THE STEADY STATE OF SANDY SOILS
RAMON VERDuooi) and KENJI IsHIHARAii)
ABSTRACT
An alternative procedure to evaluate the void ratio of triaxial test samples is introduced. This method is recommended particularly when very loose samples are tested and an important volume change occurring during the saturation process is expected. In addition, using Toyoura sand a comprehensive set of triaxial tests carried out under both undrained and drained conditions of monotonic loading is presented. For the undrained contractive responses, the results showed two stages associated with the steady state. After the peak strength, the deviator stress drops to a minimum value which can be seen as a quasi steady state, thereafter, the strength increases to an ultimate value corresponding to the actual steady state. Undrained dilative responses clearly indicated the existence of an ultimate state developed at large deformations which represents the steady state of deformation. The results indicate that the quasi steady state is slightly affected by the initial mean stress, whereas, the steady state is unaffected by the initial mean stress. Furthermore, the locus of the ultimate states achieved through drained conditions of loading was shown to be coincident with the steady state line evaluated by means of undrained tests. Finally, according to the relative position of the steady state line with respect to the isotropic consolidation curves for the loosest and densest states of a given soil, the index, Relative Contractiveness, Rc, is proposed. It is postulated that Rc is related to the inherent liquefaction vulnerability of a soil.
Key words: liquefaction, sandy soil, silt, triaxial compression test, undrained shear (IGC: D6/D7)
INTRODUCTION
In the past, the term "liquefaction" has been used to describe all phenomena that are related with the undrained response of cohesionless material where an important build up of pore water pressure as well as a significant amount of deformation take place. At least two different phenomena, however, should be distinguished: flow failure or true liquefaction and cyclic mobility. Although these concepts were presented early by Casagrande (1975) and Castro (1975), perhaps only since the last decade they have been widely recognized and accepted. The phenomenon defined as "true liquefaction" is characterized by a quick increment of pore water pressure followed by a sudden loss of strength until a residual value is achieved. The term ''cyclic mobility'' introduced by Casagrande (197 5) denotes the undrained cyclic soil response where the soil mass does not undergo any loss of strength, but it undergoes a kind of strain softening, which is mainly a consequence of the build up of pore water pressure caused by the cyclic loading. The study discussed herein is concerned with the first phenomenon. Recently, interest in the importance of developing a suitable methodology to analyze the stability of saturated
poorly compacted sandy soil deposit has increased. This fact comes as a consequence of the occurrence of large landslides in natural slopes, darn failures and flow failures of hydraulic placement of artificial island fills or reclaimed land areas along coast lines (Ishihara et al., 1991). A better understanding and a more suitable characterization of the undrained response of saturated cohesionless materials are therefore needed. Consequently, in the present study experimental evidence useful to obtain a better understanding of sandy soil behavior is presented. In addition, a parameter to identify the intrinsic potential for liquefaction of a given soil is introduced.
TESTING EQUIPMENT AND SOIL TESTED
In order to cover a wide range of confining pressures, and at the same time to have accurate measurements, two triaxial test apparatuses designed for a different level of pressure and load were used. A low and a high pressure triaxial cell for maximum pressures of I MPa and 5 MPa were designed. For each test, the most appropriate test apparatus was selected depending on the desired confining pressure and the anticipated undrained response. For instance, when large dilative behavior of the soil specimen
il Geotechnical Section !DIEM University of Chile, Plaza Ercilla 883, Santiago, Chile. Former Graduate Student, Univ. of Tokyo, Japan. iil Former Professor, Department of Civil Engineering, University of Tokyo, Bunkyo-ku 113, Tokyo.
Manuscript was received for review on May 17, 1994.
Written discussions on this paper should be submitted before January 1, 1997 to the Japanese Geotechnical Society, Sugayama Bldg. 4 F, Kanda Awaji-cho 2-23, Chiyoda-ku, Tokyo 101, Japan. Upon request the closing date may be extended one month.
was expected, the cavitation was effectively avoided by means of high back pressure using the high pressure apparatus. Lubricated as well as enlarged end plates were used in order to minimize non-homogeneities in the strain distribution throughout the samples and particularly to avoid the development of shear bands. The axial load, pore water pressure, axial deformation and volumetric strain were measured by electrical transducers and automatically stored in a personal computer. All the tests were conducted under strain-controlled condition of loading. The deformation rates were 1 and 0.5 mm/min for undrained and drained tests, respectively. The initial dimensions of the specimens were 5 em in diameter and 10 em in height for those specimens tested in the low pressure triaxial cell, and 6 em in diameter and 12 em in height in the case of samples tested in the high pressure cell.
All the tests were performed on the standard Japanese Toyoura sand. This sand has a mean diameter of D 50 =0.17mm, a uniformity coefficient of Uc=l.7, a maximum void ratio of 0.977, a minimum void ratio of 0.597, and a specific gravity of 2.65. Toyoura sand is a uniform fine sand consisting of subrounded to subangular particles and composed of 75% quartz, 22% feldspar and 3% magnetite (Oda et al., 1978).
SAMPLE PREPARATION
To prepare the specimens, the so-called moist placement or wet tamping method of sample preparation was used. Oven dry soil was mixed well with distilled water in a proportion of 5% by weight and compacted in six and ten layers in the case of the low and high pressure apparatus, respectively. After the initial density was determined, and the total weight computed, each layer was carefully compacted with identical height and amount of wet soil. Thereafter, the specimens were installed in the pedestal and C02 gas followed by de-aired water circulated throughout from the bottom to the top. After the cell was assembled, the degree of saturation was improved by means of back pressure which was considered acceptable when the B-value was equal to or greater than 0.95.
EVALUATION OF SAMPLE VOID RATIO
Samples loosely compacted are susceptible to potential error in the evaluation of the void ratio. During the saturation process a partial collapse of the unstable structure occurs and a significant variation in the sample dimension takes place, which can not be measured using ordinary test procedures (Sladen et al., 1987). Two alternative procedures to assess the void ratio of the specimens after they have been saturated were therefore developed which are described below:
a) Using sample dimensions.- This method corresponds to the ordinary procedure based on the direct evaluation of the height and diameter of the samples after C02 and de-aired water have been percolated throughout the specimens, and therefore, any possible collapse
has occurred. An improvement in the procedure has been used however, avoiding the dismanteling of the cell after the saturation of the samples has been completed. After the air in the voids of the sample has been replaced by C02, a vacuum of 0.02 MPa for the sample tested in the low pressure triaxial cell and 0.05 MPa for the sample tested in the high pressure triaxial cell was applied through the upper and lower drainage lines of the specimen with tanks A and Bas illustrated in Fig. 1(a). When the vacuum is applied, the position of tanks A and B is such that the water level in the tanks is below the sample. Next, in order to induce percolation of water throughout the specimen under vacuum, tank A is moved up from its initial position to a second location approximately 50 em above the top of the sample. As the water flows into the specimen, a sort of collapse on the very loose soil structure occurs, and accordingly, the sample dimensions change. The percolation of water is performed until in the pipe connected to the top of the sample air bubbles are not observed any more. Thereafter, tank A is moved down to its initial position and then the dimensions of the sample are measured. The diameters were taken to an accuracy of 0.01 em with a calibrated metal tape and the height was measured to an accuracy of 0.01 em by means of a calibrated caliper. Consequently, the initial volume of the sample was evaluated and modified later considering the volume change that occurs during consolidation. b) Using the water content of the specimen.-This method was developed considering that for saturated samples, the void ratio is directly related with the amount of water in the sample. For clayey soils, the procedure
Fig.
