J. Cent. South Univ. Technol. (2010) 17: 1383-1388

DOI: 10.1007/s11771-010-0646-6

Mechanism of action of cracks water on rock landslide in rainfall

WU Yong(吴永)^{1, 2}, HE Si-ming(何思明)^{1, 2}, LI Xin-po(李新坡)^{1, 2}

1. Key Laboratory of Mountain Hazards and Surface Process, Chinese Academy of Sciences,

Chengdu 610041, China;

2. Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2010

Abstract: In worldwide, the most common triggering factor of rock landslides is extended and intense rainfall. However, different from the soil slope failure caused by softening action of infiltration rainwater, the mechanism of rock landslide in rainfall is not clear. From the view of fracture mechanics, the propagation of cracks on rock slope and the development of sliding surface were researched. Then based on hydraulics formulas and using Sweden arc method, the influence of crack water on stability of rock slope was quantitatively studied. Finally, an example was given to check the theoretical approach. The result shows that the development of sliding surface of rock slope is mainly caused by crack propagation under hydrostatic pressure when the stress intensity factor K_I at crack tip is bigger than the toughness index of rock fractures K_IC, and the failure of slope is the result of hydraulic action of crack water and the softening of materials on sliding surface when the depth of crack water is bigger than a minimum value h_min.

Key words: crack water; fracture mechanics; propagation; hydraulics; Sweden arc method; rock landslide

1 Introduction

Rock landslide is a dynamic evolution process in which rock slope slides down rapidly along the sliding surface. As a kind of prevailing disaster in mountains, they generally cause serious damage and great fatalities because it usually occurs unexpectedly and move rapidly. Although many factors such as earthquake and engineering excavation can induce the rock slope failure, the most common and important one is also the rainfall water according to many investigations and engineering practices [1-2].

Many studies [3-6] were undertaken by other researchers to investigate the effect of rainfall on slope stability. TERZAGHI [7] firstly presented that rainfall-induced landslides are caused by increased pore pressures and seepage forces during periods of intense rainfall. BRAND [8-9] recognized that it is the increased pore pressure that decreases the effective stress in the soil, thus reducing the soil shear strength, and eventually resulting in slope failure. Similarly, recent works [10-12] illustrated the role of factors such as rainfall intensity, rainfall pattern and soil strength on slope stability.

However, the main focus of previous studies was placed on the effects of rainfall infiltration on soil slope stability. Very limited work can be found on the   failure mechanism of rock slope in rainfall with low conductivity, such as the way how the water flows into slope and what role of water plays are not clear,  which affects the stability of rock slope greatly.

In fact, the rock slope failure due to rainfall is a complex geological problem [13]. It involves the interaction of a number of hydraulic and geological factors. As is shown in Fig.1, rock masses usually contain a number of cracks that may become potential sliding surfaces when they propagate to connect each other or weak interlayer. While the sliding surface forms, the rainwater flows in and results in the failure of slope eventually. During this process, the decrease of mechanical properties of weak interlayer and hydraulic action generated on the new sliding surface have a major influence on the slope stability.

Fig.1 Cracks and sliding surface of rock slop

Here from the view of fracture mechanics, the mechanism of cracks propagation and sliding surface development were studied clearly firstly. Then based on hydraulics formulas, the forced state of sliding surface including the action of crack water was analyzed.  Finally, according to the Sweden arc method, the whole stability of rock slope with the influence of crack water was quantitatively studied with an example, which illustrates the failure mechanism of rock slope in rainfall eventually.

2 Mechanism of propagation of cracks on rock slope under intensive rainfall

As a kind of geologic body, rock slopes have been existing in nature for millions of years, and many microstructures such as joints and cracks have formed in weathering. Among these different fractures, some are closed and cannot drain rainfall water out timely. Thus, the high hydrostatic pressure generates, which induces the failure of cracks eventually.

Taking crack mouth as the origin, and building x axis along the cracks, the propagation model of water-filled rock crack under hydrostatic pressure can be simplified as a semi-infinite plane question (Fig.2). According to the principles of fracture mechanics [14], when an arbitrary distributed “the local stress” σ(x) acts on the crack surface, the stress intensity factor on its tip is:

                                (1)

where K_I is the stress intensity factor on crack tip; a is shape factor; h is crack depth; and σ is the maximum stress acting on crack surface and can be expressed as:

                            (2)

Here the maximum stress σ acting on crack face is:

                                    (3)

where γ_w is the bulk density of water.

