A method of and a device for evaluating collapse behaviour of a borehole wall

Abstract

A method of evaluating collapse behaviour of an open hole wall based on a constitutive soil model characterising surrounding soil of the open hole is disclosed. The method is performed by a processor and comprises the steps of: obtaining geometrical parameters of an axisymmetric slice of the open hole and the surrounding soil; creating a numerical model comprising a mesh having a plurality of elements representing the axisymmetric slice of the open hole and the surrounding soil, based on the obtained geometrical parameters; assigning simulation parameters to the numerical model, the simulation parameters comprising initial stresses, constitutive soil model properties and initial boundary conditions; determining that one or more boundary elements of the mesh develop a deformation larger than a deformation threshold, by updating the mesh during a time stepping process; removing the one or more boundary elements determined to develop a deformation larger than the deformation threshold; updating boundary conditions of the mesh; and repeating the determining, removing and updating steps until a defined criterion is met. Unlocking insights from Geo-Data, the present invention further relates to improvements in sustainability and environmental developments: together we create a safe and liveable world.

Description

A METHOD OF AND A DEVICE FOR EVALUATING COLLAPSE BEHAVIOUR OF A BOREHOLE WALLFIELD OF THE INVENTION

[0001] The present disclosure generally relates to the field of open hole stability, and more specifically to a method of and a device for evaluating collapse behaviour of a borehole wall. Unlocking insights from Geo-Data, the present invention further relates to improvements in sustainability and environmental developments: together we create a safe and liveable world.BACKGROUND OF THE INVENTION

[0002] Drilled and grouted piles from the foundation for many offshore infrastructures. These infrastructures serve various traditional industries like oil and gas, bridge construction and for new applications such as wind energy industry. The successful installation of drilled and grouted piles requires a stable open hole to be drilled first.

[0003] The analysis of an open hole is crucial for assessing borehole stability. The analysis of open hole stability refers to the assessment and evaluation of the stability of the drilled hole before the grouting process and the subsequent installation of piles. This process is crucial for ensuring the integrity and stability of the piles and their ability to withstand the loads imposed on them.

[0004] The stability analysis considers factors such as soil or rock strength, formation stability, pore pressure, and water inflow during the drilling and grouting processes. This analysis helps to determine the stability of the open hole and ensures that the grouted pile will be adequately supported by the surrounding soil or rock formations. In this context, 'grouting' denotes the injection of a cement-based fluid into a drilled hole to enhance pile stability and bonding with the surrounding geology in pile construction, especially offshore.

[0005] It is noted that a marine environment often involves uncemented soils such as sand with high permeability. In uncemented soils, the length of time over which a drilled open hole may remain stable depends on the soil strength, stiffness and drainage behaviour.

[0006] Moreover, specifics of offshore open hole pile construction - namely drilling with water, not mud, and sometimes application of a positive head drilling set-up are not seen as often in onshore construction.

[0007] The inventors are aware of an analysis of open hole stability based on finite element analyses. This analysis included time dependent analysis but with a mesh that could not exhibit failure in critical layers and with a non-calibrated soil model that could not capture appropriate soil behaviour.

[0008] No attempt was made to follow the steady propagation of any collapse beyond the point of first initiation. However, the importance of a model that can capture the propagation of collapse beyond first initiation is a conceptual leap and of much importance in drilled and grouted piles construction, especially for the offshore environment.

[0009] Based on the above, there is a general and ongoing need for a method of evaluating collapse behaviour of a borehole wall, especially evaluating the ongoing propagation of hole collapse over time with the eroding wall feature in uncemented soil.BRIEF SUMMARY OF THE INVENTION

[0010] According to one aspect of the present disclosure, there is presented a method of evaluating collapse behaviour of an open hole wall based on a constitutive soil model characterising surrounding soil of the open hole, the method performed by a processor and comprising the steps of:

[0011] - obtaining geometrical parameters of an axisymmetric slice of the open hole and the surrounding soil;

[0012] - creating a numerical model comprising a mesh having a plurality of elements representing the axisymmetric slice of the open hole and the surrounding soil, based on the obtained geometrical parameters;

[0013] assigning simulation parameters to the numerical model, the simulation parameters comprising initial stresses, constitutive soil model properties and initial boundary conditions;

[0014] - determining that one or more boundary elements of the mesh develop a deformation larger than a deformation threshold, by updating the mesh during a time stepping process;

[0015] removing the one or more boundary elements determined to develop a deformation larger than the deformation threshold;

[0016] - updating boundary conditions of the mesh; and

[0017] - repeating the determining, removing and updating steps until a defined criterion is met.

