<p>In studies related to crustal stress, the spatial distribution of three-dimensional stress is often described by the azimuth distribution of the maximum and minimum horizontal principal stresses. In this paper, we investigated whether the azimuth of the horizontal principal stress can indicate the azimuth of the three-dimensional principal stress. The results show that the azimuth of the horizontal principal stress does not always accurately indicate the azimuth of the three-dimensional principal stress, nor do the azimuths of the maximum and minimum horizontal principal stresses always correspond to the compressive and tensile axes of the three-dimensional stress. The azimuth of the maximum horizontal principal stress may be close to the azimuth of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="24_2025_3704_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${\sigma }_{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="24_2025_3704_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${\sigma }_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> axis, while the azimuth of the minimum horizontal principal stress may be close to the azimuth of the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="24_2025_3704_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${\sigma }_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="24_2025_3704_Article_IEq4.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${\sigma }_{3}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> axis. The correspondence between the azimuths of the maximum or minimum horizontal principal stress axis and the three-dimensional principal stress axis, as well as the azimuth angle between them, is closely related to the inclination of the three-dimensional principal stress axis and the relative magnitudes of the three principal stresses (shape ratio). The results of this study imply that it is not feasible to use the azimuth of the horizontal principal stress to represent the azimuth of the three-dimensional principal stress without prior knowledge of the three-dimensional stress.</p>

Can the Azimuth of the Horizontal Principal Stress Indicate the Azimuth of the Three-Dimensional Principal Stress?

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2025年5月12日

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Zhenyue Li,
Yongge Wan,
Ruifeng Liu,
Xiangyun Guo

摘要

In studies related to crustal stress, the spatial distribution of three-dimensional stress is often described by the azimuth distribution of the maximum and minimum horizontal principal stresses. In this paper, we investigated whether the azimuth of the horizontal principal stress can indicate the azimuth of the three-dimensional principal stress. The results show that the azimuth of the horizontal principal stress does not always accurately indicate the azimuth of the three-dimensional principal stress, nor do the azimuths of the maximum and minimum horizontal principal stresses always correspond to the compressive and tensile axes of the three-dimensional stress. The azimuth of the maximum horizontal principal stress may be close to the azimuth of the ${\sigma }_{1}$ $σ_{1}$ or ${\sigma }_{2}$ $σ_{2}$ axis, while the azimuth of the minimum horizontal principal stress may be close to the azimuth of the ${\sigma }_{2}$ $σ_{2}$ or ${\sigma }_{3}$ $σ_{3}$ axis. The correspondence between the azimuths of the maximum or minimum horizontal principal stress axis and the three-dimensional principal stress axis, as well as the azimuth angle between them, is closely related to the inclination of the three-dimensional principal stress axis and the relative magnitudes of the three principal stresses (shape ratio). The results of this study imply that it is not feasible to use the azimuth of the horizontal principal stress to represent the azimuth of the three-dimensional principal stress without prior knowledge of the three-dimensional stress.