裂隙水力傳導係數異向性與規模效應影響因素探討

Abstract

岩體中存在許多不連續面，如層理、葉理、節理等，工程上常以節理或裂隙代稱之。裂隙的力學與水力特性常遜於完整岩石，不僅造成岩體工程特性呈現異質性與異向性，並且隨描述尺度而變化。裂隙岩體也常被應用於描述包含許多裂隙、工程特性深受影響的岩體。 裂隙除了以其空間分布位置影響岩體的工程特性外，裂隙面本身的力學、水力特性也是重要的影響因素。現今多以流體立方律透過隙寬估計裂隙之水力傳導特性，然而在未考慮裂隙變異性之情況下，結果往往呈現數量級的差異，與裂隙面滲流異向性的巨觀現象水力存在矛盾。 另一項難以量化估計的則是裂隙力學與水力特性之規模效應，即各項描述參數會隨者裂隙的尺度而發生變化。各種調查方法皆有其適用之尺度並存在一定的侷限性。儘管已有許多經驗公式提供不同尺度之間力學描述參數的轉換，然不僅適用範圍受到限制，估計所得失準、甚至不合理的現象亦時有所聞。 本研究以裂隙的水力傳導係數為對象，藉隙寬之粗糙幾何分布探討其異向性與規模效應。藉由定水頭滲流試驗求得裂隙面之完整水力傳導係數張量，並以不同正向荷載滲流試驗，以考慮粗糙度之修改流體立方律建立裂隙面粗糙幾何與導水係數之關聯。並以全張量以及簡化非對角項之簡化張量進行數值模擬，並與試驗結果進行比較。並最後以反覆鏡射裂隙自身幾何以全張量進行滲流模擬，探討規模效應對於裂隙水力傳導特性之影響。 試驗結果顯示以橫向及縱向流向搭配量測垂直流向之水頭差即可求得裂隙面之完整水力傳導係數張量。並以不同正向荷載滲流試驗數據回歸得初始內寬及水力參數進行全張量及簡化張量滲流模擬。結果展示了滲流模擬與試驗數據呈現相同趨勢，且全張量滲流模擬之流量大於簡化張量模擬之流量，顯示非對角項對於垂直流向水頭之貢獻。最後以全張量進行擴尺分析，流量隨著裂隙面尺度擴大並無明顯變化，且水力傳導係數之非對角項受垂直流向水頭差影響甚大。

In rock masses, numerous discontinuities such as bedding planes, foliation, and joints are commonly present. When the rock mass contains multiple fractures, it is generally referred to as a fractured rock mass. The mechanical and hydraulic properties of fractures are often inferior to those of intact rock, resulting in the engineering behavior of fractured rock masses being both heterogeneous and anisotropic, and strongly dependent on the scale of observation.

Apart from the spatial distribution of fractures, the mechanical and hydraulic characteristics of fracture surfaces themselves play a crucial role in influencing the behavior of rock masses. Currently, the hydraulic transmissivity of fractures is often estimated using the cubic law based on fracture aperture. However, without accounting for the variability of fracture surfaces, the predicted results often deviate by several orders of magnitude and conflict with the macroscale hydraulic anisotropy observed in fractured media.

Another major challenge lies in quantifying the scale effect of fracture properties, as both mechanical and hydraulic parameters tend to vary with the size of the fracture. Various investigation methods are applicable only to specific scales and have inherent limitations. Although many empirical correlations have been proposed to bridge the gap between different scales, their applicability is often restricted, and the estimated parameters may be inaccurate or even unreasonable.

This study focuses on the hydraulic conductivity of rock fractures, investigating its anisotropy and scale effects based on the rough geometric distribution of fracture aperture. Constant-head seepage tests were conducted to obtain the full hydraulic conductivity tensor of fracture surfaces. Seepage tests under various normal stresses were also performed to establish a modified cubic law incorporating roughness effects, thereby linking fracture surface geometry to transmissivity. Numerical simulations were carried out using both the full tensor and a simplified tensor neglecting off-diagonal terms, and the results were compared with experimental observations. Finally, the scale effect on fracture hydraulic properties was explored by repeatedly applying mirror symmetry to the fracture geometry and conducting seepage simulations using the full tensor. Experimental results indicate that the full hydraulic conductivity tensor of a fracture surface can be determined by applying horizontal and vertical flow directions while measuring the head difference in the direction perpendicular to flow. Regression analysis of seepage test data under various normal stresses was used to estimate the initial mechanical aperture and hydraulic parameters, which were then applied in seepage simulations using both the full tensor and a simplified tensor omitting off-diagonal terms. The simulation results exhibited trends consistent with experimental observations, and the flow rates obtained from full tensor simulations were higher than those from simplified tensor simulations, highlighting the contribution of off-diagonal terms to the head gradient in the transverse flow direction. Finally, scale-dependent analysis using the full tensor revealed that flow rate showed no significant variation with increasing fracture size, while the off-diagonal components of the hydraulic conductivity tensor were found to be highly sensitive to head differences in the perpendicular direction.