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Auditoría de modelos numéricos para macizos rocosos

Dr. Alejo O. SfrisoUniversidad de Buenos Aires materias.fi.uba.ar/6408 asfriso@fi.uba.arSRK Consulting (Argentina) latam.srk.com asfriso@srk.com.arAOSA www.aosa.com.ar asfriso@aosa.com.ar

Propósito de las auditorías técnicas

• Evaluar la lógica del trabajo en función de su objetivo• Establecer si los mecanismos, variables y parámetros

relevantes han sido considerados• Mostrar que el análisis de respaldo es apropiado dentro

de los límites del conocimiento disponible• Considerar si las conclusiones están justificadas en

términos de los objetivos del proyecto• Proporcionar rastreabilidad de la información, análisis y

decisiones adoptadas

La auditoría debe ser independiente, sin limitaciones técnicas ni constractuales, y agregar valor al proyecto2

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Los ocho métodos de diseñoen ingeniería de rocas

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5. Undertake rock engineering modelling and design and recordall steps in the process.

With reference to Item 4 in the above list, an additional benefitof the technical audit is that it enables highlighting of any ‘guesswork’ based on engineering experience that is potentially subjectto both amendment with further experience and updating asscience advances.

This overall procedure was also presented within the contextof two flowcharts: one illustrating the eight basic modellingmethods (Fig. 1, noting that there are four methods A–D withincrease in complexity from left to right, each with two sub-methods depending on whether the method involves 1:1mapping or non-1:1 mapping of the project geometry); theother illustrating the seven basic steps in the rock engineeringdesign process [2]. All the aspects of Fig. 1 can be subject totechnical auditing, i.e. obtaining the site and rock massinformation from site investigation, use of the eight types ofmodelling methods (whether used singly, in combination or insequence), development of the initial design, constructionmonitoring and back analysis, leading to the final design.Similarly, the auditing is applied to the seven design stepsdiscussed in [2], these being the project purpose, key features ofthe site/rock mass/project, design approach strategy, choice ofmodelling method and appropriate code, initial design, integratedmodelling and feedback information and final design andverification/validation.

1.3. ‘Soft’ and ‘hard’ technical audits and the audit evaluation

Note that the technical auditing can be ‘soft’ or ‘hard’, with thecharacteristics as indicated in Fig. 2. Thus, for modelling, i.e. usingone or more of the eight main types of modelling methods shownin Fig. 1, either auditing type can be utilized, depending on thepurpose of the auditing. The soft audit can be used initially tosupport the development of the modelling programme. However,the hard audit is necessary for the total audit evaluation andability to state whether the modelling is adequate for the purpose.

The two demonstration auditing examples that follow are:(1) the procedure for auditing a site investigation measurement—in situ rock stress (soft audit) and (2) auditing the modelling forthe design of hydropower caverns at the Laxiwa site on the YellowRiver in China (semi-hard audit).

Whether a soft or hard audit is appropriate in any givensituation will depend on the requirement and according to thedescriptions in Fig. 2; both forms of audit are demonstrated in thefollowing sections. The limited audit illustrated for the seconddemonstration audit for the hydropower caverns in China istermed ‘semi-hard’ because it is not possible to include the fulldetail given the limitations on the paper length.

2. Demonstration example 1: the procedure for technicallyauditing a site investigation measurement—in situ rock stress(soft audit)

2.1. Background

The validity of the modelling and design of a rock engineeringproject will depend on the accuracy of the supporting information

Use of pre-existing

standard methods

Analytical methods,

stress-based

Basic numerical

methods, FEM, BEM, DEM,

hybrid

Extended numerical methods,

fully-coupled models

Precedent type analyses and modifications

Rock mass classification,RMR, Q, GSI

Database expert

systems, & other systems

approaches

Integrated systems

approaches, internet-based

Objective

Construction

SiteInvest-igation

Level 1 1:1 mapping

Level 2Not 1:1 mapping

Design based on forward analysis Design based on back analysis

Method A Method B Method C Method D

Fig. 1. Flowchart of rock mechanics modelling types used to support rock engineering design (from [2]).

