Abstract
Internal stability problems of geosynthetic reinforced structures under special consideration of the interaction behaviour are presented in this paper. The interaction behaviour between soil and geosynthetic is an important key parameter in the design of geosynthetic reinforced structures. The stability of these structures relies to a large extent on the proper transference of forces from the soil in the geosynthetic and vice versa. The main mechanisms of this load transference are friction, passive earth resistance and interlock. Depending on the loading and the position of the reinforcement layers a shear- or a pull-out mechanism could evolve. Both types of mechanisms could be examined by different test methods with a huge number of parameters influencing the test results. The effects of important key parameters on the results of the pull-out test are shown based on some examples from our test program.
Keywords: Geosynthetic, test method, shear test, pull-out test, interface behaviour
Introduction
Today geosynthetics are used in a large range of civil and geotechnical engineering applications. Geosynthetics are divided in geotextiles, which can be subdivided in wovens and non-woven geotextiles, geogrids, geomembranes, geosynthetic clay liners, geonets and geocomposites made of different products. Main functions of geosynthetics are: Drainage, filtration, sealing, erosion control, segregation, protection and reinforcement which represents a key function: By the application of a geosynthetic, a compound structure soil – geosynthetic is created, which can cope tension and compression forces. It could easily compared with reinforced concrete. A key feature of this function is the absorption of tension forces in the geosynthetic and their transfer in the surrounding soil by friction and other mechanisms.
Nowadays, geosynthetics are used as reinforcing elements in a wide variety of structures: Reinforced slopes and walls, embankments on soft soils, reinforcement in the base layers of railroad- and roadconstructions, reinforced foundation mattresses, the bridging of sinkholes or reinforced abutments (Figure 1).
Figure 1. Geosynthetic Reinforced Structures
Reinforced Slope / Wall
Mechanical Behaviour
A reinforced slope structure will be analyzed in the following example. Unreinforced slopes can be constructed with small gradients of about 45°. By exceeding the maximum shear strength shear- and sliding planes develop in steeper constructions depending on the stress state. Interacting displacements of the active and the passive zone on both sides of the sliding plane could be stopped by connecting them with a reinforcement which stretches under the displacements of the moving soil masses (Figure 2). Tension forces are generated in this connecting geosynthetic which could hold the two zones together.
Figure 2. Mechanical Behaviour of a Reinforced Slope
With the limit equilibrium method a factor of safety of a given structure is calculated by the determination of the force and/or moment equlibrium. It must be kept in mind that the movement of the sliding body must be kinematically possible. This is fulfilled with the use of rotational failure planes, logarithmic spirals or multi-piece, wedge-like failure bodies. The failure plane with the lowest factor of safety has to be checked. With complex geometries or soil stratifications a slice method, for example Krey or Bishop had to be considered. Equilibrium has to be checked at every single slice. Driving forces and retaining forces are summed up to calculate the factor of safety. Considering the available resistance it is checked whether possible sliding bodies are in a stable equilibrium which is determined if the sum of the driving forces or moments – for example from the soil or surcharge – is smaller than the sum of the retaining forces or moments. Besides the shear strength the tension forces Fi of the reinforcements layers are also counted as retaining forces. If limit equilibrium is reached precisely the safety factor of the investigated failure body is 1 and the system is on the verge of collapse (limit equilibrium state). In the design process of geosynthetic reinforced structures external and internal stability problems have to be solved.
External Stability
For external stability design the reinforced structure is simplified as a coherent body: Possible failure mechanisms include the reinforcement layers and the backfill.
Figure 3. External Stability Analysis (a. Tilting, b. Sliding, c. Bearing Capacity)
Relevant design verifications for external stability of reinforced structures should be made (Fig. 3).
Failure outside the reinforced structure: The failure plane with the lowest safety factor outside the coherent body has to be evaluated.
Tilting of the reinforced structure: Because of the high ratio width/height of reinforced structures (commonly more than 0.6) tilting is seldom a problem. Sliding: Different cases have to be evaluated: Sliding in the sub-base and sliding in the contact area between geosynthetic and sub-base. Bearing capacity failure in the contact area of the coherent body and the sub-base depending on the eccentricity and declination of the resultant load and the gradient of the terrain.