[0018] The method is based on the insight that the collapse behaviour of an open hole over time can be properly modelled by an interactive procedure in which one or more boundary elements considered as representing a fallen part of the surrounding soil are removed. The removal of such boundary elements allows updated boundary conditions to be applied to new boundary elements of the constitutive soil model representing the axisymmetric slice of the open hole and the surrounding soil. Propagation of the hole collapse over time is therefore captured by the method of the present disclosure.

[0019] The method disclosed enables a robust evaluation of the collapse behaviour of an open hole over time, facilitating pre-emptive measures for maintaining structural stability. It accomplishes this by employing an iterative procedure to simulate erosion in the soil surrounding the hole, thereby capturing the propagation of hole collapse over time.

[0020] In an example, the constitutive soil model captures friction and dilation response of the surrounding soil.

[0021] As can be contemplated by those skilled in the art, frictional forces between the soil grains play a crucial role in stabilizing the open hole. If the frictional resistance is sufficient, it helps to maintain the stability of the borehole by preventing excessive deformations or collapse. The dilation response of the soil surrounding a borehole also affects the stability of the borehole walls. Therefore, the constitutive soil model used in the present disclosure takes the friction and dilation response of the surrounding soil into consideration, which allows the stability of the open hole to be properly modelled.

[0022] In an example of the present disclosure, the constitutive soil model comprises an elastic- plastic, Mohr-Coulomb, pure frictional cohesion-free soil model.

[0023] A elastic-plastic, Mohr-Coulomb, pure frictional cohesion-free soil model is a common geotechnical model used to represent the behaviour of granular soils (like sands) in a marine environment where cohesion between soil grains is minimal or non-existent. The application of the Mohr-Coulomb soil model enhances the accuracy of the collapse behaviour prediction in uncemented, marine soils, due to its tailored representation of soil mechanics in such environments.

[0024] This soil model serves as a fundamental and widely used approach in geotechnical engineering and is well suited for representing the behaviour of soil in a marine environment.

[0025] In an example of the present disclosure, the mesh is a two-dimensional mesh.

[0026] In the case that the available computational resources are limited, a 2D numerical model, that is a 2D mesh, can be used conveniently. This helps to reduce the requiredcomputational power while still allowing the collapse behaviour of the open hole over time to be assessed.

[0027] In an example of the present disclosure, the mesh is a three-dimensional mesh.

[0028] A 3D mesh may also be used when the computational resources allow it. The 3D mesh will help to improve the accuracy of the analysis performed on the stability of the open hole. The use of 2D and 3D mesh in the numerical model allows flexibility based on available computational resources, with 3D mesh offering improved accuracy where resources allow.

[0029] In an example of the present disclosure, the determining step comprises determining that a vertical displacement of a boundary element exceeds a displacement threshold.

[0030] In this context, vertical displacement refers to the vertical movement of a boundary element, which is indicative of its detachment from the open hole wall. Velocity threshold refers to a predetermined limit for the rate of movement of a boundary element, beyond which the element is considered potentially unstable.

[0031] As can contemplated by those skilled in the art, detachment of a boundary soil element from the wall of the open hole is reflected by a vertical displacement of the boundary element. When a boundary element is found to experience a vertical displacement which is larger than a displacement threshold, it can be determined that the boundary element is not part of the soil anymore and therefore collapsed.

[0032] In an example of the present disclosure, the displacement threshold is a half of a vertical height of the boundary element. Determining vertical displacement and comparing it with a threshold allows early detection of potentially collapsing boundary elements, facilitating timely intervention.

[0033] A boundary element moving along the vertical direction for a distance which is more than half the vertical height of the boundary element is a clear indication that the boundary element has detached from the soil and therefore fallen.

[0034] In an example of the present disclosure, the updating step comprises applying boundary conditions applied to the deleted boundary elements to a new boundary element(s).

[0035] When the boundary elements decided to have collapsed are removed or deleted, elements previously masked by those removed boundary elements become new boundary elements and would be subject to the same boundary conditions as experienced by the removed boundary elements. The boundary conditions are therefore applied to those new elements to simulate the real-life situation. The development of the collapse over time can therefore be modelled.