'Soft' Audit 'Hard Audit' Audit Evaluation

Obtains the basic information for

establishing the essence of the

problem

Obtains the detailed

information on all the procedures

being used

Establishes whether the modelling is

adequate to meet the objectives

Ability to present what is

being done

Ability to state the details of what is being

done

Ability to state whether the modelling is

adequate for the purpose

Fig. 2. The ‘soft’ and ‘hard’ audits and the audit evaluation.

J.A. Hudson, X.-T. Feng / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 877–886878

(Hudson & Feng 2010)

Los dos niveles de auditoría técnica

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5. Undertake rock engineering modelling and design and recordall steps in the process.

With reference to Item 4 in the above list, an additional benefitof the technical audit is that it enables highlighting of any ‘guesswork’ based on engineering experience that is potentially subjectto both amendment with further experience and updating asscience advances.

This overall procedure was also presented within the contextof two flowcharts: one illustrating the eight basic modellingmethods (Fig. 1, noting that there are four methods A–D withincrease in complexity from left to right, each with two sub-methods depending on whether the method involves 1:1mapping or non-1:1 mapping of the project geometry); theother illustrating the seven basic steps in the rock engineeringdesign process [2]. All the aspects of Fig. 1 can be subject totechnical auditing, i.e. obtaining the site and rock massinformation from site investigation, use of the eight types ofmodelling methods (whether used singly, in combination or insequence), development of the initial design, constructionmonitoring and back analysis, leading to the final design.Similarly, the auditing is applied to the seven design stepsdiscussed in [2], these being the project purpose, key features ofthe site/rock mass/project, design approach strategy, choice ofmodelling method and appropriate code, initial design, integratedmodelling and feedback information and final design andverification/validation.

1.3. ‘Soft’ and ‘hard’ technical audits and the audit evaluation

Note that the technical auditing can be ‘soft’ or ‘hard’, with thecharacteristics as indicated in Fig. 2. Thus, for modelling, i.e. usingone or more of the eight main types of modelling methods shownin Fig. 1, either auditing type can be utilized, depending on thepurpose of the auditing. The soft audit can be used initially tosupport the development of the modelling programme. However,the hard audit is necessary for the total audit evaluation andability to state whether the modelling is adequate for the purpose.

The two demonstration auditing examples that follow are:(1) the procedure for auditing a site investigation measurement—in situ rock stress (soft audit) and (2) auditing the modelling forthe design of hydropower caverns at the Laxiwa site on the YellowRiver in China (semi-hard audit).

Whether a soft or hard audit is appropriate in any givensituation will depend on the requirement and according to thedescriptions in Fig. 2; both forms of audit are demonstrated in thefollowing sections. The limited audit illustrated for the seconddemonstration audit for the hydropower caverns in China istermed ‘semi-hard’ because it is not possible to include the fulldetail given the limitations on the paper length.

2. Demonstration example 1: the procedure for technicallyauditing a site investigation measurement—in situ rock stress(soft audit)

2.1. Background

The validity of the modelling and design of a rock engineeringproject will depend on the accuracy of the supporting information

Use of pre-existing

standard methods

Analytical methods,

stress-based

Basic numerical

methods, FEM, BEM, DEM,

hybrid

Extended numerical methods,

fully-coupled models

Precedent type analyses and modifications

Rock mass classification,RMR, Q, GSI

Database expert

systems, & other systems

approaches

Integrated systems

approaches, internet-based

Objective

Construction

SiteInvest-igation

Level 1 1:1 mapping

Level 2Not 1:1 mapping

Design based on forward analysis Design based on back analysis

Method A Method B Method C Method D

Fig. 1. Flowchart of rock mechanics modelling types used to support rock engineering design (from [2]).

'Soft' Audit 'Hard Audit' Audit Evaluation

Obtains the basic information for

establishing the essence of the

problem

Obtains the detailed

information on all the procedures

being used

Establishes whether the modelling is

adequate to meet the objectives

Ability to present what is

being done

Ability to state the details of what is being

done

Ability to state whether the modelling is

adequate for the purpose

Fig. 2. The ‘soft’ and ‘hard’ audits and the audit evaluation.