Internal Stability
Internal stability design corresponds to failure mechanisms with sliding planes which traverse the geosynthetics. Tension forces in the reinforcement have to be evaluated to guarantee a stable behaviour of the system. Reinforcement stresses are the result of an examination of a multitude of failure planes which traverse reinforcement layers (Figure 4). For every reinforcement layer it has to be checked whether the calculated tension force could be assigned to the material. Therefore it has to be checked:
Rupture of the reinforcement: For every layer it has to be checked whether the calculated forces are smaller or equal the long term rupture strength of the geosynthetic. The long term rupture strength could be calculated from the short term strength taken from a tension test, reduced by factors considering creep effects, installation damage, environmental conditions and overlapping of the material.
where
FA Long term strength of the geosynthetic
Fk Tensile strength from the tensile test
Ai Reduction factors for creep, installation damage etc.
Interaction behaviour of the reinforcement: It has to be checked whether the anchorage length is sufficient to transfer the calculated tensile force from the geosynthetic into the soil. When using the limit equilibrium method it has to be ensured that in every layer the calculated tensile force could be transferred in the passive zone beyond the failure plane.
where
FB Maximum pull-out force
s Vertical stresses at the level of the reinforcement layers
l Embedment length of the reinforcement
? Friction ratio or interface friction coefficient
f Friction angle of the soil
In every layer of reinforcement the available tensile force Fi must be smaller than FA and FB which can be absorbed by the system. The long term rupture strength could easily be ascertained by tensile in-air tests whereas the evaluation of the load transference capacity or interaction behaviour of the reinforcements requires complex in-soil tests. Standard test procedures include the shear test and the pull-out test. It has to be kept in mind that the type of test has to be chosen in correspondance with the associated interaction mode (Figure 4). In the pull-out mode an anchorage behaviour is simulated, whereas in the shear mode a uniform shear behaviour at a predetermined failure plane is simulated.
Figure 4. Shearing and Pull-Out Modes
Evaluation of Interaction Parameters
Introduction
Pull-out forces and with it the friction ratio and the interface friction coefficient are mainly influenced by the properties of the soil and the reinforcement characteristics. In the literature three key interaction mechanisms are presented (Juran et al., 1988; Milligan und Palmeira, 1987; Voskamp, 1992): Friction between the soil and the reinforcement, Soil particles in grid openings (Interlock), Passive earth resistance in front of transverse grid members. Pull-out resistances of continous reinforcement materials (structures without any openings) like geomembranes are solely mobilisied through friction whereas geotextiles could gain additional pull-out resistance due to small particles which get embedded in the material (Figure 5).
Figure 5. Load transference Geogrid
Soil Geogrids gain additional pull-out resistance from passive earth resistance and interlock effects, whereas passive earth resistance is more common with smaller soil particles and interlock effects are dominating with larger particles. The friction components of geogrids are small compared to continous structures because of their smaller surface (Koerner, 1999; Milligan und Palmeira, 1987).
Shear Test
In Germany the interface shear resistance in the direct shear test is regulated in DIN EN ISO 12957-1, „Geotextilien und geotextilverwandte Produkte, Bestimmung der Reibungseigenschaften, Teil 1: Scherkastenversuch“. A shear box with the minimum dimensions of 300 mm x 300 mm should be used with the geosynthetic specimens clamped on the lower part of the shear box. During the whole test procedure at least three transverse ribs of the geogrid must be kept inside the shear box for representative results.
The interface shear resistance is calculated as follows
where
S Shear force
A Contact area of the specimen
Continuous geosynthetic specimens can be tested with a solid block or soil in the lower part of the shear box. The interaction behaviour of geogrids is influenced by friction on the surface of the specimen and soil to soil friction components through the openings of the grid. Therefore, both parts of the shear test device have to be filled with soil (Jewell, 1996). Key parameters influencing the interface shear resistance in the direct shear box are installation density and grain size distribution of the soil, type and magnitude of the surcharge and influences of the shear device and the installation technique.
