Ecological Engineering

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1 Ecological Engineering 36 (2010) Contents lists available at ScienceDirect Ecological Engineering journal homepage: 3-D numerical investigations into the shear strength of the soil root system of Makino bamboo and its effect on slope stability Der-Guey Lin, Bor-Shun Huang, Shin-Hwei Lin Department of Soil and Water conservation, National Chung-Hsing University, No. 250, Kuo-Kung Road, Taichung, Taiwan article info abstract Article history: Received 13 April 2009 Received in revised form 6 February 2010 Accepted 3 April 2010 Keywords: 3-D numerical model Makino bamboo soil root system Ultimate pull-out resistance Shear strength increment Mechanical conversion model This study attempts to quantify the reinforcement effect of the Makino bamboo (Phyllostachys makinoi Hayata) root system on the stability of slopeland through numerical analyses and in situ tests. Based on the field surveys of Makino bamboo root morphology, a three-dimensional (3-D) numerical model of the soil root system consisting of the reverse T-shape tap root and hair roots was developed and successfully applied to the finite element simulations of in situ pull-out tests. In the simulations, the soil mass was simulated by a soil element with a perfect elastic plastic (or Mohr Coulomb) material model whereas the root system was simulated by a ground anchor element with a linear elastic material model. In addition, a mechanical conversion model with simple mathematical form, which enables a direct transformation of the ultimate pull-out resistance into the shear strength increment of soil root system was proposed. The conversion model offered a convenient way to quantify the reinforcement effect of the Makino bamboo root system required for the 3-D slope stability analyses. The numerical results indicated that the shear strength increment of the Makino bamboo soil root system ranged from 18.4 to 26.3 kpa and its effect on the slope stability was insignificant when compared with those adverse influence factors such as the steep slope angle (=50 70 ), shallow root depth (= m) and large growth height (>10 m) of the Makino bamboo forest slopeland. It can be also speculated that the tension cracks widespread over the slope surface due to the wind loading acting on the bamboo stems and the sequential rainwater infiltration is the dominating factor in the collapse failure of slopeland. For a Makino bamboo forest slopeland with medium slope (25 < slope angle ˇ <40 ), the reinforcement effect of the Makino bamboo root system can mobilize its maximum stabilization capacity when compared with those of slopeland with mild (ˇ <25 ) and steep slopes (ˇ >40 ). Conclusively, the contribution of the Makino bamboo root system to the stability of slopeland is not as significant as expected Elsevier B.V. All rights reserved. 1. Introduction In Taiwan, various ecological engineering working methods were brought in on many reconstruction projects in the disaster area of the 9/21 earthquake in After the 9/21 quake, the landslide potential of the watershed in central Taiwan largely increased due to the steep topography, fragile geological formation and heavy precipitation and consequently became a great concern to the government agencies and general publics. From year 2000 most of the public agents were requested by the Authority of Taiwan Government to apply the ecological concepts and principles to the restoration projects of the 9/21 Quake such as slope stabilization, river regulation and debris flow mitigation (Kuo, 2006). Corresponding author. Tel.: x506; fax: address: dglin@dragon.nchu.edu.tw (D.-G. Lin). In slope engineering works, vegetation was frequently incorporated with different construction methods as an auxiliary approach for slope stabilization. Currently, in Taiwan the Makino bamboo (Phyllostachys makinoi Hayata) was the most predominant among several major species of bamboo because it was selected as one of the most important plants for forest plantations (Chen, 2006). The root system of Makino bamboo was considered as a stabilizing source for the slopeland of the watershed. However, in fact, the plantation areas of Makino bamboo were almost deserted due to its low economic benefit. Besides, in central Taiwan a large area of slopeland covered with Makino bamboo collapsed and eroded away after the continuous attacks of two typhoons, Mindulle (02 July) and Aere (25 August) in 2004, as shown in Fig. 1. As a consequence, the general public started to question the policy of plantations on the watershed using Makino bamboo. Stokes et al. (2007) observed numerous shallow-slope failures and carried out a series of lateral uprooting tests in forests of big node bamboo (Phyllostachys nidularia) in Sichuan, China. They concluded that big /$ see front matter 2010 Elsevier B.V. All rights reserved. doi: /j.ecoleng