[0036] In an example of the present disclosure, the method further comprises, prior to the step of determining that one or more boundary elements of the mesh develop a deformation larger than a deformation threshold, the steps of:

[0037] - determining that a velocity of a boundary element is higher than a velocity threshold;

[0038] - performing mechanical time at constant time until element displacements of the boundary element have stabilised or the element displacements have increased to a point where the boundary element has to be deleted.

[0039] As can be contemplated by those skilled in the art, at some points when simulating the dynamic behaviours of the soils, the solution might not have properly balanced forces. At such points additional "static steps" (but the time made constant) may be performed to allow the static solution to rebalance itself, but if it cannot rebalance then this means something is collapsing.

[0040] It can be understood that high element velocities imply intrinsic instability of the attached element. Therefore, the element velocities are studied during the analysis in order to detect developing instability even before large element deformations have developed. This is done by determining whether the velocity of a boundary element is higher than a velocity threshold.

[0041] That is to say, where high velocities are detected, additional mechanical time steps are undertaken, but at constant time. These are continued until element displacements have stabilised or the element displacement have increased to the point where the associated element would be deleted; stability is then generally restored for some period of time after an element deletion. The introduction of velocity threshold and additional mechanical time steps at constant time help in early detection of developing instability, allowing pre-emptive steps to restore stability.

[0042] In an example of the present disclosure, the defined criterion comprises when a required design stable duration of the open hole is reached while the open hole remains intact.

[0043] In another example of the present disclosure, the defined criterion comprises when collapse of the open hole exceeds a collapse threshold before a required design stable duration of the open hole is reached.

[0044] By using the method of the present disclosure, the stability of an open hole can be advantageously evaluated before or during the drilling of the open hole. It can provide valuable information which can be used to understand and improve the stability of the open hole at an earlier stage or during the construction project. The disclosed method allows evaluation of openhole stability before or during drilling, providing crucial, timely information for optimizing construction processes, thereby mitigating potential safety risks and financial losses.

[0045] In an example of the present disclosure, the open hole comprises an underwater open hole.

[0046] The present disclosure is especially suitable for modelling the collapse behaviour of an underwater open hole as the used soil model reflects or characterises properties of the soil in a marine environment. The method is particularly effective for underwater open hole analysis, as the soil model used adeptly characterises properties of marine soils.

[0047] In an example of the present disclosure, the boundary conditions comprise cyclic tidal variations, with or without application of a static ‘positive head’ over and above the instantaneous water pressure imposed from the sea. Cyclic tidal variations shall refer to periodic changes in the marine environment due to tidal movements, affecting parameters such as hydrostatic pressure and thus the stability of an underwater open hole.

[0048] In a second aspect of the present disclosure, there is presented a device for evaluating collapse behaviour of an open hole wall based on a constitutive soil model characterising surrounding soil of the open hole and by utilizing a mesh having a plurality of elements representing an axisymmetric slice of the open hole and the surrounding soil, the mesh created based on parameters of the axisymmetric slice of the open hole and the surrounding soil, the device comprises a processor for performing the method according to the first aspect of the present disclosure.

[0049] In a third aspect of the present disclosure, a computer product is provided, comprising a computer readable storage medium storing instructions which, when executed on at least one processor, cause the at least one processor to carry out the method according to the first aspect of the present disclosure.

[0050] The above mentioned and other features and advantages of the disclosure will be best understood from the following description referring to the attached drawings. In the drawings, like reference numerals donate identical parts or parts performing an identical or comparable function or operation.BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to describe the manner in which the above-recited and other advantages and features of the disclosure can be obtained, a more particular description of the principles briefly described above will be rendered by reference to specific embodiments thereof whichare illustrated in the appended drawings. Understanding that these drawings depict only exemplary embodiments of the disclosure and are therefore not to be considered to be limiting of its scope, the principles herein are described and explained with additional specificity and detail through the use of the accompanying drawings in which:

[0052] Fig. 1 diagrammatically illustrates a general undrained stress path.

[0053] Fig. 2 schematically illustrates a full mesh used for an 2D axisymmetric slice of an open hole and soil surrounding in accordance with an embodiment of the present disclosure.

[0054] Fig. 3 schematically illustrates details of the mesh at the hole boundary of Fig. 2.

