A STUDY ON RELATIONSHIP BETWEEN EROSION OF DEBRIS FLOWS AND CRITICAL RAIN QUANTITY*

Wang Yuyi¹, Li Changzhi² and Zhou Renyuan¹

Chengdu Institute of Mountain Hazards and Environment,

Chinese Academy of Sciences and Ministry of Water Conservancy,

Chengdu, China, 610041, TEL: 028-5401148

State Key Hydraulics Laboratory of High Speed Flow,

Sichuan University, Chengdu, China, 610065. TEL: 028-5401148

Abstract: Own weight and dynamic condition of breccia soil control the erosion and development of debris flows. The experiment and analysis in this paper indicated the effect of principal component of the rain quantity to occurrence of debris flow. It also probed quantitatively into the relationship among the critical rain quantity and slope, specific weight of stoned soil, by observational experiment of stress properties in saturated soil and rain permeation.

Keywords: debris flow, erosion and critical rain quantity

1    INTRODUCTION

Those watershed with conditions of abundant loose soil, considerable precipitous gradient and plentiful and intensive rainfall are remarkably propitious for the occurrence of debris flow. In fact the watershed’s landform and the rain intensity are the predominant factors for the scale and strength of debris flow in a concrete region. However, it is up to now still difficult to present the two factors quantitatively for the prediction on debris flow. According to the data of debris flow in the Jiangjia Gully basin, this paper studied the principal component of rain intensity of debris in the primary ravine, the relationships among the total rain quantity, slope and soil specific weight. And it also brought quantitatively the mechanism and characteristics of the erosion of saturated soil to light, which is important for the forecast, predication and control of debris flow in mountain region.

2    STRESS CHARACTERISTICS OF SATUATED SOIL EROSION

There are two stress states called pre-limit stress and limit stress in soil of debris flow on a certain slope. The latter is a critical state in which only a little force added would lead to the movement of the breccia soil along a sliding face. In case of ultimate stress, normal stress is the max stress on n plane with function

where, F(б_n ) is the normal stress. The natural rest angle of dried breccia soil approaches or a little more than the internal friction angle, that is . The experimental data of breccia soil with various water content in the Jiangjia Gully presented that, the natural rest angle increased quickly with the accretion of water content lower than 8% (Fig.1, CD line) and reduced slowly with the decrease of water content higher than 8%. The critical water content therefore was 8% in the experiment. The statistical data for the slopes in this basin showed that the slopes with gradient over 25 degrees covered 50% of the total. Furthermore, the natural angle on slope with 25 degrees approached considerably to inter fraction angle, the breccia soil therefore is just in the state of limit balance. Hence, the slopes were remarkably unstable and would move down once a rain with certain intensity occurred.

It is usually regarded as true in the past study on reological characteristics of debris flow that, the anti-stress intensity decreases with the increase of water content. However, our experiment indicated that an abrupt critical value of anti-stress intensity (water content 11.5%) exited with the change of water content. Moreover, the critical angle of internal friction with the variation of water content is also 11.5%. And the water content with max anti-stress intensity of breccia soil is called critical water content, or saturated water content in this paper. Obviously, anti-stress intensity increased with the accretion of water content less than 11.5%(Fig.2 Curve “abc”), and decreased sharply with the increase of water content over than 11.5%(Fig.2 Curve “cd”). The experimental result indicated accurately the stress characteristics of situated soil erosion of debris flow.

3    OBSERVATION AND ANALYSIS ON THE CRITICAL RAIN QUANTITY FOR 
      SOIL EROSION OF DEBRIS FLOW

Rain is the initiative and decisive factor of the occurrence of debris flow in the three key factors for the occurrence of debris flow. Debris flow in many places, such as the Jiangjia Gully, Yunnan province (with high frequency), the Luwang Gully, Yaan, Sichuan province and Yizilida Gully in Cheng-Kun Railway (both with low frequency), were initiated by rainstorm of various intensities. Both loose soils and main gradient in the same gully of a watershed is considered as stable in a certain long time. However, the time of occurrence and the scale of hazard of a debris flow are closely relative to the rain condition, which varies temporally and spatially in the watershed. In this study, to predicate what role the rain plays in the erosion of debris flow with high accuracy, different rain data of various places were adopted when analyzed the relationship between the rain condition and the erosion of debris flow. Based on the observation of rain index for the ravine erosion, three group data, initiative rain quantity (C₁), rain intensity of occurrence (C₂) and ante rainfall  (C₃) were used to explore the rain dynamic index by method of principal component analysis.