does not involve significant difficulty, but in sandy soils some special technique is necessary, for instance, ''freezing" the sample. The authors have developed an alternative method however that seems to be simpler than the current procedures, which involve the following steps: after the test is finished, the drainage valves are closed, so that the specimen is in an undrained condition. The back pressure on the lines is completely released and the level of the water in the burette, Vi, is recorded. The drainage valves are then opened and connected to the burette. Next, the cell pressure is increased to the maximum capacity of the equipment, and then an axial loading and unloading process is applied in order to remove from the sample as much water as possible which flows into the burette. Thereafter, the cell pressure is decreased to around 0.2 MPa, the drainage valves are closed again, and the level of the water in the burette, V1 , recorded. Then, the cell pressure is totally released and the triaxial cell dismounted. Because the specimen is finally unloaded under an undrained condition, it develops a negative pore water pressure which allows the sample to remain upright. Next, the upper cap is removed and air goes into the sample (because of the negative pore water pressure) creating an apparent cohesion that permits the sample to be handled. Immediately, the membrane is removed from the sample, and by means of a spatula, all the soil attached to both the membrane and to the end platens is carefully removed. The remaining water content of the soil sample, w,, is then measured. Therefore, the void ratio of the specimen can be computed from the following expression:
(V1- Vi+w, Wd) e Wd Gs (1)
where, Wd is the dry weight of the sample and Gs is the specific gravity of the soil.
The first method is basically the common practice to evaluate the void ratio of a sample, while the second method is an alternative procedure. To investigate the effectiveness of this alternative procedure, three series of samples were prepared repeating as close as possible all the steps involved in the preparation. Figure l(b) shows the results of these three series of tests. It can be observed that the scattering in the void ratios evaluated through the water content is much smaller than the one obtained by the ordinary procedure using the sample dimensions. This fact is indicative of the repetitiveness and effectiveness of the proposed procedure. In addition, as shown in Fig. l(b), the results using these two procedures consistently indicated that the void ratios measured through the water content were smaller than the void ratios computed from the sample dimensions. For dense specimens however, the difference between these two methods was negligible. The discrepancy between these two methods may arise from the subsequent steps wherein the triaxial cell is assembled and likely, some additional volume change takes place which can not be computed by the first method. The procedure based on the measurement of the water content at the end of the test has therefore
been adopted as a more reliable procedure to evaluate the void ratio. Hence, void ratios estimated by this method have been used as the representative values of the samples and reported in this paper.
MONOTONIC UNDRAINED RESPONSE
Three series of undrained monotonic compression tests with consolidation pressures varying in a wide range and constant void ratios achieved after consolidation, were carried out. Figure 2 for example, shows the stressstrain curves and the corresponding effective stress paths for a series of tests with a common void ratio after consolidation of e=0.735. The effective mean stress is evaluated as p' =(a1 +2a3)/3 and the deviator stress as q=(a1-a3). As can be seen, the soil response is such that an ultimate condition is developed at large deformation which is identical to all the specimens, independent of the initial confining pressure. It is important to note that during unloading the effective stress paths are coincident, suggesting that a special common fabric was developed at large deformation.
Another series of tests performed with a void ratio after consolidation of e=0.833 and different initial confining pressures is shown in Fig. 3 in terms of stressstrain curves and effective stress paths. For initial confining pressures of 2 and 3 MPa, the response of the specimens shows a drop in strength, and consequently, the specimens develop a minimum strength which occurs between 5 to 10% of axial strain. It is of interest to note, that the minimum strength developed is
mean stress, p' (MPa)
Fig. 2. Undrained triaxial tests for e=0.735: a) stress-strain curves; b) effective stress path
Fig. 3. Undrained triaxial tests for e=0.833: a) stress-strain curves; b) effective stress path
slightly affected by the initial effective confining pressure. It should also be noted that, despite the large difference in the stress-strain behavior at an early stage of the loading, the samples tend to have the same ultimate strength at a large level of deformation. In addition, in this series, the effective stress paths during unloading are coincident with each other suggesting the development of a common fabric at the stage of large deformation. The stress-strain curves and the corresponding effective stress paths for another series of tests performed with a void ratio after consolidation of e=0.906-0.908 and with effective confining pressures varying from 0.1 to 2 MPa are shown in Fig. 4. As can be observed, for the complete range of pressure used, the soil behavior indicates a peak deviator stress, and the higher the initial confining pressure the higher the peak deviator stress. A minimum strength is developed at a medium range of axial deformation between 4 to 16%. As the previous results, the minimum strength seems to be only slightly affected by the initial confining pressure, while the ultimate deviator stress developed in these three specimens is the same, regardless of the value of the initial confining pressure. It is also of interest to note that for the specimen consolidated under 0.1 MPa, the effective stress path reaches the ultimate state to the right of the initial state indicating that, the response is finally dilative, even though in the range of axial deformation between 1 to 6%, the behavior was clearly contractive with a small drop of strength. It is important to mention that, in this case, the condition of continuous deformation under a constant shear stress level is not strictly satisfied at large deformation. The rate of varia-
stress, p' (MPa)
tion nevertheless is rather small, so in this situation the state of stress developed close to 26% of axial strain has been considered as the condition associated with the ultimate state. The authors believe that the stresses developed at this level of deformation are from any practical point of view, close enough to the actual ultimate condition in the case of sandy soils.
This series of undrained test results have shown two soil responses, a dilative one with a deviator stress that is always monotonically increasing up to an ultimate state achieved at large deformation where the soil sample deforms continuously under a constant shear stress, and constant effective mean stress. Another soil response is the contractive one with the development of a minimum strength that is followed by a dilative behavior where the strength is regained and it eventually reaches an ultimate value at large strains. The latter soil response indicates two particular conditions that require especial attention: a) the minimum strength and b) the ultimate state developed at large strain level. These stages are of particular importance due to the fact that they represent different levels of strength. It is apparent that these two conditions can be associated with the steady state of deformation (Poulos, 1981), because the requirements of continuous deformation under constant shear stress and constant normal stress are to some extent satisfied. The additional requirement of constant volume is automatically satisfied during undrained tests and the condition of constant velocity is fully satisfied by the strain controlled loading system.