2 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig. 1. Collapse failures of Makino bamboo forest slopeland after typhoons. node bamboo is a suitable species for use in erosion control, but is probably less useful in preventing soil mass movement. Genet et al. (2009) investigated the influence of plant diversity on slope stability and found that bamboo contributed little to slope stability due to its shallow root system. In Taiwan, the relevant studies of Makino bamboo were mainly concentrated on its growth characteristics, biomass investigations, population distributions, and utilizations rather than its mechanical properties and slope stabilizing mechanism. Previously, a large amount of direct shear tests and mechanical models of soil root systems were carried out and proposed to quantify the reinforcement effect of root systems on soil mass (Waldron, 1977; Wu et al., 1979, 1988a,b; Waldron and Dakessian, 1981; Abe and Ziemer, 1991; Operstein and Frydman, 2000; Cazzuffi and Crippa, 2005). However, compared with the sample preparation and equipment installation of the direct shear test of soil root systems conducted by the above researchers, the pull-out test is much easier to perform and time saving. Therefore, the main goal of this study is to develop a conversion model to predict the shear strength increment of the Makino bamboo soil root system using the pull-out resistance of its roots. We will also apply the conversion model to the stability analyses of the Makino bamboo forest slopeland in real watersheds. In addition, models of soil root interaction were proposed for evaluating the contribution of roots to shear strength and comprehensive reviews can be found in many works (Coppin and Richards, 1990; Morgan and Rickson, 1995; Gray and Sotir, 1996; Wu et al., 2004). Nevertheless, the studies on the mechanical properties and the reinforcement effect of bamboo roots with shallow rooting depth and large growth height are rare. In this study, several representative test pits were excavated in the field to survey the morphology of the Makino bamboo root system and a series of in situ pull-out tests were carried out to evaluate the anchorage resistance of roots. Meanwhile, the tensile and shearing tests of single roots with different diameters were also performed to determine the strength of the root material.

3 994 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig. 2. Illustration of the morphology of the Makino bamboo root system. 2. Materials and methods 2.1. Surveys of the morphology of the Makino bamboo root system Several test pits were excavated in the field site to survey the morphology of the Makino bamboo root system. The diameter at breast height (DBH) of Makino bamboo ranged from 50.0 to 60.0 mm and the growth age was on average 1 3 years. The root system of Makino bamboo was mainly composed of a reverse T- shape tap root (or vertical tap root + lateral tap root) and plenty of hair roots as presented in Fig. 2. The vertical tap root extends downward to a depth of around m (=L VT ) and grows laterally to a range of about m (=L LT ). The average diameter of tap root ranges from 13.0 to 25.0 mm (=d). In addition, the hair roots of Makino bamboo sprouts from the knot of the lateral tap root and spread widely over the soil layers adjacent to the surface of the ground. The biomass of the hair roots is around 2 3 times that of usual plants and decreases with the increase of depth. The average diameter of hair root is about mm (=d) and its extended length can reach to 0.60 m (=L VH or L LH ). In general, the root system of Makino bamboo can grow and extend downward to a depth of around m from the surface of the ground Laboratory tests of root material Table 1 summarizes the laboratory testing results of tap root materials. The strength tests were carried out by strain control with a loading speed of 10 mm/min using a universal test machine with capacity of 1 MN. According to the testing results, the tensile resistance of a Makino bamboo single root t can be approximated by t (kn) = [ d 2.03 ] for the root diameter d (mm) by a regression fitting procedure. Moreover, the Young s modulus of Makino bamboo tap root material E r ranges from to kpa and was determined by the secant modulus at 50% of maximum tensile stress of the stress/strain curves of tensile tests. It was indicated that the average tensile strength of live cut bamboo root was MPa, lower than that of dead dry root at MPa and this implied that withered Makino bamboo root can still provide reinforcement to the soil mass. However, it should be noted that the reinforcement effect may be attenuated due to the separation of the body of the dead dry roots body from the desiccated soil mass In situ pull-out tests The field site of the pull-out test was located on the Da-Xi forest land No. 167, Fu-Hsing Township, Tao-Yuan County, Taiwan and attributed to the watershed of the Shi-Men Reservoir. The soil material was classified into silty clay (CL) or clayey silt (ML) by the United Soil Classification System. The average saturated and unsaturated unit weights of soil stratum were 19.0 and 18.0 kn/m 3, respectively. The average water content of soil samples was about 7% in the dry season and 45% in the rainy season. The layout of the pull-out equipment is illustrated in Fig. 3. The load cell (capacity: 50 kn) was firstly connected with the pullout loading recorder (equipment type: SMD-10A) and constant rate pull-out unit (rate adjustable from to mm/min), and finally mounted on a portable triangular frame. The pullout loading recorder connected with the computer enables a data acquisition of pull-out resistance and pull-out displacement. The growth age of Makino bamboo for the pull-out test ranged from 1 year to 3 years. Nine sets of the pull-out tests in total (Nos. T1 T9) were carried out under a constant rate of mm/min. However, due to the large variation of testing results, only tests T4, T5, T6 and T8 with similar pull-out curves were presented for comparisons (see Fig. 10). Table 1 Average tensile and shear strengths of Makino bamboo single roots. Root material type Average diameter d (mm) (no. of samples tested) Average tensile strength t (MPa) (no. of samples tested) Live cutting 20.6 ± 1.32 (s = 2.83) (20) ± 5.06 (s = 10.85) (20) Dead dry 20.6 ± 2.64 (s = 2.30) (5) ± (s = 9.80) (5) Root material type Average diameter (mm) (no. of samples tested) Average shear strength r (MPa) (no. of samples tested) Live cutting 19.6 ± 2.51 (s = 2.19) (5) 9.04 ± 5.50 (s = 4.78) (5)