[0055] Fig. 4 shows checking whether a vertical displacement of a boundary element is larger than a displacement tolerance.

[0056] Fig. 5 shows that the boundary element is deleted from the mesh as its vertical displacement exceeds the deformation threshold.

[0057] Figs. 6, 7 and 9 respectively illustrate detail of the mesh at the hole boundary at times of 5 minutes, 2 hours and 25 minutes, and 7 hours 6 minutes in an example simulation, presenting a series of plots showing the deformed and updated mesh geometry at various snapshots through time.

[0058] Fig. 8 illustrates excess pore pressure in an example simulation at the moment of 2 hours and 25 minutes.

[0059] Fig. 10 schematically illustrates, in a flow chart type diagram, a method of evaluating collapse behaviour of an open hole wall based on a constitutive soil model characterising surrounding soil of the open hole according to an embodiment of the present disclosure.DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0060] Embodiments contemplated by the present disclosure will now be described in more detail with reference to the accompanying drawings. The disclosed subject matter should not be construed as limited to only the embodiments set forth herein. Rather, the illustrated embodiments are provided by way of example to convey the scope of the subject matter to those skilled in the art.

[0061] The present disclosure is detailed below with reference to analysing the stability of an underwater open hole. Those skilled in the art will appreciate that the present disclosure is not limited to the analysis of open holes drilled under water but is applicable for applications involving uncemented soils.

[0062] For the purpose of studying the collapse behaviour of an open hole, a soil model that can characterise soil surrounding the open hole is needed. The soil model represents the mechanical behaviour and properties of the surrounding formation, allowing the response of the soil to various loading and boundary conditions to be investigated.

[0063] In the present disclosure, an elastic- plastic (strain hardening / strain softening), Mohr-Coulomb, pure frictional (no cohesion) soil model is used. The model used has a particular relationship that defines the dilation angle as a function of plastic shear strain, configured to achieve specific predictions of drained volumetric (dilational) strain and undrained shear strength for the given linear elastic soil modulus. The drained volumetric strain and the undrained strength are the critical soil strength / stiffness parameters that control the open hole stability process. An equation has been derived which predicts the undrained shear strength achieved through dilation for the Strain Softening / Hardening model used in the present disclosure.

[0064] Figure 1 diagrammatically illustrates a general undrained stress path. The vertical and horizontal axes shown are t' & s', representing the shear stress and mean effective stress respectively. The shear stress and mean effective stress are derived from the major (cr'i) and minor (<5'3) principal effective stresses as follows:

[0065] t' = (<J'I-<J'3) / 2 and s' = (<J'I+<J'3) / 2 (1)

[0066] The equation to predict the undrained strength can then be derived as follows,

[0068] where K is the elastic bulk stiffness of the soil, 8vpias is the plastic volumetric strain, s'o is the mean effective stress when the soil reaches the yield envelope, c|)' is the effective friction angle of the soil, and Abspis the ratio of change in the 2D mean effective stress (ie. As') to that in 3D (ie. Ap' = (Ac'i+Ac 2+Ao'3) / 3).

[0069] Absp is defined only for the section of the stress path along the yield envelope, and is calculated as follows,

[0071] The plastic volumetric strain is related to the dilation angle (y) and can be expressed as,

[0072] Aevpias= j —Ate, = jsin y.de,

[0073] where svis volumetric strain, and 8Sis shear strain.

[0074] In this particular embodiment, the dilation angle is defined as a linear function of the plastic shear strain (ePs) in the form:

[0075] V=A0-Bosps> 0 (5)

[0076] In this case the total plastic volumetric strain that can result from dilation may be evaluated as,

[0077] [cos( A0- B0eps) - cos( A0)] (6)

[0078] Note that the convention used here for the plastic shear strain, 8ps, is consistent with that used in some conventional soil modelling software; spsequals half the engineering (or deviatoric) shear strain (ss), hence:

[0080] where si and 83 are the major and minor principal strain, respectively.

[0081] An appropriate assessment of hole stability accounting for soil consolidation requires the modelling of realistic undrained strengths, realistic rates of dilation and realistic magnitudes of volumetric compaction, combined with realistic consolidation properties. The equation presented above predicts the first of these, that is, the undrained strengths suas a function of the next two (i.e., via 8vpias and K).

[0082] The above-described model is widely used in geotechnical engineering due to its versatility. It can be applied to a broad range of soil types, including both cohesive and cohesionless soils. It is commonly used for analysing granular soils and rock masses.