The condition of minimum strength has been referred
Fig. 4. Undrained triaxial tests for e=0.907: a) stress-strain curves; b) effective stress path
to as the quasi steady state, (Alarcon-Guzman et al., 1988; Ishihara, 1993; Verdugo, 1992) whereas, the condition reached at large level of strain is likely associated with the actual steady state. The shear stress mobilized at the minimum strength stage is definitely smaller than the stress mobilized at the ultimate steady state, however, the strain level required for the ultimate state is much larger than the strain associated with the minimum strength.
THE QUASI STEADY STATE
From those specimens where a drop in strength takes place, the minimum strength condition or the quasi steady state has been plotted in Fig. 5 in terms of void ratio and effective mean stress. The initial states of void ratio and consolidation pressures are indicated by squares. As can be observed, for the wide range of initial effective confining pressures and void ratios used, there exists a clear correlation between the void ratio and the effective mean stress developed at the stage where the minimum strength is mobilized. This line is referred to as the quasi steady state line (Verdugo, 1992; Ishihara, 1993). In spite of the clear trend shown in Fig. 5 by the quasi steady state line, some scatter in the data is apparent. This is due to the fact that the mobilized minimum strength is affected to some degree by the initial consolidation pressure. The larger the initial effective confining pressure, the larger the minimum strength and the corresponding effective mean stress. Nevertheless, the experimental results indicate that this effect is not significant and accordingly, it would be possible to draw a single line representing an average condition of the quasi steady state in the e-p' plane and use it as a convenient reference line to facilitate the evaluation of the minimum strength. It has been shown elsewhere (Verdugo, 1992; Ishihara, 1993) however, that this line is strongly affected by both the initial fabric and structure of a soil mass. The use of the quasi steady state line is therefore restricted to those cases where the soil deposit and the soil sample tested in the laboratory have similar fabric.
The contractive response is only developed by those samples with an initial combination of void ratio and effective mean stress that can be represented by a point lo-
Fig. 6. Strength envelope at the quasi steady
cated well above the steady state line in the e-p' plane. This observation confirms previous results reported by Castro (1969); Castro et al. (1982); Been et al. 1985; Dobry et al. (1985), and Poulos et al. (1985), among others. It is of particular importance to mention that the state of minimum strength coincides with the condition of phase transformation introduced by Ishihara et al. (1975). The phase transformation was defined however to imply a temporary state of transition from contractive to dilative behavior of sand, irrespective of whether it involves a temporary drop in shear stress or not. The quasi steady state has to be seen therefore as the particular case of phase transformation where a temporary drop in shear stress takes place over a limited range of shear strains.
Regarding the resistance developed during the quasi steady state, it can be easily understood that the shear stress mobilized at this stage of deformation is a consequence of frictional resistance between the particles of the soil. The effective normal stress and shear stress should therefore be uniquely correlated through some angle of internal friction. To explore this aspect, the shear stress, q I 2, and the effective mean stress, p', attained at the quasi steady state have been plotted in Fig. 6. As can be observed, the state of stresses at the quasi steady state can be represented fairly well by a straight line passing through the origin in the q I 2-p' plane. The angle of internal friction obtained from these data is close to 31 o.
THE STEADY STATE OR ULTIMATE STATE FROM UNDRAINED TESTS
Under undrained loading condition, irrespective of the initial state of the specimens, when the strain level is large enough, the soil mass tends to be in a state of continuous deformation under constant shear stress and constant mean stress. This stage of the soil response is quite apparent in those tests shown in Figs. 2 and 3 when the axial strains are larger than 20-25%. As can be observed in Fig. 4 however, there are responses where the deviator stress and the effective mean stress are still increasing af-
Fig. 5. Quasi
ter an axial strain of 28%. Nevertheless, the increments are small and always at a decreasing rate, hence in these cases, the stresses at an axial strain around 26% have been taken as representative of the ultimate state of the specimens. In Fig. 7, a good correlation can be observed between the specimen void ratios and the effective mean stress developed at large deformation, which corresponds to the steady state line. The initial states of the samples are indicated in Fig. 7 by squares showing that, in contrast to the quasi steady state line, the steady state line can be obtained independently of the initial state of the specimens. In addition, experimental results reported by Verdugo (1992) and Ishihara (1993) have shown that the steady state line is unaffected by the initial fabric as long as the soil mass is homogeneous.
Concerning the frictional resistance developed at this state, Fig. 8 shows the shear stress, q/2, and the effective mean stress, p', computed from each test. As can be seen, all the data points fall in a straight line passing through the origin indicating that a unique friction angle is mobilized at the ultimate state or steady state which is in perfect agreement with experimental data reported by Negussey et al. (1988) using ring shear tests. For Toyoura sand, the experimental results indicated that the slope of this line is close to 0.62, confirming a friction angle in the
Fig. 8. Strength envelope at the
steady state of deformation of around 31 o.
MONOTONIC DRAINED RESPONSE
A series of conventional triaxial tests with constant lateral stress under drained condition of loading were performed for three different states of packing; very loose, loose and medium. The deviator stress versus axial strain and void ratio for consolidation pressures of 0.1 and 0.5 MPa, are shown in Figs. 9 and 10, respectively. As can be observed, under a small level of strain, the stress-strain curves are different depending upon the initial density of the sample. As the level of strain becomes large however, all the curves merge into a single one. Similar behavior is observed in terms of deviator stress and void ratio. Initially, at zero level of shear stress, the starting void ratios are different, but as the strain level increases, the curves tend to achieve a common void ratio and a common deviator stress, which confirms experimental results reported by Casagrande (1936), Roscoe et al. (1958) and Been et al. (1991). The soil response achieved at a large level of strain under drained condition of loading therefore can be seen as the corresponding drained steady state of deformation
For all the tests performed under drained condition of loading, Fig. 11 shows the paths in terms of void ratio and mean stress. The circles indicate the data points related to the steady state condition evaluated from undrained tests, and the black squares indicate the ultimate
SAND
Fig. 9. Drained triaxial tests for cr 0=0.1 MPa: a) stress-strain curves; b) void ratio versus deviator stress
Fig. 7.