4 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig. 3. The pull-out equipment and its connection with the Makino bamboo root system. Based on the pull-out tests of the Makino bamboo root system, the ultimate pull-out resistance P u should be correlated with the growth age Yr, diameter at breast height D and soil water content w as: P u = Yr D 0.22 w, in which the multiple linear regression model was used to construct the model equation. In the regression model, the co-linearity of P u, Yr, D and w are evaluated by their Variance Inflation Factors (VIF) and the characteristic of normal distribution of the model is verified by the standard residuals plots from residual analyses Numerical simulation of pull-out test Abe (1991) estimated the reinforced shear resistance of roots through the pull-out resistance of roots. Operstein and Frydman (2000) carried out 43 pull-out tests to measure the vertical pullout load of Alfalfa roots from a waste chalky fill, with varying stone content. Lin et al. (2005) summarized the testing results of various types of mechanical tests in a soil root system and it was indicated that the pull-out resistance of a soil root system was influenced by climate change, soil properties, and the growth age of the plant. Conclusively, the morphology of plant roots in soil stratum dominates the anchorage of a plant to resist the uprooting force (Ennos, 1990, 1991; Stokes et al., 1996). Dupuy et al. (2005a,b) investigated the anchorage of roots by two-dimensional (2D) numerical analyses and used the density-based approach to model the architecture of roots. This study performed a series of 3-D finite element analyses to simulate the pull-out behaviors of a Makino bamboo root system. The numerical results of pull-out force versus pull-out displacement curves were compared with those from the field measurements to verify the effectiveness of numerical procedures. Eventually, an optimum artificial geometry configuration can be determined to represent the natural morphology of the Makino bamboo root system Numerical model Unlike the 2D plane strain model, the 3-D model enables a more realistic simulation on the stiffness and the configuration of root systems. The dimensions of the 3-D numerical model are 3 m 3m 3 m (length width height) and the geometry boundaries were specified as a fully constrained boundary (without displacement: X = Y = Z = 0) as shown in Fig. 4. According to the root morphology of Makino bamboo in Fig. 2, the root system consisted of two components: (1) the reverse T-shape tap roots: grows and extends downward to a depth of L VT = 0.15 m beneath the surface of the ground and laterally stretches to a length of L LT = 0.50 m (2 m 0.25 m) with an average diameter of d = 19.0 mm and (2) the hair root: the lengths of

5 996 D.-G. Lin et al. / Ecological Engineering 36 (2010) vertical hair root is L VH = 0.50 m and lateral hair root is L LH = 0.25 or 0.35 m. The average diameter of hair root is 1.5 mm. Fig. 5 illustrates the detail of a 3-D numerical model of the root system. By adjusting the length and the number of layers of lateral hair root, four types (S1 S4) of numerical root model can be established and used for numerical experiments as shown in Table 2. Fig D numerical model of pull-out test of the Makino bamboo soil root system Input of material model parameters The soil material was simulated by soil elements with a Mohr Coulomb model and the cohesion c and friction angle determined by direct shear tests were 24 kpa and 15.6, respectively. The Young s modulus of soil material E = 2000 kpa, Poisson s ratio = 0.3 and the dilation angle =0 were specified based on the engineering characteristics of low plasticity silty clay or silty soil (CL/ML). In addition, the relative displacement at the soil root interface during the pull-out test was modeled by two strength parameters c int and int. At the interface, the c int and int were given by: c int (=R int c) and int (=R int [tan 1 tan ]), in which, the strength reduction factor R int = 0.5 was adopted. The root material was simulated by a ground anchor element with a linear elastic model. The ultimate tensile resistance of single root t was determined by d 2.03 (see previous section) of 6.82 and 0.04 kn for tap root diameter d = 19 mm and hair root diameter d = 1.5 mm, respectively. Moreover, the average Young s modulus of root material was E r = 312 kpa. Table 3 presents the required input model parameters of soil and root materials. Fig D numerical model of the Makino bamboo root system (unit: cm).