[0083] This model incorporates the concept of failure criteria based on the stress state of the soil. By defining the cohesion and friction angle parameters, it can capture both shear strength and dilatancy behaviour of soils. This allows for the prediction of failure mechanisms and the determination of stability in various geotechnical applications.

[0084] Moreover, the Mohr-Coulomb model is compatible with common geotechnical analysis methods, such as limit equilibrium analysis, slope stability analysis, and finite element analysis. It can be readily incorporated into these methods to assess the stability and deformation characteristics of soil and rock masses.

[0085] It will be understood by those skilled in the art that alternative soil constitutive models may be adopted, as long as the model can capture the friction / dilation response of appropriate soils.

[0086] Friction and dilation response as used in the present disclosure refer to the intrinsic properties of soil, wherein friction refers to the resistance against the displacement of soil grains against each other, and dilation refers to the volumetric expansion or contraction of the soil upon shearing.

[0087] Through judicious selection of appropriate parameters, the above described soil model is used in the present disclosure to evaluate or simulate the collapse behaviour of a drilled unsupported open hole over time. The disclosure is a ‘recipe’ for assessing the stability of a drilled open hole in nominally uncemented, purely frictional soil. The recipe is a process comprised of models and procedures, which together provide a unique capability not achieved prior to this disclosure.

[0088] The soil parameters used in the described model ideally are derived from laboratory tests on site specific test data that measure the key parameters for the applicable in situ soil conditions.

[0089] However, in lieu of such site-specific test results, empirical correlations may also be considered, where the dilational properties are defined in terms of state parameter or relative density and confining stress.

[0090] In implementing the method of the present disclosure, over the depth range of interest for drilled and grouted piles, the soil is characterised into a number of main layers. In an example, the soil is characterised into eleven layers termed Unit 1 to Unit 11. A driven primary pile is used throughout Unit 1 to Unit 3, therefore the analysis is focused on Unit 4 and below.

[0091] Analyses are performed to assess open hole stability during drilling of insert piles in Unit 4 to Unit 12. Soil parameters used in the analysis are listed in Table. 1.

[0092] Table 1 Soil Parameters for analyses

[0093] The analysis of the present disclosure is performed using a finite difference program which is commonly used for geotechnical analysis. The program utilises an explicit rather than an implicit solver. This makes it more suitable for modelling propagating collapse problems of this type as compared to the more common implicit solver used in other known analysis tools. Tools using implicit solvers will likely exhibit numerical convergence difficulties with this kind of problem and are unlikely to be able to model anything past the very first point of instability.

[0094] In contrast, the model as disclosed in the present disclosure can robustly capture the ongoing propagation of an initial point of instability all the way up to complete collapse. Other embodiments of the invention may use alternative finite element analysis programs that utilise explicit solvers if they could be managed in such a way as to maintain numerical stability.

[0095] Analysis is performed based on the parameters as listed in Table 1 using the equations described above, with the relevant soil group parameters selected as appropriate for each soil unit. Parameters that define the initial stress state in the soil are presented in Table 2.

[0096] Table 2 In situ stress Parameters for the axisymmetric model

[0097] In the present disclosure, a numerical model comprising a two-dimensional, 2D, axisymmetric slice of the open hole and surrounding soil is created, with boundaries defined sufficiently far away as to not impact the results obtained. A 2D numerical model is relatively simple and takes less computational resources. It can therefore be conveniently used to analyse the stability or collapse behaviour of the open hole.

[0098] It will be understood by those skilled in the art that in an alternative embodiment a full 3-dimensional numerical model of the soil and open hole may also be used, if the computational resources permit so.

[0099] The numerical model used in the present disclosure comprises a mesh covering the geometry of a 2D axisymmetric slice of an open hole and soil surrounding the open hole. The axisymmetric model is used to simulate the full depth of an interested part of the open hole. A lower part of open one may also be modelled, thereby providing a “stress distribution” layer for the applied overburden stresses.

[0100] Axisymmetric slice is defined as a slice of the hole and surrounding soil characterized by symmetry around an axis, typically the central vertical axis of the drilled hole. Deformation threshold shall refer to the maximum allowable deformation in boundary elements of the mesh, beyond which the element is considered unstable and thus, is removed.