Fig. 10. Drained triaxial tests for a 0=0.5 MPa: a) stress-strain curves; b) void ratio versus deviator stress
SANo:·····
11. State diagram evaluated from both drained and undrained triaxial tests
conditions achieved by the drained tests which should be associated with the drained steady state. As can be observed, there is a very good agreement between the steady state conditions obtained from both undrained and drained tests. It is important, however, to note that even though the general trend presented by the drained tests is clear, the scatter in the data points concerning the ultimate state of these tests is much more significant than those obtained for the case of undrained tests. In this regard, it seems that drained tests are not the most suita-
12. Stress ratio, q/p', versus axial strain
ble tests to evaluate the steady state line with undrained tests being more preferable.
In addition, for three different initial densities and for consolidation pressures of 0.1 and 0.5 MPa, the stress ratio, q I p', versus the axial strain are shown in Figs. 12(a) and (b), respectively. It can be seen that at a large strain level, the mobilized stress ratio, q I p', is constant and independent of the initial density and confining pressure. This fact indicates that, for the level of pressures and densities investigated, the friction angle mobilized at a large strain level is unique and unaffected by sample density and consolidation pressure. In addition, the computed value of q/2p' is close to 0.62 which is about the same value obtained from undrained tests. The friction angle mobilized at the steady state condition therefore is a unique value regardless of the density, level of pressure, and type of loading (drained or undrained).
CHARACTERISTIC LINES IN THE e-p' PLANE
The e-p' plane provides a good representation of the steady state line, and it may also be useful to define boundaries which can characterize the soil response. For sandy and silty soils it is conceptually possible to define an upper boundary using the isotropic consolidation curve for the loosest state that a given cohesionless soil may attain. This curve is equivalent to the normal consoli-
Fig.
Fig.
for a) a 0=0.1 MPa and b) a 0=0.5 MPa
dated curve for clays in the sense that defines a limit over which a combination of void ratio and effective mean stress can not exist. It is important, however, to keep in mind that this curve may be different for different sample preparation procedures as shown in Fig. 13 (Ishihara, 1993). It is recommended that the consolidation curve for the loosest state be evaluated by means of a sample performed by the moist placement (wet tamping) method of preparation and then saturated. Based on the authors' experience, this method of sample preparation permits the achievement of the loosest packing compared to any other method of sample preparation. In some soils it even provides a larger void ratio than the maximum void ratio evaluated using either the USA or the 1apanese codes (Verdugo, 1992).
Similar to the upper boundary defined by the consolidation line of the loosest state, it is possible to define a lower boundary. For the common range of pressures anticipated in engineering practice, the isotropic consolidation curve for the densest packing provides the lowest limit of states in the e-p' plane. For Toyoura sand both the isotropic consolidation curve for the loosest and densest state are shown in Fig. 13 (Ishihara, 1993). It is readily apparent that for the case of the densest state, the volumetric strains caused by isotropic loading are very small even though the confining pressure is significantly high. For practical purposes therefore this curve can be approximated by a horizontal straight line passing through the minimum void ratio. This simplification is obviously limited by the pressure from which the particle crushing began to be important. According to the test results shown in Fig. 13, in the case of Toyoura sand this pressure would be greater than 4 MPa which includes most of the cases encoutered in practice. There are other soils such as carbonate containing sands and decomposed granite sandy soils however that are much more crushable. For these soil types the proposed simplification is still valid, but for a smaller region. Nevertheless, if the particular soil under consideration seems to be extremely crushable, the simplification can be avoided and the corresponding isotropic consolidation test for the densest state performed.
LIQUEFACTION VULNERABILITY
A lack of a suitable parameter exists at present to classify any given soil according to its intrinsic vulnerability against liquefaction. Some general ideas have been presented in this regard, and they have basically been established based on the shape of the grain size distribution curves (Tsuchida, 1970; Ishihara et al., 1980). It is well known however that there are others factors that also control the liquefaction vulnerability of a cohesionless soil, for example, particle shape, particle hardness, fines content (Verdugo, 1989), and plasticity of the fines. All of these factors that are not dependent on the state of a soil mass, and are material properties, are somewhat reflected in the location of the steady state line and on the position of both the consolidation curves of the loosest and densest state. In order to define a parameter that reflect to some extent the intrinsic potential of liquefaction of a given material, therefore these three references curves will be considered.
In a cohesionless material, the projection of the steady state line in the e-p' plane represents the combination of void ratio, and effective mean stress attained ultimately when the soil is deformed greatly. For a homogeneous soil mass, the steady state line is a unique reference line unaffected by the type of soil deposition and initial state conditions of density and pressure. It is also independent of whether the load is drained or undrained. For an undrained loading condition, the steady state line provides a very stable and physically meaningful reference line dividing those states that ultimately develop either positive or negative pore pressure. Although it may be thought that the quasi steady state line can also be used as a reference line, this idea does not work when an intrinsic soil property is expected to be defined. This restriction comes from the fact that the quasi steady state line is strongly affected by the initial soil fabric (Verdugo, 1992; Ishihara, 1993).
The isotropic consolidation curves for the loosest and densest states provide a set of boundaries for any possible soil state. If attention is drawn to the position of the steady state line with respect to these two boundaries, it is possible to realize that when the steady state line is located very close to the upper boundary defined by the isotropic consolidation line of the loosest state, as shown in Fig. 14(a), the area, Ac, that is associated with those states where the soil mass can be potentially unstable is small. Conversely, Fig. 14(b) shows a material with a steady state line closer to the isotropic consolidated curve of the densest state, hence with a dilative area, Ad, rather small. In this situation, there exists a significant possibility for the soil deposit to be in such states that can develop a contractive response associated to a flow failure or "true liquefaction". Consequently, it is suggested that according to the relative position of these curves with respect to each other, it is possible to evaluate the intrinsic vulnerability of a given soil against liquefaction. Thus a parameter of the form of Ac / (Ac +Ad) seems to be an appropriate parameter concerned the intrinsic liquefac-
Fig. 13. Isotropic consolidation curves for Toyoura sand samples prepared using three different methods (Ishihara, 1993)
LIsotropic consolidation line, loosest state
consolidation line, densest state Steady state line
Effective mean stress, p'
LIsotropic consolidation line, loosest state
Isotropic consolidation line, densest state
Effective mean stress, p'
Fig. 14. Representation of a soil with a) small vulnerability against liquefaction; b) large vulnerability against liquefaction
tion potential. Figure 15 illustrates the areas Ac and Ad considering the general trend of the steady state line and the isotropic consolidation lines for the loosest and densest states. It is important to note, that for high pressure the loosest and densest states merge with each other which has been shown experimentally by Vesic et al. (1968) and Miura et al. (1984), among others. In addition, it is well known that under a sufficiently high pressure, the soil behavior is fully contractive independent of the initial void ratio. This means that in the e-p' plane the steady state line, for high pressures, must be lo-
cated to the left and below the isotropic consolidation lines. It is clear, however, that for a low pressure and an initial dense state, the soil behavior is dilative which implies that the steady state line has to be located to the right of the isotropic line for the densest state. Therefore, in the e-log p plane, the steady state line has to cross the isotropic consolidation line for the densest state.