Fig.2 Calculation model of hydraulic fracture

                              (4)

where a=0.682 8 [15].

Obviously, K_I grows continually with the increment of crack water and results in the propagation of crack while it satisfies:

K_I＞K_IC                                     (5)

where K_IC is the toughness index of rock fractures.

For the cracks filled with water, the value of K_I just depends on their depth. Hence, to summary up the above equations, a critical depth h_c can be given to determine whether the water-filled cracks can propagate:

                             (6)

When the crack is full of water and its depth is bigger than h_c, the crack starts to extend. Thus, the criterion on crack propagation can be expressed as:

h≥h_c                                       (7)

Specially note that the critical depth is a very useful parameter in hazard control engineering. Because only those cracks whose depth is bigger than h_c can propagate and cause the failure of slope in intense rainfall, it is easy to ascertain dangerous rock slope by contrasting the crack depth with h_c.

3 Hydraulic action of crack water

When the depth satisfies Eq.(7), the crack will start to propagate and keep extending until it connects with the weak interlayer in intense rainfall. Thus, a new sliding surface, as a seepage channel, is formed. Then, with the flowing of rainwater, the sliding surface is softened and the slope static balance is broken by hydraulic action, which results in the failure of rock slope eventually.

It is often assumed that the failure of slope is confined to circular planes. As shown in Fig.3, a typical rock mass whose sliding surface is an arc with radius of R can be divided into N slices equally according to Sweden arc method, where θ and l are respectively the central angle and base length of each slice, i is the ordinal of slice and G_i is the mass of slice i.

3.1 Hydrostatic pressure on sliding surface

Fig.4 shows the action of crack water seepage on bottom of slice i. Assume the seepage free head at points

Fig.3 Analysis model based on Sweden arc method

Fig.4 Action of seepage of crack water on sliding surface

, 0≤x≤l         (9)

where β_i is the inclination of the bottom of slice i and can be obtained by the following equation:

                       (10)

where δ is the inclination of OM in Fig.3; and point M is the tip of crack on trailing edge of slope.

Integrating x in Eq.(9), the equivalent concentrated force of hydrostatic pressure at bottom of slice i is obtained as:

                  (11)

Thus, the average compressive stress vertical to sliding surface caused by seepage can be written as:

              (12)

3.2 Hydrodynamic pressure on sliding surface

Besides, a kind of dynamic water pressure also generates when seepage flows through the continuous fillings on sliding surface, which decreases the slope stability directly by dragging slope body downward [17-18] constantly.

According to the continuum theory [19], the dynamic pressure in seepage region is:

                                  (13)

where f_s and J are the dynamic water pressure vector and hydraulic gradient vector, respectively.

By integrating to Eq.(13), the concentrated force of seepage dynamic pressure acting on fillings of slice i is given:

               (14)

where w and n are the width and porosity of fillings on sliding surface, respectively; and J_i is the hydraulic gradient can be expressed as:

                        (15)

where h_i-1+lsin β_i-h_i is the head loss of seepage on sliding surface of slice i.

According to the principle of force balance, the drag force of seepage acting on bottom of slice i can be determined by:

             (16)

Specially note that the seepage drag force t_w does not always exist unless the seepage can keep flowing when the water depth is bigger enough. According to the continuum theory, the minimum water depth that allows seepage to occur can be expressed as

                    (17)

where η is the unit length head loss of seepage.

3.3 Force analysis on sliding surface of slice i

As shown in Fig.5, the stability of slice i is determined by inter-slice forces P_i and P_i+1, mass G_i, resultant normal force N_i and shear resistance T_i. While with the flowing of crack water in, it begins to decrease for hydraulic action mentioned above.

Due to the action of hydrostatic pressure σ_w in Eq.(12), the average normal stress on sliding surface of slice i decreases to:

                       (18)

Fig.5 Forces acting on typical slice

Hence, the average shear strength τ_f can be given by the Mohr-Coulomb failure criterion as follows:

  (19)

where φ is the internal friction angle of sliding surface; and c is the cohesion of fillings. Specially, when c=0 there is no fillings on sliding surface.