[0101] In an example, a total soil height of 25 meter covering Unit 4 to Unit 9 of the soil is modelled, with an average element height of 40 cm. In the radial direction a graded mesh was used starting from small elements close to the hole wall (the first element had a width of 30 cm) grading to much larger elements at the fixed outer boundary, which was located 60 m from the centre of the hole.

[0102] An initial hole radius of 1.275 meter is assumed (diameter = 2.55 m). The mesh geometry has been shaped to include a slope of 40° from the bottom left hand corner of the mesh up to the top of Unit 5. This is done to ensure that gradual mesh “erosion” would not develop to a shallower angle than the defined friction angle. Without this feature it is found that slope “erosion” would propagate unrealistically throughout the mesh as an inevitable consequence of the rectangular geometry of each element. This is because a rectangular element of uncemented soil naturally tries to “reshape” itself by slumping back to a 40° slope, but with the procedure used here, the entire element would be deleted instead and the whole process starts over again.

[0103] Figure 2 schematically illustrates a full mesh used for the 2D axisymmetric slice of the open hole and soil surrounding in this example. Figure 3 schematically illustrates details of the mesh at the hole boundary. Though no axis unit is shown in Figures 2 and 3, those skilled in the art will understand that the axes represent dimensions of the open hole in for example meters.

[0104] The lower section of Unit 4 is also included in the model. However, since the purpose of this additional layer is to ensure an appropriate distribution of overburden stress into the weaker layers below, it is assumed that this layer is sufficiently strong to resist collapse and hence only elastic soil properties are defined for Unit 4. Hence, no conclusions as to the true behaviour of Unit 4 is deduced from this particular analysis.

[0105] To simulate the soil above the upper mesh boundary an in situ vertical effective stress of 299 kPa along the top boundary of the mesh is applied.

[0106] In an exemplary embodiment, the steps in the analysis comprising the steps of imposing the in situ conditions, prior to hole drilling, fully unloading the hole wall instantaneously under undrained conditions, and allowing consolidation to occur, observing the steady dissipation of excess pore pressures, increase in hole wall movements and progressive mesh erosion as instabilities (“collapse”) develop over time.

[0107] The mesh as illustrated in Figures 2 and 3 is designed to be updated during a time stepping process. Elements of the mesh that develop excessive deformation are automatically deleted from the mesh in order to simulate detachment of soil elements from the wall of the hole, that is, collapse of the soil elements.

[0108] After an element is deleted the boundary conditions applied to the original element (e.g. water pressure and total pressure applied on the wall of the hole) are reapplied to the new boundary element. Without this modelling approach, it is only possible to estimate the point at which initial failure occurs at the hole wall, which provides limited insight.

[0109] The approach used in this invention allows the full development of collapse over time to be simulated. The procedure described above is implemented using a programming language that is inbuilt within the finite difference program.

[0110] Figures 4 and 5 schematically illustrate the above-described procedure. In Figures 4 and 5, both the vertical and horizontal axes are in decameter.[OHl] The criterion for deleting a boundary element is based on the vertical displacement of one or more of the elements nodes exceeding a prescribed displacement tolerance, which is also referred to as a deformation threshold and is selected to be sufficiently high as to always be associated with high element velocities implying intrinsic instability of the attached element.

[0112] The displacement tolerance is also optimised to avoid unnecessary analysis time stepping trying to stabilise intrinsically unstable elements, which given they are already unstable, do not materially affect any other aspect of the analysis. Generally, it has been found that a vertical displacement tolerance or deformation threshold of half the element height is the most appropriate value to use. In practice the deformation threshold may be selected in a range of a quarter of the element height to three quarter of the element height.

[0113] Deformation threshold of half the element height may appear to be a relatively modest value to define “collapse”, but was selected based on the observed performance in some preliminary analyses where it was found that half of vertical element displacement would always be associated with high element velocities and hence intrinsically implied instability of the element.

[0114] Deleting an element after only half of element vertical movement was found to reduce run times considerably (since it avoided a large amount of unnecessary analysis time stepping trying to stabilise an intrinsically unstable element), but since such elements were already unstable, this should not materially affect any other aspect of the analysis.

[0115] In an example as illustrated in Figure 4, it is checked whether a vertical displacement of a boundary element 41 is larger than a displacement tolerance. Here a vertical height of the boundary cell is 40 cm, and the displacement tolerance is taken as half of the height of the boundary cell.