From a practical point of view, the complete evaluation of the areas Ac and Ad is difficult, because it would be necessary to use very high pressure in order to evaluate the consolidation curves to the point where they merge with each other. It seems reasonable nevertheless, to make a simplification and only take into account the ratio between the range of void ratios where the soil is contractive and the total range of void ratios where the soil can exist for an arbitrary value of effective mean stress of 0.1 MPa. In order to account for the intrinsic potential of liquefaction of a given soil, the index property, Relative Contractiveness, Ro is proposed which is expressed as follows, (emax)I- (ess)I
(emax)I- (emin)I
Figure 16 shows schematically (emax)h (emin)I and (ess)I which denote respectively, the maximum, minimum and steady state void ratios, all for an effective mean stress of 0.1 MPa. If the proposed approximation of the isotropic line for the densest state is used, the value of (emin) 1 would be equal to emin. It should be noted that the defined relative contractiveness, Rc, is not a parameter specifying a state of the soil, but is rather an index representing an intrinsic material property which is largely dependent on the grain composition of a soil. It is important also to keep in mind that the actual resistance against liquefaction is a function of the state of the material. From a theoretical point of view, Rc may have values between 0 and 1. A value of Rc= 1 represents a hypothetical soil that for any initial states will have a contractive response, whereas Rc=O represents a hypothetical soil that will always have a dilative response. For real soils, Rc should have a tendency to be closer to 0 or 1 according to the intrinsic capacity of contraction or dilatation of the soil. For Toyoura
Effective mean stress, p'
Fig. 15. State diagram indicating the contractive and dilative regions
Effective mean stress, p'
Fig. 16. Definition of the relative contractiveness, R,
sand, Fig. 17 shows the location of the loosest and densest isotropic consolidation curves and the steady state line. It is important to note that the loosest state achieved by the moist placement sample preparation method reproduces a state looser than the one obtained by the conventional procedure using dry soil. In addition, in Fig. 17 for 0.1 MPa, the corresponding values of (emax) 1, (emin)I and (ess)I are shown. For this sand the relative contractiveness has a value, Rc=0.25, which can be considered as a fairly small contractive material.
Different sandy soils containing low plastic fines and silty soils classified as ML were tested following the same procedure explained above; the corresponding relative contractiveness, Rc, was evaluated and plotted against the fines content in Fig. 18. The set of data for each soil is presented elsewhere (Verdugo, 1992). The soil with 100% fines was produced from the Toyoura sand crushing it by means of a ball-mill. As can be seen in Fig. 18, the value of Rc tends to increase with increasing fines content leading to the conclusion that the more low plastic fines content, the greater would be the opportunity for the soil to exist in the field in a contractive state that can induce flow failure or liquefaction.
Fig. 17.
Fig. 18. Effect of the low plastic fines content on
CONCLUSIONS
It has been shown that in those cases of undrained loading with peak strength, there exist two conditions that may be associated with the steady state of deformation. The first one corresponds to the development of the minimum strength, and it has been named the quasi steady state. It is developed at a small to medium level of deformation, typically between 1 to 16% of axial strain. The second condition is achieved at a high level of deformation, typically beyond 25% of axial deformation, and it is associated with the ultimate state developed by the soil sample. This ultimate condition corresponds to the actual steady state, and it is always achieved irrespective of the initial state of the soil sample and whether the response is contractive or dilative. Conversely, the quasi steady state can only occur when the initial states of the soil are well above the steady state line, so the response is contractive.
The experimental results strongly indicated that the steady state or ultimate condition is not affected by the initial confining pressure. The results have shown, however, that the quasi steady state is slightly affected by the initial confining pressure, but for practical purposes it seems reasonable to assume that it is independent.
A series of undrained tests conducted under different initial effective confining pressures, but at the same void ratio after consolidation, have indicated identical effective stress paths during unloading from the steady state condition. This observation strongly supports the idea of Casagrande regarding the existence of a unique fabric developed during the steady state.
The results of drained tests at large deformations indicate the existence of an ultimate state without volumetric strain and continuous deformation under constant shear stress. The ultimate states evaluated from drained tests are in good agreement with the steady state obtained from undrained tests. At large deformations, therefore, both undrained and drained loading conditions converge to the same curve in the e-q-p' space, which corresponds to the steady state line.
Based on the range of void ratios where the soil response is contractive with respect to the total range of void ratio where a soil can exist for an effective mean stress of 0.1 MPa, the parameter, Relative Contractiveness, Ro is proposed to evaluate the intrinsic potential of liquefaction for a given soil. The larger the value of Rc the larger the intrinsic potential of liquefaction for a given soil.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the financial support provided by the Ministry of Education, Science and Culture, Government of Japan (MONBUSHO) which made this present study possible.
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Other documents randomly have different content
pleasaunce, for the maltster said he had other uses for his money than to be wasting it on gaudy nonsenses like flowers.
But returning now to the old wing, let us peep in for a moment on old Adam Lockit, the gatehouse keeper, in his sanctum deep hidden in the recesses of the vaulted archway piercing the tower, and giving on its outer side upon the drawbridge, which was still let down at dawn, and drawn up at sunset, by the massive old iron chains working through the wall.
Not a snugger corner in the whole establishment than this of Master Lockit's. Within the last year or so, since he has not been so young as he used to be, and the dragging at those heavy chains has come to be a bit of a pull upon him, though he is a hale enough man for his threescore and ten, he has condescended to accept the assistance of a lad, employed originally as a Jack-of-all trades in the malting-yard, but promoted to the dignity of domestic factotum by reason of sundry excellent qualities. Foremost among these stand unimpeachable honesty and placid temper. A characteristic less distinguishing Barnaby Diggles, for so the lad was named, was animal courage. He was, in other words, an arrant coward; in the matter at all events of hobgoblins and things of the sort. He was, however, but just turned of sixteen; and time as yet had never tried his mettle with any real and substantial danger. Meanwhile, nothing so much charmed him as having his imagination tortured with ghost stories by the village gossips; unless, indeed, it was to sit and incline his ears to the hundred and one yarns of all countries and ages that Adam Lockit loved at least as much to spin.
Barnaby Diggles. The gatehouse room.
When Barnaby is not to be found after his day's work for love nor money, you are safe to run him to earth in the gatehouse room. A Sindbad's valley it is to him, a Hassan's cave, with all its treasures of crossbows and battle-axes, and catapult relics; its bits of chain-armour, its battered helmets, stags' antlers, and huntinghorns, for all and each of which Adam had his story to tell, as vividly as if he had been honoured by the personal acquaintance of Joan of Arc and William Rufus, or gone a buck-hunting in Hainault Forest with the merry monks of Waltham or bluff King Hal.