6 D.-G. Lin et al. / Ecological Engineering 36 (2010) Table 2 Makino bamboo numerical root samples for the numerical simulation of the pull-out test. Numerical root sample no. Reverse T-shape tap root Vertical hair root Lateral hair root S1 Yes No No S2 a Yes Yes; L VH = 0.55 m Yes; L LH = 0.35 m; 3-layers S3 Yes Yes; L VH = 0.55 m Yes; L LH = 0.25 m; 3-layers S4 Yes Yes; L VH = 0.55 m Yes; L LH = 0.25 m; 2-layers Yes = with configuration; no = without configuration; L VH = length of vertical hair root; L LH = length of lateral hair root. a Due to the similarity of the numerical outputs of the 3-D pull-out tests only S2 was used for discussions. Table 3 Material model parameters for the numerical simulation of pull-out test (a) soil stratum (b) root system. Soil model c (kpa) (deg.) sat (kn/m 3 ) E (kpa) (deg.) (a) Mohr Coulomb model Root system Root diameter d (mm) Cross-sectional area a (mm 2 ) Ultimate tensile resistance t (kn) (b) Tap root Hair root Young s modulus E r = kpa for root system Implementation of the numerical simulation The simulation of the pull-out test was implemented by continuously applying an incremental pull-out loading to the root system and recording the calculated pull-out displacement increment. The simulation was ceased as the cumulative loading reached the ultimate pull-out resistance P u of the testing curve Numerical simulation of direct shear test Operstein and Frydman (2001) simulated the direct shear behavior of cylindrical samples with and without roots using a 2D finite difference plane strain numerical scheme to examine the reinforcement effect of roots. However, it required some numerical schemes to convert the 2D numerical results into actual 3-D problems. In this study, the identical 3-D numerical model with the pull-out test of the Makino bamboo soil root system was used for the simulation of the direct shear test. In such a way, the shear strength increment of the soil mass due to roots S r can be determined from the numerical results and eventually correlated with the ultimate pull-out resistance P u Numerical model As shown in Fig. 6, the dimensions of the numerical model were 3 m 3m 3 m (=length width height) and the central testing block of the soil root system was 0.6 m 0.6 m 0.15 m (=length width thickness). The trench surrounding the block was excavated to a depth of 0.15 m to simulate the space required for equipment installation. The direct shear box of steel plate was included in the model. The shearing plane was specified at a depth of 0.15 m, which exactly coincided with the elevation of the intersection point of the vertical and lateral tap root (or reverse T-shape tap root) as indicated in Fig. 5 (see front view). The outermost geometry boundaries of the numerical model were assumed to be constrained without displacement Input material model parameters Two sets of soil model parameters were adopted for the numerical simulation of direct shear test as presented in Table 4. Soil sample No-A is the same as that of the pull-out test (see Table 3(a)). Soil sample No-B is similar to No-A being only different in c (=25 kpa) and (=30 ) values. The root material parameters are the same as those of the pull-out test (see Table 3(b)). In addition, the direct shear box of steel plate was simulated by a wall element with linear elastic model and the model parameters were listed in Table Implementation of the numerical simulation In total, four groups of numerical simulations were performed on the direct shear test of the Makino bamboo soil root system, namely, S3-A, S3-B, S2-B and S4-B. For instance, the S3-B representing the numerical sample was composed of the numerical root sample S3 (see Table 2) and the soil sample No-B (see Table 4). The normal stress on the shearing plane for the four specimens in each group was varied by 2.7, 7.7, 12.7 and 32.7 kpa ( = o + )in which the overburden stress o = 0.15 m 18 kn/m 3 = 2.7 kpa and the normal stress increment was = 0, 5, 10 and 30 kpa, respectively. The shear loading increment was applied continuously on Table 4 Soil material model parameters for the numerical simulation of the direct shear test. Soil sample Soil model c (kpa) (deg.) sat (kn/m 3 ) E (kpa) (deg.) No-A Mohr Coulomb model No-B a Mohr Coulomb model USCS: No-A: silty clay (CL) with water content 12%; No-B: clayey silt (ML) with water content 7%. a Due to the similarity of the numerical output of the direct shear tests and slope stability analyses, only soil sample No-B was used for the discussion. Table 5 Material parameters of the steel plate direct shear box. Structural element type Thickness t s (mm) Young s modulus E s (GPa) Unit weight s (kn/m 3 ) Poisson s ratio s Wall element