[0116] In Figure 5, it is illustrated that the boundary element 41 is deleted or removed from the mesh as its vertical displacement exceeds the deformation threshold. After that, the boundary conditions are applied to a node 42 which becomes the new boundary element after the previous boundary element 41 is deleted.

[0117] The boundary conditions may comprise for example water pressure and total pressure applied on the wall of the hole. The boundary conditions may also comprise one ormore of cyclic tidal variations, change of water pressure due to pull out of tools, damage due to impact of tools / equipment against the hole, items being lowered down the hole and so on.

[0118] Drilling with a static positive head in our model requires only an incremental change in the applied boundary conditions, as compared to the scenario with no positive head. However, the latest embodiment of our invention permits more complex boundary conditions to be applied, allowing for the realistic influence of cyclic tidal variations to be addressed in addition to any applied static positive head.

[0119] The above procedure is repeated until the hole collapses before a design duration is reached, or until the design duration is exceeded while the hole is still stable.

[0120] In an example simulation, Figures 6, 7 and 9 respectively illustrate detail of the mesh at the hole boundary at times of 5 minutes, 2 hours and 25 minutes, and 7 hours 6 minutes, presenting a series of plots showing the deformed and updated mesh geometry at various snapshots through time. Figure 8 illustrates excess pore pressure at the moment of 2 hours and 25 minutes.

[0121] From Figure 6 it can be seen that instability first develops in Unit 8 after only 5 minutes. It is found that spalling of the first column of elements has occurred throughout most of this layer after only 8 minutes.

[0122] Element “erosion” continues steadily in Unit 8 and after about two and a half hours (Figure 7) a substantial overhang extending approximately 2.5 m from the hole wall has developed in the overlying Unit 7. At this time the first element spalls away from the edge of the roof of Unit 7 material. Figure 8 shows that negative excess pore pressures required to support this large overhang are apparent. Material continues to spall away from the roof of Unit 7 and the overhang continues to develop in this layer.

[0123] Furthermore, Figure 9 shows that after just over 7 hours, first spalling occurs from Unit 6.

[0124] With the procedure described above, a single analysis can assess both the vertical hole stability in Units 5 to 9, and assess the stability of any overhangs, since the latter are automatically created if and when local collapse is initiated anywhere as the analysis proceeds through time.

[0125] A general check of the element velocities during the analysis may also be performed in order to detect developing instability even before large element deformations have developed. Where high velocities are detected, additional mechanical time steps are undertaken, but at constant time. These are continued until element displacements have stabilised or the element displacement have increased to the point where the associated elementwould be deleted; stability is then generally restored for some period of time after an element deletion.

[0126] The above described method of the present disclosure is schematically illustrated using a flow chart of Figure 10. A brief description of the flow 10 shown in Figure 10 is given as follows.

[0127] At step 101, geometrical parameters of an axisymmetric slice of the open hole and surrounding soil is obtained. The geometrical parameters may be obtained by direction measurement of a drilled open hole or based on design parameters of a hole to be drilled.

[0128] At step 102, a numerical model comprising a mesh having a plurality of elements representing the axisymmetric slice of the open hole and the surrounding soil is created, based on the obtained geometrical parameters. The numerical model is created using a program or a software implementing the soil model as described in the present disclosure, which will be used to analyse the collapse behaviour of the open hole over time.

[0129] At step 103, simulation parameters are assigned to the numerical model. The simulation parameters comprise initial stresses experienced by the soil surrounding the open hole, constitutive soil model properties and initial boundary conditions applied to the elements of the numerical model.

[0130] At step 104, a time stepping process is performed, updating the mesh representing the the axisymmetric slice of the open hole and the surrounding soil. The time stepping process is performed until it is determined that one or more of the boundary elements of the mesh have developed a deformation larger than a deformation threshold. The way of determining is described above with reference to Figure 4.

[0131] At step 105, the boundary elements determined to develop deformation larger than the deformation threshold are removed or deleted from the mesh. After that, at step 106, the boundary conditions of the mesh are updated. This is performed by applying the boundary conditions to elements which have become new boundary elements after removing the boundary elements determined to develop deformation larger than the deformation threshold.

[0132] At 107, the above steps 104 to 106 are repeated until a defined criterion for ending the evaluation procedure is met.