Also because the action of seepage dynamic pressure in Eq.(16), sliding force t_d has to be modified  as:

         (20)

4 Stability analysis of slope under rainfall

Sum up all arguments, the sliding moment M_d of sliding mass can be expressed as:

        (21)

And anti-sliding moment is:

 (22)

where h₀ is the crack water depth on trailing edge, and h₀=h when the crack is full of water; h_N is the head of outcrop water in the slope front part. Specially note that with the increment of h₀, h_N also becomes large [20].

Combining Eq.(22) with Eq.(23), the stability factor of rock slope is defined as:

                                   (23)

Note that when γ_w=0, k is slope stability factor without influence of crack water.

5 Example and analysis

Here take a typical high cut slope in Hanyuan section of Sichuan-Tibet highway as an example. The slope is composed of cretaceous sandstones and a dominant crack with depth of 16 m has developed on trailing edge during long term weathering (Fig.6). According to field investigation, the crack which influences the slope stability mostly has extended to weak interlayer. The bulk density of slope material is 24.75 kN/m³ and the potential sliding surface is an arc with radius R of 20 m (see Table 1).

Fig.7 shows the relationship between stress intensity factor K_I and depth of crack water h₀ calculated by  Eq.(4). The result reveals that K_I gets larger quickly with the increase of h₀, and reaches the value of fractures toughness index (K_IC=0.442 MPa·m^1/2) when h₀ increases to a critical depth h_c=11 m. Then, the propagation occurs.

Fig.6 Stability analysis sketch of high-cut slope

Table 1 Related parameter of rock and crack

Fig.7 Relationship between stress intensity factor K_I and depth of crack water h₀

While the crack extends to the weak interlayer, the sliding surface forms and becomes the channel of seepage. According to Eq.(17), to ensure the crack water to flow into the fillings on sliding surface, the minimum depth of crack water must be bigger than h_min=3.31 m. Obviously, the depth of crack given in example (h=16 m) satisfies the condition in intense rainfall.

In order to study the influence of crack water depth h₀ on slope stability, the values of k with different h₀ values were calculated according to Eq.(23). As shown in Fig.8, when h₀＜h_min, there is no seepage flow on sliding surface and the whole slope stability is only determined by hydrostatic pressure of crack water. Hence, with the increment of h₀, the stability factor k decreases nearly linear from initial value of 1.74 to 1.32.

Fig.8 Influence of depth of crack water on slope stability without action of seepage (h₀＜3.31 m, c=2.8 MPa, φ=34?)

On the contrary, with the flowing of crack water into weak interlayer when h₀＞3.31, the seepage hydrodynamic pressure generates, and the mechanical properties of sliding surface decrease gradually, which all are bad for slope stability.

Fig.9 shows the variation of stability factor with the mechanical properties when h₀=h_min. The result illustrates k decreases continually from 1.32 to 0.90 with the change of (c, φ) from initial value (2.8 MPa, 34?) to saturation value (2.0 MPa, 24?). Obviously, even without consideration of hydrodynamic pressure, the crack water also plays an important role in slope stability when seepage occurs in sliding surface.

As shown in Fig.10, the slope stability will keep decreasing with the increment of water in crack when  h₀＞h_min. Theoretically, the whole stability factor would reach its minimum k=0.54 when the crack is full of water.

Fig.9 Influence of mechanical properties (c, φ) of sliding surface on slope stability (h₀=3.31m)

Fig.10 Influence of depth of crack water on slope stability when seepage occurs (h₀＞3.31 m, c =2 MPa, φ =24°)

6 Conclusions

(1) The main reason for the failure of rock slopes with deep cracks in rainfall is the hydraulic action and softening action of crack water flowing in sliding surface.

(2) With the increase of water depth h₀, the stress intensity factor K_I grows quickly until its peak value of K_IC.

(3) The critical depth is an important parameter which determines whether the crack filled with water can propagate. Only the cracks whose depth is bigger than h_c can extend and cause the slope failure in intense rainfall.

(4) In order to ensure the seepage to flow in the fillings on sliding surface, the minimum depth of crack water must be bigger than h_min.

(5) Compared with the change of mechanical properties (c and φ) on sliding surface, the influence of seepage dynamic pressure on slope stability is smaller.

(6) The effect of crack water on slope stability can be expressed as: (a) propagating cracks and form sliding surface by hydrostatic pressure; (b) softening sliding surface by seepage flow and breaking force balance for seepage dynamic pressure.

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(Edited by YANG You-ping)

Corresponding author: WU Yong, PhD; Tel: +86-15928074439; E-mail: wyhongyu@163.com