7 998 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig. 6. Numerical model for the direct shear test of the soil root system (unit: cm). the steel plate of the shear box and finally ceased as the shear stress on the shearing plane reached the peak value Stability analyses of Makino bamboo forest slopeland The reinforcement effect of the root system on the slope stability was investigated by many researchers (Waldron, 1977; Wu, 1976, 1994; Wu et al., 2004; O Loughlin and Ziemer, 1982; Operstein and Frydman, 2002; Lin et al., 2007). In summary, the reinforcement effect of the root system on the slope stability was considered by adding a group of root inclusions into the soil mass or using an equivalent reinforced layer with shear strength increment S r (or cohesion increment of c) to represent the soil root layer. In addition, Ekanayake and Phillips (1999) and Ekanayake et al. (2004) derived the factor of safety of soil with roots at a known shear displacement of direct shear tests using an energy approach. By a simple and practical way, Osman and Barakbah (2006) predicted the slope stability by the parameters of soil water content and root profiles. In conclusion, the main difficulties in evaluating the reinforcement effect of root systems result from the spatial random distribution of the physical and mechanical properties of plant roots. In this study, the soil root system of Makino bamboo forest slopeland was modeled by an equivalent reinforced layer with a cohesion increment of c Numerical model The geometry model of Makino bamboo forest slopeland is displayed in Fig. 7. The slope height of 10 m (=H) is maintained while the slope angle ˇ varied from Grade-4 to Grade-7 according to the standard of the slopeland grading system in Taiwan. The grading system gives the following gradations: Grade- 4 (ˇ =20, H/L = 36.4%); Grade-5 (ˇ =25, H/L = 46.6%); Grade-6 (ˇ =40, H/L = 83.9%) and Grade-7 (ˇ =50, H/L = 119.2%). The side boundaries and bottom boundaries of the geometric model were restrained without displacement ( X =0; Y =0; Z = 0) Input model parameters To evaluate the effect of the Makino bamboo root system on the slope stability, the relative factor of safety, RFS (=FS r /FS o ), proposed by Operstein and Frydman (2002) was used. At first, a critical cohesion c o was back calculated to maintain the slope without root system at a critical state equilibrium condition for a safety factor FS o = 1.0. Subsequently, the identical slopes with Makino bamboo roots were analyzed for a safety factor FS r. In such a way, the RFS enables an evaluation of the exact contribution of roots to the shear strength increment of the soil root system. As shown in Table 6, the critical cohesions c o of 7.47, 8.58, and kpa can be determined for slopes with different slope angle ˇ of 20 ;25 ;40 and 50. The soil material model parameters were the same as those of the soil sample No-B in Table 4 and the shear strength increment due to root c = 20.7 kpa (see Table 7) was obtained from the simulations of the direct shear test on the Makino bamboo root system. The growth distribution depth of the Makino bamboo root system L r = 0.8, 0.9 and 1.0 m were considered by an equivalent reinforced layer with different thicknesses. Table 6 Soil material model parameters for slope stability analyses with and without Makino bamboo root systems. Soil model c (kpa) (deg.) sat (kn/m 3 ) E (kpa) (deg.) Mohr Coulomb model c o Critical cohesion for slopeland with various slope angle Slope angle ˇ (deg.) H/L (%) (slope grade a ) 36.4% (Grade-4) 46.6% (Grade-5) 86.9% (Grade-6) 119.2% (Grade-7) Critical cohesion c o (kpa) a In Taiwan, slopeland is classified into Grade-1 to Grade-7 according to its slope angle.

8 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig D numerical model of Makino bamboo forest slopeland (a) geometry dimension (unit: m) and (b) finite element mesh Implementation of stability analysis Slope stability analyses were performed on a series of fictitious slopes with and without Makino bamboo root systems using the c reduction method of 3-D finite element program Plaxis-3-D-Foundation (2008). In the c reduction approach the input strength parameters c and tan of soil material are successively reduced to c r and tan r, respectively, to trigger the slope failure. The method defined the overall safety factor of slope FS=(c/c r ) = (tan /tan r ) Adverse influence factors on the stability of Makino bamboo forest slopeland Coppin and Richards (1990) indicated that although the surcharge effect was considered an adverse effect in the case of trees, surcharge can also be beneficial, depending on slope geometry, the distribution of vegetation over the slope, and the soil properties. However, Gray and Megahan (1981) presented that the surcharge of trees is beneficial only when slope angles are small and this implied an extremely adverse situation to the Makino bamboo forest slopeland which is generally steep with a slope angle of as shown in Fig. 1. Meanwhile, Wu et al. (1979) estimated that the weight of the trees can reach about 5.2 kpa from the number of trees per unit area and their sizes as determined from the survey. In addition, Coppin and Richards (1990) also demonstrated that wind loading becomes significant when the wind velocity is higher than 11 m/s and both the up- or down-hill wind loadings can destabilize the slope especially in larger trees with shallow root systems. In 2004, Typhoons Mindulle (02 July; wind velocity = m/s; rainfall intensity = mm/day) and Aere (25 August; wind velocity = m/s; rainfall intensity = mm/day) invaded Taiwan and caused severe collapse failure and erosion of Makino bamboo forest slopeland. In such circumstances, the shallow root depth of m and large growth height over 10 m of Makino bamboo became extremely unfavorable to the slope stability. Tension cracks were widespread over the surface of the slopeland after the typhoons and it can be speculated that the overturning moment, induced by the wind loading which was, responsible for the occurrence of tension cracks and the collapse of slopeland, was eventually triggered by the subsequent infiltration of rainwater into the cracks during the typhoons. 3. Results and discussion 3.1. Verification of numerical procedures of pull-out test As shown in Table 2, due to the similarity of the numerical outputs of S1 S4, only the simulation results of numerical root sample S2 (with reverse T-shape tap root and length vertical hair root L VH = 0.55 m and 3-layers of lateral hair root with length L LH = 0.35 m) were used for discussion. Fig. 8 displays the defor- Fig. 8. Deformation mode of the Makino bamboo root system S2 at the final loading stage of the numerical simulation of the pull-out test (P = pull-out force, ı v = pull-out displacement).