[0133] The defined criterion can be that the required design stable duration of the open hole is reached while the open hole remains intact. The open hole remains intact can be considered as a limited number of boundary elements of the mesh are considered as fallen off. As an example, when the number collapsed boundary elements of the mesh accounts for lessthan a threshold value, such as 5% or less of the total number of boundary elements of the mesh, the open hole is considered as remaining intact.

[0134] The defined criterion may also be that the excessive collapse has happened before the required design stable duration of the open hole is reached. This may be determined when collapse of the open hole exceeds a collapse threshold before reaching the required design stable duration of the open. As an example when 30% of boundary elements of the mesh are considered as collapsed, it can be decided that there is excessive collapse of the boundary elements, then the assess procedure may also be stopped.

[0135] The method of the present disclosure therefore allows the stability of the open hole over time to be evaluated in a practical way, allowing the construction work to be conducted as planned or adjusted where necessary.

[0136] The invention has been described by reference to certain embodiments discussed above. It will be recognized that these embodiments are susceptible to various modifications and alternative forms well known to those of skill in the art.

[0137] Further modifications in addition to those described above may be made to the structures and techniques described herein without departing from the spirit and scope of the invention. Accordingly, although specific embodiments have been described, these are examples only and are not limiting upon the scope of the invention.

Claims

CLAIMS1. A method of evaluating collapse behaviour of an open hole wall based on a constitutive soil model characterising surrounding soil of the open hole, the method performed by a processor and comprising the steps of: obtaining geometrical parameters of an axisymmetric slice of the open hole and the surrounding soil; creating a numerical model comprising a mesh having a plurality of elements representing the axisymmetric slice of the open hole and the surrounding soil, based on the obtained geometrical parameters; assigning simulation parameters to the numerical model, the simulation parameters comprising initial stresses, constitutive soil model properties and initial boundary conditions; determining that one or more boundary elements of the mesh develop a deformation larger than a deformation threshold, by updating the mesh during a time stepping process; removing the one or more boundary elements determined to develop a deformation larger than the deformation threshold; updating boundary conditions of the mesh; and repeating the determining, removing and updating steps until a defined criterion is met.

2. The method according to claim 1, wherein the constitutive soil model captures friction and dilation response of the surrounding soil.

3. The method according to claim 2, wherein the constitutive soil model comprises an elastic- plastic, Mohr-Coulomb, pure frictional cohesion-free soil model.

4. The method according to any of the previous claims, wherein the mesh is a two- dimensional mesh.

5. The method according to any of claims 1 to 3, wherein the mesh is a three-dimensional mesh.

6. The method according to any of the previous claims, wherein the determining step comprises determining that a vertical displacement of a boundary element exceeds a displacement threshold.

7. The method according to claim 6, wherein the displacement threshold is a half of a vertical height of the boundary element.

8. The method according to any of the previous claims, wherein the updating step comprises applying boundary conditions applied to the deleted boundary elements to a new boundary element(s).

9. The method according to any of the previous claims, further comprising, prior to the step of determining that one or more boundary elements of the mesh develop a deformation larger than a deformation threshold, the steps of: determining that a velocity of a boundary element is higher than a velocity threshold; performing mechanical time stepping at constant time until element displacements of the boundary element have stabilised or the element displacements have increased to a point where the boundary element has to be deleted.

10. The method according to any of the previous claims, wherein the defined criterion comprises when a required design stable duration of the open hole is reached while a percentage of collapsed element is lower than a threshold value.

11. The method according to any of the previous claims, wherein the defined criterion comprises when collapse of the open hole exceeds a collapse threshold before a required design stable duration of the open hole is reached.

12. The method according to any of the previous claims, wherein the open hole comprises an underwater open hole.

13. The method according to any of the claim 12, wherein the boundary conditions comprise cyclic tidal variations, specifically with or without application of a static positive head over and above an instantaneous water pressure imposed from the sea.

14. A device for evaluating collapse behaviour of an open hole wall based on a constitutive soil model characterising surrounding soil of the open hole and by utilizing a mesh having a plurality of elements representing an axisymmetric slice of the open hole and the surrounding soil, the mesh created based on parameters of the axisymmetric slice of the open hole and the surrounding soil, the device comprises a processor for performing the method according to any of the previous claims 1 to 13.

15. A computer program product, comprising a computer readable storage medium storing instructions which, when executed on at least one processor, cause the at least one processor to carry out the method according to any of the claims 1 to 13.

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