the FLAC3D Mohr–Coulomb model.

The numerical calculation was conducted using FLAC3D 7.0. The final model contained 28,791 computational zones and 16,145 gridpoints, comprising Brick, Wedge, Pyramid, and Tetra zones. All computational zones were assigned the Mohr–Coulomb constitutive model, with the corresponding mechanical parameters inherited through the geological-to-numerical mapping procedure. The model was initialized under gravitational loading and subsequently solved to obtain a mechanically balanced state. The numerical calculation in this study was used primarily to verify the continuity and executability of the geological-to-numerical mapping process rather than to evaluate the predictive accuracy of the engineering response.

Figure 7 presents the calculated displacement-magnitude distribution of the mapped numerical model under the prescribed gravitational loading and boundary conditions, with displacement expressed in meters. The displacement field is presented as an illustrative output of the completed computational workflow and provides a basic check that the mapped model can proceed through numerical solution without interruption. Accordingly, the result is used to demonstrate numerical executability and workflow continuity rather than to independently validate the predictive accuracy of the engineering response. The calculated displacement field remained spatially continuous without apparent non-physical discontinuities or anomalous localized divergence, indicating that the mapped model produced a mechanically coherent numerical response under the adopted loading and boundary conditions.

Analysis and discussion

The foregoing results demonstrate that the proposed framework can support a continuous transition from geological information representation to numerical computation. At the input-constraint level, the introduction of virtual boreholes provides additional spatial constraints for reconstructing the stratigraphic framework. The mean stratigraphic-sequence similarity increased from 0.483 ± 0.312 to 0.553 ± 0.371, while the mean value of depth discrete hierarchical consistency rate increased from 0.233 ± 0.263 to 0.440 ± 0.470. Meanwhile, the Mean Absolute Error of Stratum Thickness decreased from 0.120 ± 0.180 to 0.080 ± 0.120. These changes indicate that the incorporation of supplementary virtual-borehole constraints improves the reconstruction of stratigraphic sequence, depth-wise stratigraphic consistency, and stratum-thickness representation. However, the relatively large standard deviations indicate that noticeable spatial variability remains among individual validation boreholes. Therefore, the mean value of 0.440 should not be interpreted as a universal engineering-acceptance threshold or as evidence of high predictive accuracy. Instead, these evaluation indicators are used to quantify the relative improvement in stratigraphic consistency and thickness reproduction introduced by the supplementary geological constraints. At the model-conversion level, the reconstructed geological information model can subsequently be transformed through geometric solidification and volumetric discretization into a numerical computational model, demonstrating the continuity and numerical executability of the proposed geological-to-numerical mapping procedure.

From an engineering implementation perspective, the main contribution of the proposed framework lies in establishing a continuous transition from geological information representation to numerical computation, as shown in Figure 8. Rather than introducing a new independent reconstruction, meshing, or domain-optimization algorithm, the framework coordinates geometric solidification, structural adaptation, parameter mapping, and engineering-oriented computational-domain adaptation to progressively transform the geological information model into a geometric solid model, volumetric mesh model, and executable numerical model (Satyanaga et al., 2023). Although Rhino and Griddle are used in the present implementation, the underlying mapping logic is not inherently restricted to these platforms (Tawelian and Mickovski, 2016).

Several limitations should nevertheless be acknowledged. First, the mapping quality remains dependent on the completeness and reliability of the input geological information. Although virtual boreholes improve spatial constraints in sparse areas, they cannot replace actual geological observations and may introduce local smoothing. Second, the present framework mainly addresses stratigraphic interfaces and basic geomechanical attributes; more complex geological conditions, such as highly developed faults, discontinuities, and abrupt lithological changes, require further investigation. Third, the influence of local geometric adaptation on subsequent numerical responses has not been quantitatively evaluated.

Although the proposed framework incorporates engineering-oriented computational-domain adaptation, the present case study did not systematically investigate the influence of different domain extents on boundary sensitivity or computational efficiency. Therefore, quantitative domain-size selection and boundary-effect evaluation remain topics for further investigation.

In addition, the numerical calculation in this study is intended primarily to demonstrate workflow continuity and numerical executability rather than predictive accuracy. Because no independent field measurements or benchmark solutions are available, the present results should not be interpreted as validation of engineering-response accuracy. The current workflow also retains a certain degree of software dependence and manual intervention. Future work should therefore focus on more complex geological structures, quantitative adaptation criteria, improved automation, and validation using independent engineering data.

To address the mismatches in geometric representation, structural discretization, parameter and solution-condition organization, and spatial extent during the transition from a 3D non-solid geological information model to a numerical computational model, this study proposes a coordinated mapping-adaptation framework. The framework integrates geometric solid reconstruction, local structural adaptation, parameter and solution-condition mapping, and engineering-oriented computational-domain adaptation to establish a continuous transition from geological information representation to numerical computation. The present case demonstrates this capability at the framework level, whereas quantitative evaluation of computational-domain size selection and boundary sensitivity remains outside the scope of the current study.

Employing a geological engineering case study in southwestern China, the results demonstrate that, with the introduction of virtual boreholes, the stratigraphic-sequence similarity of the 3D geological information model increases from 0.483 to 0.553, and the mean value of depth discrete hierarchical consistency rate improves from 0.233 to 0.440. Meanwhile, following geometric solid generation on the Rhino platform and volumetric mesh discretization using the Griddle plug-in, the model exhibits clear overall zonation, and interlayer boundaries are well preserved at the discretized level. The model successfully completes parameter assignment, boundary-condition specification, and subsequent numerical model construction. These findings support the consistency and practical executability of the proposed geological-to-numerical mapping procedure, while the reported stratigraphic evaluation indices should be interpreted as measures of relative improvement rather than as independent evidence of predictive accuracy.

The proposed method provides a feasible pathway for enabling 3D geological information models to support geotechnical numerical analysis, especially in applications such as slope engineering, underground engineering, and foundation engineering, where geological structure representation needs to be further transformed into computational analysis. Future research should focus on the inheritance of complex geological semantic information, the development of adaptation rules tailored to different analysis objectives, and the automation and standardization of the model conversion workflow to improve the method’s applicability in increasingly complex engineering environments. These results support the consistency and executability of the geological-to-numerical mapping process. They do not independently establish the predictive accuracy of the engineering response because no field measurement, physical-model test, or independent benchmark was available. The principal limitations include dependence on input-data quality, possible smoothing introduced by virtual constraints, potential effects of geometric adaptation on sub-resolution features, manual platform-specific operations, and the current restriction to geomechanical FEM/FDM analyses. Future work should focus on uncertainty-aware virtual-borehole generation, automated topology and mesh-quality control, multiphysics parameter mapping, and validation against independently measured engineering responses.