J.A. Hudson, X.-T. Feng / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 877–886878

(Hudson & Feng 2010)

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Un ejemplo de auditoría: 38 pregun-tas garantizan la calidad del modelo

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conducted within the eleven subject headings listed in Table 2.The individual auditing questions and the answers for the designapproach used in this case are listed in Table 3 with the elevensubject headings listed under four subject areas.

The audit subject areas in Table 2 are different from those inTable 1 because now we are dealing with a design problem, ratherthan site investigation measurements. However, the same logic isfollowed in Table 3 beginning with the objective, Subject Area 1,and following the key steps through to the conclusions, in thiscase the modelling adequacy, in Subject Area 4.

Subject Area 2 in Table 3 concerns the conceptualization of theprocesses being modelled, the specification of the modellingcontent, the modelling solution requirements and the modellingsolution technique. This is a crucial area because, as indicated bythe associated sub-questions in Table 3, there needs to bejustification of the exact modelling approach in terms ofcomprehensiveness of the physical variables represented andthe specification of all the conditions.

Subject Area 3 in Table 3 concerns the modelling techniqueitself: the numerical code used, the supporting data, sensitivityanalyses and presentation of the results. Because our rockmechanics and rock engineering knowledge is continuouslyincreasing and numerical models are continuously being improved,the auditing questions themselves may need to be adjusted tocapture the critical aspects in this subject area. The key issues areensuring that there is a check on the appropriateness of the model,that there have been checks on how the model is used, ensuringthat uncertainties are captured by sensitivity studies as far as isreasonable, and that the modelling results appear valid.

Subject Area 4 in Table 3 covers model adequacy moreexplicitly through the identification of actual or potential errorsand the possible need for corrective action.

In the current absence of any internationally agreed check onthe rock engineering design process (as occurs in other engineer-ing areas such as aircraft design), the auditing procedureillustrated in this demonstration example 2 shows how theanswers to the questions listed in Table 3 enable confirmationthat an adequate procedure is being followed or has beenfollowed. The auditing can be used during or after the modellingactivity. Needless to say, contemporaneous auditing is preferredso that any corrective action can be immediately implemented.

3.3. Comments on the Laxiwa case example

It was noted earlier that the technical auditing of this caseexample has been termed ‘semi-hard’ because it is has not beenpossible to include all the relevant details in the paper. However, theaudit, via the eleven subject areas and thirty-eight questions withtheir detailed answers in Table 3, illustrates the style of the hard auditand how the answers reveal the procedures used and their suitabilityin determining the cavern excavation sequence and appropriatesupport. To demonstrate this example as a truly hard audit wouldrequire illustration of the more penetrating investigation of thecorrectness of the supporting data, numerical analyses, etc.

Noting that, in this case, the manner in which the answers tothe auditing questions are given has been left open, to make theaudit more efficient the form of the answers should be specified inmore detail, e.g. whether a narrative or numerical answer isrequired to a particular question.

4. Conclusions

In order to ensure that the procedures used in rock mechanicsmodelling and rock engineering design are appropriate for the

Fig. 5. (a) 3D model for numerical analysis and (b) calculation model for excavation of the Laxiwa cavern group.

Table 2The 11 subject headings for the semi-hard technical audit of the rock mechanicsmodelling supporting the cavern excavation design for the Laxiwa project on theYellow River, China.

1. THE MODELLING OBJECTIVE The purpose of the modelling?2. CONCEPTUALIZATION OF THE PROCESSES BEING MODELLEDThe sub-system(s) being isolated for study. The physical processes involved.3. SPECIFICATION OF THE MODELLING CONTENTWhat are the physical variables, connecting relations, parameters, boundary

conditions, initial conditions, etc.4. MODELLING SOLUTION REQUIREMENTSWhat type of model output is required, given the stated modelling purpose?5. MODELLING SOLUTION TECHNIQUEHow is the required model output to be obtained?6. NUMERICAL CODE UTILIZEDWhich numerical code is to be used? How do we know that the code is

operating correctly?7. SUPPORTING MODEL DATA & DATA INPUT METHODWhat are the necessary supporting data? How are they to be obtained? How

are they to be input?8. MODEL SENSITIVITY ANALYSISHow does the model output depend on the model input in terms of whether a

sensitivity analysis is required?9. PRESENTATION OF MODELLING RESULTSIs it possible to demonstrate that the numerical code is operating correctly?