9 1000 D.-G. Lin et al. / Ecological Engineering 36 (2010) Table 7 Shear strength increment of Makino bamboo soil root systems determined by numerical simulation of the direct shear test. Testing group c (kpa) (deg.) measurement (deg.) calculation c + c (kpa) c (= S r) (kpa) S3-A a S3-B b a S2-B S4-B (1) Mohr Coulomb shear strength envelope of soil mass without root system: = tan (2) Mohr Coulomb shear strength envelopes of soil mass with root system: = tan 15.9 for S3-A; = tan 29.8 for S2-B, and = tan 30.1 for S4-B. a The average c (=20.7 kpa) of S3-A and S3-B was used for c reduction slope stability analysis. b Due to the similarity of the numerical outputs, only the numerical result = tan 29.9 for S3-B was used for discussion. mation mode of the root system and it is obvious that the tap root and lateral hair root are stretched upward as the pull-out force is ascending. Nevertheless the vertical hair root seems insignificant in providing the pull-out resistance. As shown in Fig. 9, the displacement distribution contour in pull-out direction (or Y-direction) can be generated along a specific profile (profile A 0 A 1 ). It can be observed that the pull-out displacement is mainly concentrated on the tap root and its surrounding lateral hair root rather than the vertical hair root. As shown in Fig. 10, there were 4 sets of in situ pull-out tests in total (T4, T5, T6 and T8) which were selected for the comparison with the simulations (S1, S2, S3 and S4). S1 S4 represented numerical root samples with different configurations of Makino bamboo (P. makinoi Hayata) root system as listed in Table 2. According to Fig. 10, several comments can be made: 1. The simulated pull-out curve of numerical root sample S1 (without hair root) was in good coincidence with that of the in situ test T4. This indicates the pull-out resistance can be captured using the numerical root sample simply configured by the reverse T- shape tap root whereas the hair roots only play a minor role in the simulation. This is due to the fact that the gross crosssectional area of tap root approximates 160 times that of the hair root in the Makino bamboo root system. 2. The pull-out curves of numerical root samples S2 S4 (with hair root) exhibited a steeper slope than S1 as the pull-out loading was lower than 3 kn in the initial testing stage. This is due to the additional anchorage of hair roots which are extensively scattered over the soil mass surrounding the tap roots. However, as the pull-out loading was higher than 3 kn, the slope of the pullout curve of samples S2 S4 appeared milder than S1. This can result from the large pull-out displacement of tap root which in turn transferred to the hair roots and the surrounding soil mass in the sequential testing stages. Eventually the anchorage effect of hair roots descends promptly in response to the failure of surrounding soil mass and caused a milder slope of testing curve and lower ultimate pull-out resistance. In conclusion, the simulated pull-out curves of samples S2 S4 reasonably fell on the range of measurements. 3. The ultimate pull-out resistance P u of the numerical root sample S2 was greater than that of S3 and this verifies that the length (or the extent of lateral spreading) of lateral hair root L LH has significant influence on the anchorage of the root system during the pull-out test. In addition, the P u value of S3 was almost equivalent to that of S4 and this indicates the number of layers of lateral hair root only plays a minor role in the mobilization of pull-out resistance Numerical simulations of direct shear test Fig. 9. Pull-out displacement contour of the Makino bamboo root system under pull-out loading. Figs present the simulation results of numerical sample S3-B under maximum shear loading conditions ( = 58.9 kpa, ı h = 46.5 mm). The S3-B consisted of the numerical root sample S3 (see Table 2) and the soil sample No-B (see Table 4). The shear stress was calculated by T/A (T = external applied shear loading, A = area of shearing plane) and the shear displacement ı h was coincidental with the horizontal displacement of the steel shear box. As shown in Fig. 11, an overall lateral movement of Makino bamboo (P. makinoi Hayata) root system mobilizes after shearing. Figs. 12 and 13

10 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig. 10. Comparison between the simulation and measurement of the pull-out test on the Makino bamboo root system (T: for measured and S: for simulated). display the maximum internal shear displacement occurs at the central area of the shearing plane whereas the maximum internal shear stress develops at the area adjacent to the steel shear box. Fig. 14 shows the Mohr Coulomb shear strength envelopes of soil mass with and without the Makino bamboo root system and the envelopes can be expressed by: = tan 29.9 =(c + c)+ tan 29.9 and =25+ tan 30 = c + tan 30, respectively. Consequently the shear strength increment due to roots S r = 20.8 kpa (=the cohesion increment c) can be determined. The simulated envelopes repeatedly verified the validity of previous studies by Wu (1976), Wu et al. (1979), Waldron (1977) and Waldron and Dakessian (1981) which attributed the shear strength increment of soil root system S r to the cohesion increment c, whereas the frictional angle remained unchanged. Comparatively, O Loughlin and Ziemer (1982) summarized some typical values of the increase in soil cohesion c due to roots and which may range from 1 to 17.5 kpa. In this study, the average shear strength increment of 20.7 kpa (= c) of direct shear tests S3-A and S3-B was used for the stability analyses of Makino bamboo forest slopeland. Table 7 summarizes the shear strength increment c of Makino bamboo soil root system determined from the numerical results of direct shear tests S3-A, S3-B, S2-B and S4-B Formulation of the mechanical conversion model between pull-out resistance and shear strength increment of the soil root system It was recognized that the sample preparation and test pit excavation for the direct shear test were more tedious and time consuming than the pull-out test of the soil root system. To cope with this situation, a mechanical conversion model between the ultimate pull-out resistance and the shear strength increment of the soil root system becomes crucial. The model enables a direct Fig. 11. Deformation mode of the Makino bamboo soil root system (S3-B) under different shear loading conditions of the direct shear test.