What gruesome tales too, Master Lockit, sitting of bitter winter nights in his warm ingle neuk. could tell you between the whiffs of his pipe, about yonder spiral staircase, "There, just behind you," which goes winding up past the nail-studded iron clamped door, shutting in the old wing's upper storey. Ever so high, aloft to the tower roof, with the spiked vane atop of its tall twisted chimney. "But he was speakin' mainly," he was, Adam would say, "of where it went round an' round, an' down an' down to what was just wine and wood cellars now, but 'twas no such honest end as that they were scooped out for hunnerds and hunnerds, if so be 'twarn't thousands o' years agone. And Master Rumbold might say what he pleased, an' deny it you as he liked, 'twere just for all the world a honeycomb o' cells an' passages, openin' right an' left into dungeons, till you come out by the weir, over against the ruins o' Nether Hall."
"Go on! go on!" Barnaby would gasp, writhing in ecstasy at the recital. "Slidikins! I'm all goose-flesh from top to toe! Master Lockit, go on!"
Master Lockit's word pictures.
"More idiot you," Adam would rejoin, puffing away with immeasurable but secret content in the effect produced by his word picture of their hidden surroundings. "What is it to the likes of us? An't such things all done with now? I'm speakin', I am, of the good old times when royal kings an' queens theirselves wasn't safe on their gold thrones, for blows in the dark."
"Happen it might come again," Barnaby would murmur, staring with hopeful rounded eyes into the blazing logs; but when the old belfry clock overhead boomed its warning to bed, Master Diggles stumbling half blind with terror to his sleeping-room in the gabled roof, was a sight not easily to be forgotten.
That same iron-clamped door atop of the tower staircase opened—if indeed one may so speak of a door which so rarely was put to its use—into a chamber called the Warder's Room. Not having been inhabited for a generation or two, it was of course reputed to be haunted by a "White Woman," and that was no more than truth and fact; for many an hour Ruth spent in it, weaving romances out of her own brain, for the mail-clad knights and wimpled ladies whose pictured forms gleamed dimly from the rich oak wainscoted walls, and the designs and quaint devices of their
panellings which accorded with those on the walls of Ruth's room, lying immediately beyond.
Ruth romancing.
Ruth had a theory that this suite of rooms on the upper storey of the gatehouse wing had in olden times been occupied by the lord and lady of the ancient mansion; and the notion was probably a correct one, since in no part of the place were traces of such magnificence to be seen as here. Fragments of painted glass glowed in the mullioned windows, showing scraps of monstrous griffin-like heads and scaly tails, and enscrolled letters, of which only one word in one of the upper lights of Ruth's window remained entire—"Loyaulté."
Time and wear had so polished the wood of this chamber's richlyparqueted floor that its smooth surface reflected, like some quiet pool, the tall-backed chairs of tawny and gilt Cordovan leather, ranged stiffly against the walls, and about the long narrow oaken table covered with its faded velvet drapery; and the massive proportions of the huge carved oaken chest, capacious enough to shut in one of the mailed knights, or even portly brown-frocked Abbot Benedict Ogard of Waltham Abbey himself, who smiled, come fair weather come foul, come day come night, so unctuously down on you from his recess beside the loftily-coped fireplace.
Ruth could very well recall the time when the lower portion of the walls of this room had been hung with Flemish tapestry, embroidered with subjects from the Old Testament and early Grecian lore. One winter, however, when King Frost intruded so tyrannically in-doors that people shivered in their beds, Maudlin Sweetapple had stripped down the greater part of this tapestry to make curtains for Ruth's room. If in cutting away the tattered and hopelessly unmendable parts of it, she had patched the stuff together again in such fashion as to leave Solomon in all his glory turning a summersault on the extreme tip of Jonah's whale's nose, and Goliath's gory head frowned grimly from the neck of the Trojan horse, did it not all serve every whit as well for keeping the wind away?
The warder's room.
No doubt the situation of the Warder's Room, cut off as it was so completely from the rest of the house, had first obtained it its ghostly renown; one not likely to dwindle, by the knowledge that its outer door giving on the staircase was always kept
A grim greeting locked. This, however, was no more than an ordinary precaution; since the room stood literally in the very portal of the whole house, though time had brought its changes, and various small doors in the new wing now admitted by the wicket the maltster's few visitors and his workpeople to the maltyard.
The master of the house himself did not set foot inside the Warder's Room twice in a year; and when on that May morning, before starting for Nether Hall, Ruth entered it, according to her daily custom, to let a little fresh air and sunshine into its grim silence, she had been startled at perceiving her father standing with folded arms and sombre brows near the hearth, gazing into its cold blackness as if lost in moody thought. On becoming conscious of her presence, however, he had roused up from his abstraction, and with a hurried and absent "Good morrow, child," he turned and went out, locking the door behind him.
CHAPTER V. HOW MASTER RUMBOLD TOLD LAWRENCE LEE
WHAT THE VERY AIR MIGHT NOT HEAR.
This recollection of the morning, troubles Ruth strangely now, as she sits in the broad window-seat of her own room, her eyes fixed indeed on the fair moon-lit scene before her, but for once seeing nothing of its beauty. Vague fears and suspicions and dread of coming evil weigh down her heart, as one by one she threads together the incidents of this May-day, which was to have been such a golden one. It is all in vain that she laughingly tells herself her father has every right to perambulate his own premises. All in vain she argues that Lawrence Lee may be as sulky as a bear with a sore
head, if it gives him any pleasure; and no concern of hers. Certainly not. All the same too, of course, it is to her if a legion of coal-barges come their way, so long as it is not she who stands in Master Sheppard's shoes.
For her part, however, Ruth could not consider the landlady of the "King's Arms" at all a bad sort. On the contrary, she entertained a great liking for her. Folks were fond of saying that Mistress Sheppard had a shrewish tongue; but Ruth had never felt its edge. The good woman was as foolish as everybody else in the matter of spoiling the little mistress of the Rye House; and though she would as soon tell a prince of the blood a piece of her mind, as she would the stable-boy of her own establishment, if she saw fit, she would have vowed the old dun-cow to be white as milk, if it could have afforded Ruth any satisfaction; or declared that Master Richard Rumbold was the most urbane and delightful gentleman in all the country, though no love, to put it mildly, was lost between her and her opposite neighbour.
The hostess of the "King's Arms."