Figure 6 Schematic cross-section of the shear test device
The shear test is assigned to the “Shearing Mode” (Figure 4). The single-sided shear plane is enforced in the test by geometrical constraints between both parts of the shear box. Because of the fixture of the geosynthetic at the lower part of the shear box no tensile forces will be transferred in the geosynthetic. Therefore with the presented mode of testing no elongations of the reinforcement material can be taken into account. Forces are distributed along the shear plane uniformly.
Pull-Out-Test
In Germany the interface shear resistance in the pull-out test is regulated in DIN EN 13738, „Geotextilien und geotextilverwandte Produkte, Bestimmung des Widerstandes gegen Auszug aus dem Boden“. Therein a lab-based test procedure is presented to determine the pull-out resistance of geotextiles and geotextiles-related products in the soil. A pull-out device with minimum dimensions of 1,50 m x 0,60 m x 0,30 m (L x W x H) should be used. Vertical surcharge should be applied by a flexible membrane and the pull-out of the geosynthetic out of the soil should be performed in a displacement-controlled mode in a horizontal direction (Figure 7). ASTM D 6706-01 describes smaller box dimensions. A pull-out behaviour is identified if displacements of the specimen are monitored over its entire embedment length. The first test stage is reached when a movement of the embedded end of the specimen is monitored wheras the final stage is reached upon a movement of the specimen with equal velocities at the front and at the embedded end (rigid-body motion). A large scale pull-out test device is used at the Institute of Geotechnical Engineering and Mine Surveying to examine the effects of huge number of influence parameters under static and cyclic loading conditions. Detailed information about the test device can be found in Meyer et al. (2004) and Nernheim and Meyer (2004).
Figure 7. Schematic cross-section of the
Pull-out test box
If the horizontal force is plotted against the displacement mostly a distinct peak can be monitored which is called maximum pull-out force or peak (Figure 8). The interface shear resistance in the pull-out test is calculated as follows:
where
F Pull-out force
b Width of the geosynthetic specimen
l Embedment length of the geosynthetic specimen
The force is divided in the upper and lower shearing plane of the specimen (Figure 5) which leads to a double-sided shear plane of the system. The pull-out force is applied to the footprint of the specimen. In the case of non-continous specimens (for example geogrids) this leads to a mixture of the effects of different load transference mechanisms. Key parameters of the pull-out tests are extracted in the following table.
Table 1. Influence parameters for the pull-out test
Surcharge
The magnitude of the vertical surcharge evolves as a key parameter because the influence on the test results is significant and in practise this parameter is variable with the installation depth of the reinforcements layers. The horizontal force – displacement charts show a significant increase of the peak pull-out force and a larger displacment until the peak is reached with an increase in the vertical surcharge (Figure 8). This results firstly from an increase in friction because of the additional surcharge, secondly from the increase of the horizontal stresses sb in front of the transverse members. The peak pull-out resistance tp is increasing approximately in a linear relationship to increasing vertical stresses s in the pull-out plane for both tested geogrids. Significant differences could be monitored between index- and model tests in sand whereby the gradient of the straight line (friction component) is comparable. This could be due to higher constraints at the front wall because of arching effects in the index tests.
Figure 8. Influence of Surcharge on the Pull-out behaviour
Installation density
The influence of the installation damage is evaluated in index tests with sand 0/4 and a mean embedment length of 0.50 m. The peak pull-out force is increasing with higher installation densities whereas the displacement of the specimen which is reached at the peak sp seems to be uninfluenced by the density (refer to the woven geogrid in figure 9). In the range of low and medium densities there are barely any differences between the woven and the extruded geogrid (Figure 9). It is presumed that the vertical surcharge resulted in an additional compaction of the soil with the installation density of 1,70 g/cm³. This effect might have lead to comparable densities during the test. The higher surcharge of 60 kN/m² intensified this effect. Between 1,75 and 1,80 g/cm³ smaller increases in the horizontal force could be monitored at the steel strip compared to the grid specimens. It can be concluded that load transference mechanisms in front of the transverse members get greater advantages from higher densities than the friction based load transference mechanism of the steel strip. If a bearing capacity failure theory for the load transference in front of the transverse members is assumed, the load transference potential increases significantly because of higher densities and an increase in the friction angle (Jewell, 1996).