11 1002 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig. 12. Internal shear displacement contour of the Makino bamboo soil root system (S3-B) under shear loading condition ( = 58.9 kpa, ı h = 46.5 mm) (a) location of profile (b) contour distribution. transformation of the ultimate pull-out resistance P u (kn) into the shear strength increment of the soil root system S r (kpa) and an immediate application to the stability analyses of Makino bamboo forest slopeland. The shear strength of the soil root system can be given by: = c + S r + tan, in which, S r is the shear strength increment contributed by the root system. Using the numerical results of shear strength increment S r and of the ultimate pullout resistance of S2-B, S3-B and S4-B as summarized in Table 8, a mechanical conversion equation can be given by: S r (kpa) = m ln P u + n = 50 ln P u 59 in which, m, n = conversion parameters related to the morphology of the root system. For the Makino bamboo root system, the parameters m and n are equal to 50 and 59, respectively. The mechanical conversion equation can be plotted into a functional curve of S r = f(p u ) as shown in Fig Stability analysis of Makino bamboo forest slopeland Using the c reduction stability analyses, the reinforcement effect of the root system, the sensitivity of root distribution depth L r (=0.8, 0.9 and 1.0 m) and the slope angle ˇ (=20,25,40 and 50 )of

12 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig. 13. Internal shear stress contours of Makino bamboo soil root system (S3-B) under shear loading condition ( = 58.9 kpa, ı h = 46.5 mm) (a) location of profile (b) contour distribution. Fig. 14. Shear strength increment of the Makino bamboo soil root system (S3-B). Fig. 15. The relationship of ultimate pull-out resistance and shear strength increment of the Makino bamboo soil root system.

13 1004 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig. 16. Potential sliding modes and contours of total displacement increment of earth slope at failure with a Makino bamboo soil root system. Makino bamboo forest slopeland were investigated. Fig. 16 displays the potential sliding mode of Makino bamboo forest slopeland with root distribution depth of L r = 1.0 m and varied slope angles. It can be observed that the influence of reinforced layer of root system on the factor of safety was insignificant. The colorfed legend represents the total displacement increments at slope failure which do not have a physical meaning, but give an indication of the most likely failure mechanism. As listed in Table 9, the maximum RFS is (4.6% increment of factor of safety due to roots) for the case of ˇ =40 (H/L = 83.9%, Grade-6, L r = 1.0 m) and this indicates the influence of the Makino bamboo root system on the stability of slopeland is very limited from the viewpoint of engineering mechanics. As shown in Fig. 17, for a mild slopeland (ˇ <25 ) the Makino bamboo root system merely plays a minor role on the slope stability. For a medium slopeland (25 < ˇ <40 ), the influences of reinforcement (increas- Table 8 Numerical results of the shear strength increment and ultimate pull-out resistance of a Makino bamboo root system used for the formulation of the mechanical conversion model. Testing group Pull-out test Direct shear test P u (kn) d (m) L p (m) S r (= c) (kpa) S2-B S3-B S4-B d = average diameter of tap root, L p = pull-out displacement at ultimate pull-out resistance and c = cohesion increment due to roots. ing RFS) and distribution depth (variation of L r ) of the root system on slope stability become apparent. Similar to the mild slopeland, in a steep slopeland (ˇ >40 ) the increasing stability of the slope due to roots seems negligible when compared with the increasing driving force components. In conclusions, the contribution of the Makino bamboo root system has little effect on the stability of slopeland and this coincides with that of big node bamboo presented by Stokes et al. (2007). They indicated that the root system of big node bamboo with very shallow rooting depth is probably less useful in preventing soil mass movement and contributes little to slope stability. Table 9 The relative factor of safety (RFS) of slopeland with Makino bamboo root systems. Slope angle ˇ ( ) slope gradient H/L (%) (Grade No.) Root distribution depth L r (m) Relative factor of safety RFS ( FS %) (0.5%) (0.5%) (Grade-4) (0.9%) (1.3%) (1.4%) (Grade-5) (1.5%) (3.3%) (4.2%) (Grade-6) (4.6%) (1.7%) (1.9%) (Grade-7) (2.5%) Slope stability increment: ( FS %) = (FS r FS o) 100%/FS o and FS o = 1.0.