The original data were the rain intensity index of debris flow erosion in the primary ravine of the Jiangjia Gully (Tab.1). Tab.2 was the eigenvalue, percentage and load of the principal component analysis on the above 3 variables. And Tab.2 presented that the first and the second principal components provided 99.8% information of the rain index of debris flow erosion in primary ravine, C₁ and C₃ were excellently related to first principal component, C₂ to the second. Therefore, it can be determined definitely that in the primary ravine of debris flow erosion, the initiative rain quantity (C₁) and the ante rainfall (C₃) were the first principal component of rain index, and the intensity of occurrence (C₂) was the second one.

4    EXPERIMENT AND ANALYSIS ON RELATIONSHIP BETWEEN INITIATIVE
       RAIN QUANTITY AND GRADIENT

In this experiment, breccia soils with water content of 5%, 7%, 11.5%, 12.5% were piled orderly into sloping field with angle (β), and rain intensity of 6mm per minute were provided for the dynamic of debris flow. And the total rain was observed and recorded from the very beginning both to the slope flow and to the collapse. Fig.3 gives the experimental result.

Breccia soils suffered rain since experiment began. And small soil particles got down along the permeating water and changed their positions, the gradient of the slope therefore became smaller and smaller. At the same time, the coarse particles began to roll and involve into slope flow due to the increase of rain. And curve (1) in Fig.3 presented the relationship between total rain from the very beginning to the evolution of slope flow and ante water content. It indicated that a considerable consistency between anti-stress-intensity variation and this curve. The curve changed very slowly under lower limit water content while fell down quickly once water content over 11.5%, and only a little rain could bring to surface flow. And the correlation coefficient y and t-text were –0.994 and remarkable notability (t_0.01)*, respectively.

                   (1)

                   (2)

Coarse particles accumulated at the foot of slopes (point of slope stress concentrated) due to the slope flow ^[2] and collapse from slope flow came into being when flow in the gully rushed the piled breccia soil there away. The correlating curve between the rain needed by occurrence of collapse and ante water content of soil showed that in the key moment of debris flow erosion, the needed rain of collapse was obviously influenced by the ante water content, which was similar to the concerning studied conclusions ^[7]. Line segments in Fig.3 had different slopes, the trend of segment CD’s decrease was 4.7 times that of segment AB, which indicated that rain needed by collapse lessened remarkably when water content of debris was over than 11.5%.

                       (3)

                       (4)

                  (5)

Line regress coefficients ‘a’ and ‘b’ in Eq. (3), (4) and (5) corresponded to the slopes (β) of experimented breccia soil with various ante water contents.  coefficients ‘a’ and ‘b’ of segment CD in Fig.3 had the following relationship to gradient (β), with correlation coefficients –0.738 and –0.839, respectively.

Substituting Eq. (6) into Eq. (3), (4) and (5) gives the relationship among needed rain of debris flow’ s initiation and specific weight ( ), gradient of breccia soil slope (β):

where,ρ_H ,ρ₀ are specific weights of soil and water. And Eq. (7) first brought to light the relationship among required rain quantity of debris flow’ s initiation and specific weight, gradient of breccia soil slope, and plays an important role in searching for hazards mitigation of debris flow erosion ^[9] .

5    ANALYSIS ON MECHANISM OF BRECCIA SOIL STRESS EROSION ON SLOPE

5.1    Break of stress balance due to gravity

The stability of soil on a slope is controlled by its gravity and anti-stress intensity besides the tectonic stress. Assuming on a slope with gradient of α, and gravity of G, tangential component of F and normal component (δ_n), the breccia soil there possesses certain anti-sliding force τ, namely, the anti-stress intensity (See Fig.4).

Substituting into  gives

                                   (8)

In case of limit balance, , so

                             (9)

If coherency , then the limit balance is:

 or                               (10)

Therefore, gravity erosion will happen to the loose breccia soil on a slope when the gradient of the slope is over than the internal friction angle.