Figure 9. Influence of Installation density on the Pull-out behaviour
Embedment length
The embedment length of the reinforcement is one of the key parameters because in practice it is varied until it reaches the optimum. At the beginning of the tests a comparable increase in horizontal forces could be monitored regardless to the embedment length (Figure 10). With increasing embedment lengths an increase in the peak pull-out force Fp could be monitored: This relationship could be described for the woven and extruded geogrids in a good approximation as a linear regression (Figure 10).
Figure 10. Influence of Embedment length on the Pull-out behaviour
Load transference
In the following charts (Figure 11) the displacements of several tell-tale displacement transducer located at different positions in throughout the embedded geogrid are related to the displacements at the front of the specimen. At small surcharge levels the geogrid acts like a rigid body and the whole specimen is activated. At higher surcharges elongations evolve in the front part and the displacments of the embedded parts of the geogrid are smaller than at the front. This indicates a high transference of tension forces from the specimen in the soil in the front part which is reduced in the middle and rear parts of the grid. At low degrees of utilization (the peak horizontal force Fp is taken as a reference) the horizontal forces are transferred in the soil in the front part of the grid. With increasing horizontal forces a larger part of the geogrid is activated because forces need longer embedment lengths to be transferred in the soil completely. At peak force (100 % Fp) the area integral of load transference over the embedment length reaches its maximum value. The movement of the geogrid heads for a rigid-body motion.
Figure 11. Activiation of the embedded geogrid
Discussion
This evaluation shows some significant differences between shear- und pull-out tests. In contrast to the shear test tension forces are applied to the reinforcement in the pull-out test, resulting in elongations of the geosynthetic material. Load transference takes place depending on the displacements of the specimen: Larger displacements in the front part of the specimen result in a higher load transference like at the worm of a screw. The pull-out test shows in theory a double-sided shear-plane above and below the geosynthetic specimen whereas the shear test shows a single-sided shear plane. Load transference mechanisms in front of the transverse members are activated depending on the opening size of the geogrid. In theory comparisons of pull-out forces between shear and pullout tests are only possible with reinforcement materials with a very low extensibility and a continuos structure because elongations and opening sizes should not have any effect on the results. Shear tests could result in higher interface friction coefficients than pull-out tests with fine-grained soil because there might be additional shearing of soil to soil through the openings of geogrids. On the other hand gravel could lead to higher pull-out test results because of significant influences of interlock effects in the pull-out test. The evaluation of the effects of key parameters in pull-out tests shows that already minor changes of the influence parameters could lead to significant changes in the peak pull-out force. Therefore precise values should be taken as input to get useful and sensible pull-out and interface friction values. The analyses show a almost linear relationship between peak pull-out force and embedment length and surcharge in the considered range of data. Therefore the use of the equation to calculate FB in a simplified way could be confirmed.
Conclusions
The interface interaction behaviour is a key parameter in the design of geosynthetic reinforced structures. The bearing behaviour of these structures is based on the transference of tension forces from the soil to the geosynthetic and vice versa by friction, passive earth resistance and interlock effects. It should be kept in mind that – depending on the type of loading and the position of reinforcement layers – a shear or a pull-out mode might exist. It was shown that both loading types could best be simulated in a special test device. The results of these tests are influenced by a huge number of parameters. The influence of some key parameters on the results of the pull-out tests are shown with our own experimental data. A realistic choice of test type and proper influence parameters for practical use is suggested because of the large variance of the results with small changes of the influence parameters. The parameter “surcharge” will be extended in additional test steps to simulate the cyclic effects of traffic on the anchorage behaviour of geosynthetics. The results will be presented in the future.
References
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