14 D.-G. Lin et al. / Ecological Engineering 36 (2010) Fig. 17. The relationship of relative factor of safety and slope angle of Makino bamboo slopeland with various root distribution depths. 4. Conclusion According to the field investigations and numerical calculations of the Makino bamboo (P. makinoi Hayata) soil root system, several conclusions were made as follows: 1. Based on the field surveys of root morphology, a 3-D numerical model of the soil root system can be developed and successfully applied to the simulation of in situ pull-out behavior. The model simply consisted of a reverse T-shape tap root and a limited number of hair roots. The numerical results also indicated that the pull-out loading is mainly carried by the tap root whereas the hair roots only play a minor role in providing the pull-out resistance. 2. A regression equation of the ultimate pull-out resistance P u correlated with the growth age Yr (year), diameter at breast height D (mm) and soil water content w (%) as: P u = Yr D 0.22 w can be used to estimate the ultimate pull-out resistance of roots. 3. Through a series of numerical simulations of the direct shear test, a mechanical conversion model with simple mathematic form, S r (kpa) = 50 ln(p u ) 59, enables a direct transformation of the ultimate pull-out resistance P u (kn) into the shear strength increment of soil root system S r (kpa) is proposed. 4. The average c (= S r ) of the Makino bamboo root system is estimated in the range of kpa and its reinforcement effect on the slope stability is very limited due to the very shallow rooting depth. 5. The steep slope angle (=50 70 ), shallow root distribution depth (= m) and large growth height (>10 m) were critical to the collapse failure of Makino bamboo forest slopeland. The reinforcement effect of root systems on the slope stability was relatively small when compared with the influences of the wind loading and torrential rainfall from Typhoons Mindulle and Aere in It was then believed that the tension cracks and the sequential rainwater infiltration widespread over the slope surface triggered the collapse failure of slopeland. 6. Based on the numerical results, for a Makino bamboo forest slopeland with medium slope (25 < slope angle ˇ <40 ), the reinforcement effect of the Makino bamboo root system can be mobilized to its maximum stabilization capacity when compared with those of slopeland with mild (ˇ <25 ) and steep slopes (ˇ >40 ). Acknowledgements This research project was granted by the National Scientific Commission, Executive Yuan. The authors appreciate the financial support from the Commission for the research project entitled Quantitative Evaluation on the Stability of Soil Root System in Vegetated Slope. Project number: NSC E References Abe, K., Estimation of reinforced shear resistance of rooted soil by pull-out resistance of the roots. J. Jpn. Soc. Revegetation Techn. 16 (4), Abe, K., Ziemer, R.R., Effect of tree roots on a shear zone: modeling reinforced shear strength. Can. J. For. Res. 21, Cazzuffi, D., Crippa, E., Shear strength behavior of cohesive soils reinforced with vegetation. In: 16th International Conference on Soil Mechanics and Geotechnical Engineering, OSAKA, Japan, September 12 16, pp Chen, Y.R., Field investigations of root system and it s influence on the landslide of Makino bamboo forest, Master Thesis, Department of Soil and Water Conservation, National Chung-Hsing University, Taichung, Taiwan. Coppin, N.J., Richards, I.G., Use of Vegetation in Civil Engineering. Construction Industry, Research and Information Association (CIRIA), United Kingdom. Dupuy, L., Fourcaud, T., Stokes, A., 2005a. A numerical investigation into factors affecting the anchorage of roots in tension. Eur. J. Soil Sci. 56, Dupuy, L., Fourcaud, T., Stokes, A., Danjon, F., 2005b. A density-based approach for the modelling of root architecture: application to Maritime pine (Pinus pinaster Ait.) root systems. J. Theor. Biol. 236, Ekanayake, J.C., Phillips, C.J., A method for stability analysis of vegetated hillslopes: an energy approach. Can. Geotechnol. J. 36, Ekanayake, J.C., Phillips, C.J., Marden, M., A comparison of methods for stability analysis of vegetated slopes. In: Ground and Water Bioengineering for Erosion Control and Slope Stabilization. Science Publisher, Inc, pp Ennos, A.R., The anchorage of leek seedlings: the effect of root length and soil strength. Ann. Bot. 65, Ennos, A.R., The mechanics of anchorage in wheat Triticum aestivum L. II. Anchorage of mature wheat against lodging. J. Exp. Bot. 42 (245), Genet, M., Stokes, A., Fourcaud, T., Norris, J.E., The influence of plant diversity on slope stability in a moist evergreen deciduous forest. Ecol. Eng., doi: /j.ecoleng Gray, D.H., Megahan, W.F., Forest vegetation removal and slope stability in the Idaho Batholith, Research paper INT-271, Intermoutain Forest and Range Experiment Station, Ogden, Utah.

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