Are the modelling results clearly presented?10. SOURCES OF ERRORSWhat are the main sources of errors?11. MODELLING ADEQUACYDoes the modelling seem adequate for the purpose? Are there any problem

areas? Is any corrective action required?

J.A. Hudson, X.-T. Feng / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 877–886 881

(Hudson & Feng 2010)

conducted within the eleven subject headings listed in Table 2.The individual auditing questions and the answers for the designapproach used in this case are listed in Table 3 with the elevensubject headings listed under four subject areas.

The audit subject areas in Table 2 are different from those inTable 1 because now we are dealing with a design problem, ratherthan site investigation measurements. However, the same logic isfollowed in Table 3 beginning with the objective, Subject Area 1,and following the key steps through to the conclusions, in thiscase the modelling adequacy, in Subject Area 4.

Subject Area 2 in Table 3 concerns the conceptualization of theprocesses being modelled, the specification of the modellingcontent, the modelling solution requirements and the modellingsolution technique. This is a crucial area because, as indicated bythe associated sub-questions in Table 3, there needs to bejustification of the exact modelling approach in terms ofcomprehensiveness of the physical variables represented andthe specification of all the conditions.

Subject Area 3 in Table 3 concerns the modelling techniqueitself: the numerical code used, the supporting data, sensitivityanalyses and presentation of the results. Because our rockmechanics and rock engineering knowledge is continuouslyincreasing and numerical models are continuously being improved,the auditing questions themselves may need to be adjusted tocapture the critical aspects in this subject area. The key issues areensuring that there is a check on the appropriateness of the model,that there have been checks on how the model is used, ensuringthat uncertainties are captured by sensitivity studies as far as isreasonable, and that the modelling results appear valid.

Subject Area 4 in Table 3 covers model adequacy moreexplicitly through the identification of actual or potential errorsand the possible need for corrective action.

In the current absence of any internationally agreed check onthe rock engineering design process (as occurs in other engineer-ing areas such as aircraft design), the auditing procedureillustrated in this demonstration example 2 shows how theanswers to the questions listed in Table 3 enable confirmationthat an adequate procedure is being followed or has beenfollowed. The auditing can be used during or after the modellingactivity. Needless to say, contemporaneous auditing is preferredso that any corrective action can be immediately implemented.

3.3. Comments on the Laxiwa case example

It was noted earlier that the technical auditing of this caseexample has been termed ‘semi-hard’ because it is has not beenpossible to include all the relevant details in the paper. However, theaudit, via the eleven subject areas and thirty-eight questions withtheir detailed answers in Table 3, illustrates the style of the hard auditand how the answers reveal the procedures used and their suitabilityin determining the cavern excavation sequence and appropriatesupport. To demonstrate this example as a truly hard audit wouldrequire illustration of the more penetrating investigation of thecorrectness of the supporting data, numerical analyses, etc.

Noting that, in this case, the manner in which the answers tothe auditing questions are given has been left open, to make theaudit more efficient the form of the answers should be specified inmore detail, e.g. whether a narrative or numerical answer isrequired to a particular question.

4. Conclusions

In order to ensure that the procedures used in rock mechanicsmodelling and rock engineering design are appropriate for the

Fig. 5. (a) 3D model for numerical analysis and (b) calculation model for excavation of the Laxiwa cavern group.

Table 2The 11 subject headings for the semi-hard technical audit of the rock mechanicsmodelling supporting the cavern excavation design for the Laxiwa project on theYellow River, China.