One reason for this among divers others, was their difference of opinion concerning the sign of her hostelry. What easier, the maltster always insisted, than to change it from the "King's Arms" to the "Commonwealth Arms?" or some such reasonable name? There could be no offence, he argued, to anybody in that. But Mistress Sheppard maintained there was, and much offence too. She would stand by and see no such senseless choppings and changings. There had never been anything common about the place, since place it was; and shouldn't be while she was above ground. And what did the man want of such notions? And Master Sheppard, if he could have answered that question, as perhaps he might, maintained a discreet silence, as indeed is the only safe course when one finds one's self betwixt two stools, as his lot in life placed him; for he was never certain whether he stood more in awe of his wife or of Master Rumbold. Once, it is true, he ventured so far as to hint to her, that for the good of the house, and the sake of peace, it might be well to think over Master Rumbold's suggestion, and that he, Sheppard, was agreeable, if so be—but having got thus far he was pulled up by Mistress Sheppard, who said she "was not agreeable; that those who didn't like the sign might spare their custom, and the good o' the house'd be none the worse for lack o' their company." And so the sign
remained true to its colours, and an eyesore and a thorn in the flesh to roundhead Master Rumbold.
Smouldering fires.
Differences between neighbours were, however, unfortunately common enough in those troubled times; for troubled they were. It is true that the old quarrel between the king and the parliament, which had brought Charles the First to his sad death at Whitehall, had been patched up very neatly more than twenty years ago now, when his son, King Charles the Second, had been restored to the throne; but the feelings of the people were like smouldering fires, and ready as ever to break out in discontent. The country, moreover, was divided, not now, as then, into those who did approve of its being governed by a king and those who did not; but there were many loyal enough sober-minded folks, and holding quite varying forms of religious belief, who were sorely disappointed with the manner in which the king, whom they had helped to restore with so much expense of precious lives and of money, governed; or, more properly, neglected to govern. Yes, a careless "Merry Monarch"—all very well to call him so—but your merry men and women are frequently cruelly selfish ones, and contrive to bring tears into other people's eyes every time they are pleased to laugh.
Then, too, there were many who dreaded the day when Charles's brother, the Duke of York, should succeed him on the throne. There seemed hardly any doubt that he had adopted the Roman Catholic form of belief; and a strong impression prevailed that Charles was also greatly inclined to do the same.
The Merry Monarch.
How far this was true can, perhaps, never be fairly determined. The king's pleasures always interested him vastly more than religious questions of any kind, and the fears of those who dreaded to see England fall back under popish rule were probably exaggerated. It is very certain that these ideas were fed by dangerous men, who for their own selfish ends spread alarms of popish plots and conspiracies which existed nowhere but in their own mischievous brains; and many harmless peace-abiding Roman Catholics were hunted to prison and death, solely for the crime of being faithful to the creed they had been reared in. These did not, however, remain entirely unavenged, for the
love of fair play and of justice triumphed in the end; and the wretches who had persecuted their fellow-men under the pretence of religion were many of them severely punished, and few pitied them.
The father of Lawrence Lee had died, fighting for King Charles the First on Worcester field; while Richard Rumbold had lost his eye in the selfsame struggle, serving the Parliamentary forces.
A dark desire.
Rumbold hated the Stuart race; and when he used to hear Madam Lee teaching her little Lawrence to flourish his chubby hands and cry, "God save the king!" an ugly sneer would begin to gather about his lips, though he would hold them fast shut, for the Nether Hall folks were prosperous and well-to-do; and the maltster, if he could avoid it, never quarrelled with money. It was, besides, no easy matter to pick a dispute with this young Lee, who troubled his head so vastly little about the affairs of the nation, and whose whole mind was taken up in the management of his farm.
As to his heart, it was divided between his mother and his old playmate and constant friend Ruth; and though Ruth's play-days were fast ebbing away, and the old games were now frowned upon by her as silly and rompish, Lawrence cared for her every whit as much as ever; and Rumbold perceiving this, thought he saw in it a turn for the serving of his own purposes. And when one day, about the time of this story's opening, the maltster being in one of his gloomier moods, which, indeed, had grown so strangely frequent that he was rarely out of them, chanced to launch forth into one of his tirades against the king and his government, and said that "sooner than see daughter of his, wife of a man who loved a Stuart, be that Stuart Charles or James, or Tom, Dick, or Hal, he would see her in her coffin."
An angry altercation.
"Love!" replied Lee, turning a little pale as the maltster spoke, "is a strong word, Master Rumbold."
"Your father loved the first Charles Stuart," said Rumbold with knitted brows.
"Ay, to the death!" sighed the young man; "but I'll warrant 'tis little enough his present majesty remembers that."
Rumbold looked up quickly, and the dull glitter of his eye brightened into a glance of searching scrutiny as he fixed it on Lawrence. "An ungrateful race always, these Stuarts," he said with a shrug.
"Nay, I say not that," rejoined Lee. "Your poor bedesman may know every scratch and mark upon his little scraped-up hoard; but can your rich trader tell you one from another of his coffered guineas? And king's friends are so. Countless as the grain I sow in my fields."
"To be as soon scattered to the winds, and trod under foot," growled Rumbold. "Put not your trust in princes."
"I'd as lief trust one," smiled Lawrence, who knew his Bible too, "as any other child of man."
"You speak idly, as a parrot chatters," said Rumbold in displeased tones; "and, in truth, I have long taken you for a—"
He paused with a jerk. The word on his lips was scarcely one calculated to win over the young man to his ideas, and he substituted the milder epithet of "featherbrain."
"I thank you for your compliment, Master Rumbold," said Lawrence swelling a little, and glancing silently, but proudly, round on his neat barns and ricks, among which they chanced to be standing. "I flattered myself my brains were none so empty."
"Psha!" returned Rumbold; "a man may be a Mr. Worldly Wise, and still a fool and a beggar touching the treasure that waxeth not old. Think you that the storing of barns and the breeding of fat oxen will bring a man peace at the last?"
"It may help to it, I doubt," answered the young proprietor, "if it so be that that man uses bounteously the wealth his barns and his cattle bring him.
Not hoarding it greedily, but sharing it with those who need it. Then heaven, I take it, is like to bless our store."
The maltster wagged his head impatiently.
"Though in sooth," went on Lawrence, "I require not you to remind me, Master Rumbold, that though a man bestow all his goods to feed the poor, and hath not real charity, he is sounding brass indeed; and Heaven, that seeks pure gold only, will have none of him. I know, of course, as well as you do, that a clear conscience—"
"And what," interrupted Rumbold, wincing involuntarily as Lee uttered these last words, and gazing gloomily into the muddy duck-pool at his feet, "what may be your notion of that?"
"Of a clear conscience?" lightly laughed Lawrence. "Why, first and last, at all events, that its owner never do his neighbour any wrong."