5.2    Permeating liquefaction and vibration of breccia soil due to initiation of rainstorm

Erosion process of liquefaction: effective stress (σ) is the vertical stress supported by soil framework, porous stress (P_we) is the stress supported by porous water, and the total stress(σ_n) is the sum of the former two, that is:

                                (11)

Some gravity free water is left in soil when water content is over than situated. When rainstorm happened, the obstructed water and incompressibility of water and gases (P_we) will lead to decrease of pore degree, then to the increase of pressure. Moreover, the loose and big particles begin to be suspended due to water infiltration, which changes the framework pressure into surplus pore pressure. The effective stress (σ) perpendicular to the shear plane begins to decrease due to the increase of the pore pressure, and approaches to zero while

At the same time, the anti-stress intensity of soil is closing to the minimum, which lead to the erosion of gravity:

                           (12)

In addition to this, the water cover comes into being because surface flow cannot infiltrate in time during rainstorm ^[8]. And at the same time, the pore pressure increases abruptly because the water in pores under the cover is not capable of dissipation, which results in the touching liquefaction of breccia soil. The following formula presents the pore water pressure under water cover:

                    (13)

Where, h₂ is the depth of soil under water cover, h₁ the depth of water up the water cover (See Fig. 4). Substituting Eq. (13) into Eq. (12) gives

            (14)

As , substituting Eq. (14) with assumption of , into Eq. (9) gives the critical flow slope of debris flow (tanα＇) as follow

             (15)

According to the data of observation and analysis on the Jiangjia Gully, the soil within the development area of debris flow was remarkably loose, with pore degree high enough 62~50%. And debris flow there had a vibration acceleration of 2~3 m/s^2[5,10], that was, earthquake of 7 degree or so. Therefore, only small scale of vibration and liquefaction intensity would result in occurrence of collapse. During the collapse before debris flow, the pore pressure caused by the abrupt decrease of pores due to ante turbulence and vibration of a periodicity could not dissipate while the new pressure overlap in the next periodicity. Just like this, surplus pore pressures accumulated more and more, the depth of h₂ increased continually till the side pressure among particles was high enough to withstand the liquefaction ^[10]. The forepart debris flow undermined the slope feet of stress gathering points, and aggravated the larger scale of collapse, which leaded to the large scale and continuous debris flow lasting enough to several to tens hours.

References

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[3]  Wu Jishan, et al. Debris Flow Observation and Study in the Jiangjia Gully, Yunnan. Beijing: Science press, 1990.18~200.

[4]  Fang Xiangke, Jiang Dingsheng, et al. Analysis on anti-shear intensity of lower original soil in the Loess plateau. Journal of Soil Erosion and Water and Soil Conservation, 1997,3(4): 69~74.

[5]  Wang Yuyi, Biyu Yan. Snearing Stress, Strain and Debris Flow. Inter. Sym. Interprevent, 1992.307~317.

[6]  Zhang Chao, Yang Bingeng. Fundamentals of Quantitative Geography. Beijing: High Education Press, 1991.309~317.

[7]  Zhang Liping, Tang Keli. Experiments of Artificial Simulation Rainfall and Setting water Initiating Accumulated Material in Debris Flow Origin Place, Journal of Mountain Science, 1999,17(1:45).

[8]  Wang Yuyi, Zhou Renyuan, et al. Study on Relationship between Initiation and Permeation System of Debris Flow. Journal of Soil Erosion and Water and Soil Conservancy,1997,3(4):76.

[9]  Sassa K, Watanabe H. Possible Mechanism of the Debris Flow. Landslide News, 1997(1): 9~10.

[10] Zhang Zhuoyuan, et al. Principle of Engineering Geology Analysis. Beijing: Geology Press, 1989. 57~133.

     Table  1  The initiative rain quantity of debris flow at primary ravine of the Jiangjia Gully basin

    Table  2  Results of Principal Component Analysis (PCA)

                      Fig.1  Relationship of natural angle of               Fig.2  Relationship between        
                                repose and angle of internal friction                anti-stressintensity and water
                                with water content                                            content

Fig.3  Relationship between needed      Fig.4  Sketch map of gravity and
                      Rain and water content                        water dynamics on a slope