1. THE MODELLING OBJECTIVE The purpose of the modelling?2. CONCEPTUALIZATION OF THE PROCESSES BEING MODELLEDThe sub-system(s) being isolated for study. The physical processes involved.3. SPECIFICATION OF THE MODELLING CONTENTWhat are the physical variables, connecting relations, parameters, boundary

conditions, initial conditions, etc.4. MODELLING SOLUTION REQUIREMENTSWhat type of model output is required, given the stated modelling purpose?5. MODELLING SOLUTION TECHNIQUEHow is the required model output to be obtained?6. NUMERICAL CODE UTILIZEDWhich numerical code is to be used? How do we know that the code is

operating correctly?7. SUPPORTING MODEL DATA & DATA INPUT METHODWhat are the necessary supporting data? How are they to be obtained? How

are they to be input?8. MODEL SENSITIVITY ANALYSISHow does the model output depend on the model input in terms of whether a

sensitivity analysis is required?9. PRESENTATION OF MODELLING RESULTSIs it possible to demonstrate that the numerical code is operating correctly?

Are the modelling results clearly presented?10. SOURCES OF ERRORSWhat are the main sources of errors?11. MODELLING ADEQUACYDoes the modelling seem adequate for the purpose? Are there any problem

areas? Is any corrective action required?

J.A. Hudson, X.-T. Feng / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 877–886 881

conducted within the eleven subject headings listed in Table 2.The individual auditing questions and the answers for the designapproach used in this case are listed in Table 3 with the elevensubject headings listed under four subject areas.

The audit subject areas in Table 2 are different from those inTable 1 because now we are dealing with a design problem, ratherthan site investigation measurements. However, the same logic isfollowed in Table 3 beginning with the objective, Subject Area 1,and following the key steps through to the conclusions, in thiscase the modelling adequacy, in Subject Area 4.

Subject Area 2 in Table 3 concerns the conceptualization of theprocesses being modelled, the specification of the modellingcontent, the modelling solution requirements and the modellingsolution technique. This is a crucial area because, as indicated bythe associated sub-questions in Table 3, there needs to bejustification of the exact modelling approach in terms ofcomprehensiveness of the physical variables represented andthe specification of all the conditions.

Subject Area 3 in Table 3 concerns the modelling techniqueitself: the numerical code used, the supporting data, sensitivityanalyses and presentation of the results. Because our rockmechanics and rock engineering knowledge is continuouslyincreasing and numerical models are continuously being improved,the auditing questions themselves may need to be adjusted tocapture the critical aspects in this subject area. The key issues areensuring that there is a check on the appropriateness of the model,that there have been checks on how the model is used, ensuringthat uncertainties are captured by sensitivity studies as far as isreasonable, and that the modelling results appear valid.

Subject Area 4 in Table 3 covers model adequacy moreexplicitly through the identification of actual or potential errorsand the possible need for corrective action.

In the current absence of any internationally agreed check onthe rock engineering design process (as occurs in other engineer-ing areas such as aircraft design), the auditing procedureillustrated in this demonstration example 2 shows how theanswers to the questions listed in Table 3 enable confirmationthat an adequate procedure is being followed or has beenfollowed. The auditing can be used during or after the modellingactivity. Needless to say, contemporaneous auditing is preferredso that any corrective action can be immediately implemented.

3.3. Comments on the Laxiwa case example

It was noted earlier that the technical auditing of this caseexample has been termed ‘semi-hard’ because it is has not beenpossible to include all the relevant details in the paper. However, theaudit, via the eleven subject areas and thirty-eight questions withtheir detailed answers in Table 3, illustrates the style of the hard auditand how the answers reveal the procedures used and their suitabilityin determining the cavern excavation sequence and appropriatesupport. To demonstrate this example as a truly hard audit wouldrequire illustration of the more penetrating investigation of thecorrectness of the supporting data, numerical analyses, etc.

Noting that, in this case, the manner in which the answers tothe auditing questions are given has been left open, to make theaudit more efficient the form of the answers should be specified inmore detail, e.g. whether a narrative or numerical answer isrequired to a particular question.

4. Conclusions

In order to ensure that the procedures used in rock mechanicsmodelling and rock engineering design are appropriate for the

Fig. 5. (a) 3D model for numerical analysis and (b) calculation model for excavation of the Laxiwa cavern group.

Table 2The 11 subject headings for the semi-hard technical audit of the rock mechanicsmodelling supporting the cavern excavation design for the Laxiwa project on theYellow River, China.

1. THE MODELLING OBJECTIVE The purpose of the modelling?2. CONCEPTUALIZATION OF THE PROCESSES BEING MODELLEDThe sub-system(s) being isolated for study. The physical processes involved.3. SPECIFICATION OF THE MODELLING CONTENTWhat are the physical variables, connecting relations, parameters, boundary

conditions, initial conditions, etc.4. MODELLING SOLUTION REQUIREMENTSWhat type of model output is required, given the stated modelling purpose?5. MODELLING SOLUTION TECHNIQUEHow is the required model output to be obtained?6. NUMERICAL CODE UTILIZEDWhich numerical code is to be used? How do we know that the code is

operating correctly?7. SUPPORTING MODEL DATA & DATA INPUT METHODWhat are the necessary supporting data? How are they to be obtained? How

are they to be input?8. MODEL SENSITIVITY ANALYSISHow does the model output depend on the model input in terms of whether a

sensitivity analysis is required?9. PRESENTATION OF MODELLING RESULTSIs it possible to demonstrate that the numerical code is operating correctly?

Are the modelling results clearly presented?10. SOURCES OF ERRORSWhat are the main sources of errors?11. MODELLING ADEQUACYDoes the modelling seem adequate for the purpose? Are there any problem

areas? Is any corrective action required?

J.A. Hudson, X.-T. Feng / International Journal of Rock Mechanics & Mining Sciences 47 (2010) 877–886 881

Un ejemplo de auditoría: 38 pregun-tas garantizan la calidad del modelo

• ¿Se ha establecido con claridad el propósito del modelo? • ¿Cómo se sabrá cuando la modelación esté completa?• ¿Qué sistemas de macizo rocoso fueron considerados?• ¿Qué procesos físicos principales fueron considerados?• ¿Cuál es la variable independiente principal?• ¿Cómo se perturba el sistema para activar mecanismos?• Lista de las variables físicas• Lista de los acoplamientos termo-hidro-mecánicos• ¿El modelo es 1D, 2D, 3D o alguna combinación?• ¿Se modela un continuo o un discontino?• Especificación de las condiciones de borde6

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Un ejemplo de auditoría: 38 pregun-tas garantizan la calidad del modelo

• Especificación de las condiciones iniciales• ¿Cómo se establece la condición final?• ¿Cuál es la salida requerida del modelo?• ¿Cumplen los resultados con el objetivo del modelo?• ¿Cómo se obtiene el resultado? ¿Un código, una corrida?

¿O un conjunto de experimentos numéricos?• ¿Hay controles de calidad? Control de datos de entrada,

validación con soluciones conocidas, corridas duplicadas?• ¿Qué código numérico se emplea?• ¿Porqué se emplea ese código?• ¿Dónde se originó el código?

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Un ejemplo de auditoría: 38 pregun-tas garantizan la calidad del modelo

• ¿Cómo se validó el código?• Lista de tipo y justificación de condiciones de borde• Lista de datos de entrada incluyendo fuente y justificación• ¿Hubo que ajustar datos antes de su entrada al código?• ¿Cómo dependen los resultados de los valores de los

parámetros de entrada?• ¿Se ha realizado un análisis de sensibilidad? ¿Que tipo?• ¿Cómo resume resultados del análisis de sensibilidad?• ¿Se puede demostrar que el programa funciona bien?• ¿Se puede demostrar que los datos son hipótesis

razonables para un macizo rocoso?8

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Un ejemplo de auditoría: 38 pregun-tas garantizan la calidad del modelo

• ¿Cómo se presentan los resultados del modelo?• ¿Se ajusta la presentación de resultados con el objetivo?• ¿Ha corregido algún error hasta ahora?• Lista de los errores potencialmente significativos• ¿Puede alguno de esos errores invalidar el resultado,

concepto y conclusiones?• Las preguntas anteriores ¿indican que en principio el

modelo es adecuado para su propósito?• Si no, liste las áreas problemáticas• ¿Qué acción correctiva se requiere?• ¿Debe repetirse esta auditoría luego de correcciones?

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