Lawrence speaks out. A wrangle.
"And who is my neighbour?" muttered Rumbold, as if speaking to himself, and still keeping his eye moodily fixed on the turgid water. "Answer me that, Lawrence Lee."
"Who is not?" replied Lee, repressing a yawn, but with a cheery smile. "I take it, we're neighbours all. Everything that breathes; from old Shock here"—and he bestowed a friendly pull on the grizzled ears of the sheep dog, who stood poking his cold nose into his master's hand—"up to the king himself. What's the matter, Master Rumbold?" for the maltster started and bit his nether lip, as if in some sudden pain.
"Nothing, boy," he said. "What should be?"
"The king himself—God bless him!" continued Lee, waxing unusually eloquent, for ordinarily he was not a man of many words. "And that if we do—"
"Do, do!" cried Rumbold, wincing again. "The old story. Always with your sort. And faith may go to the wall. Well, if we do what forsooth?" he
added, not without curiosity.
"Nay, if it please you better," answered Lawrence good-humouredly, "for it is all one;—if we don't do harm, and work no evil against any man:"—
"Upon him who doeth evil, evil must be done," said Rumbold in deep melancholy tones.
"That," returned Lawrence, recoiling a pace and gazing in perplexity at his companion, "that was not the teaching, Master Rumbold, of Him who died for all men. I doubt 'tis the same as if one should say, Evil must be done that good may come."
"Ay," muttered Rumbold, folding his arms upon his breast and setting his lips firmly, "it must."
"Why? Fie, now, fie!" laughed Lawrence, fixing his eyes with something of uneasy curiosity in their clear, dark depths, on Rumbold's face. "That, they say, is the Jesuits' watchword. Who would have thought to hear it from the lips of godly Master Rumbold?"
"You mock me," returned Rumbold; "I am the worst of sinners."
"Nay, nay, but I trust not," said Lee, getting really uncomfortable.
"You mock me, I say," reiterated Rumbold.
"Heaven forbid!" ejaculated Lee. "It is rather that you mock me; for by my faith I do not understand you to-night, Master Rumbold."
The whisper of a conspirator.
"Listen," hoarsely said Rumbold, turning suddenly on Lee, and gripping him by the elbow; "you shall understand. I will explain, but not here," he went on, dropping his voice to a whisper, and casting a far-seeing, cautious glance round. "Not here: there may be eavesdroppers. Hark! what's that?"
"Only the beasts munching their supper in the stables," said Lee. "They will tell no tales."
"The very air must not hear," said Rumbold.
"Why, if it is so particular as all that, then," rejoined Lawrence, still half jestingly, but growing less and less light about his heart, "come this way." And pushing open a wicket, he conducted his companion along a rather miry slip of by-road towards the apple orchard, which stretched behind and around the ruined gatehouse, whose jagged outlines were beginning to stand out grim and gaunt in the sickly rays of the moon. Wading through the long grass so thickly carpeting the ground up to the tower, that its base was completely hidden, Lee conducted Rumbold to the top of a small flight of broken stone steps, so lost in an overgrowth of ivy trails and brambles as to be invisible to stranger eyes; but Lee, with a thrust of his hand, parted the leafy screen, and signed to Rumbold to follow him down the steps, which led to a low, iron-clamped and heavily padlocked door deeply sunken in the wall of the tower's foundations.
A secret vault
"'Tis a well-screened spot, is it not?" said Lee, answering Rumbold's inquiring glances.
"Well secured," said the cautious Rumbold, who had not much opinion of mere unaided twigs as safeguards, and seemed more disposed to admire the huge iron padlock adorning its latch. "What do you store here?"
"Nothing."
"Nothing?"
"The place—except for a few bones, which may have been man's or sheep's for aught I know, or ever gave a thought to—is full of emptiness."
"Yet you keep it as sealed as if it shut in untold riches."
"As for the matter of that, it does, too, in a roundabout sort of way," said Lawrence smiling and colouring a little. "Or it may do so; for 'tis said— though I will not answer for the truth of it, that if you follow your nose far enough, the way it leads, you will find yourself in the vaults under your own gatehouse. Our houses—yours and mine—Master Rumbold, were built
in queer times; when a man could not call his life his own. And when he dared not show his face above ground, slipped away as he could under it."
"And a fig then for his pursuers," said Rumbold, as he stepped into the vault, whose darkness was only lightened by the moon-rays feebly struggling in through the grating of a loophole high up in its walls. "A fig for them, hey?"
"As you say," said Lawrence, faintly echoing the low laugh of his companion, which reverberated far away, in mocking unearthly discords, as though challenging the pair to explore the place's long-forgotten intricacies. "I doubt they must have been as successful as if they sought needles in a bottle of hay."
"Shut the door!" said Rumbold.
Lawrence obeyed, and what further Richard Rumbold had to say was heard by no eavesdroppers save the slug and reptile creatures who had long made the place their own.
In darkness. A change for the worse.
Some hours later the door opened again, and one of the two men reappeared. Peering first cautiously right and left, he locked the door behind him and stole hurriedly up the steps. The figure of this man is assuredly that of Lawrence Lee, but strangely unlike his light bright step is that stumbling, swaying gait; and can that ashen white face, those eyes startled and staring, as if they had met some fearful thing, indeed be his? And where is Rumbold?
CHAPTER VI.
SOMETHING IN THE WATER.
One thing only was quite certain, that the maltster was to be seen next morning at the usual hour among his men. As for Lawrence Lee, whatever Rumbold had confided to him remained a secret as far as the nature of it was concerned. To hide, however, from Ruth that something was amiss with him was a more difficult task, and he had failed in it.
During these last weeks, moreover, the Rye House had grown into a very prison of dulness. Rumbold, always a sombre and taciturn man, had come to be like a stone statue moving about the place, never speaking but when absolutely compelled.
The recollection of all this, and of the events of the past day, crowd bewilderingly now upon Ruth's mind, as she sits, with her chin resting upon her hand, gazing out into the night, from which the young May moon is slowly fading. Only a few stars cheer the surrounding darkness, excepting yonder where the yellow lamp-light streams through the close-drawn curtains of the guest-parlour window of the King's Arms.
A cure for care.
Many a summer evening, when Mistress Sheppard's guests tarried as late as this, Ruth could remember catching the echoes of merry laughter and snatches of songs from that window; but though the night was warm as a July one, not a sound was to be heard save the low hooting of the owls and the gurgling of the water in the moat.
She stretched her head from the window, to listen for the familiar sound of her father's heavy footfall up the wicket-path.
How late he stayed!
And Lawrence? had he gone home yet in his boat? Surely. And yet—ah! well. What was it all to her? Why vex her head about it? Why not go to sleep and forget her fancies? Fancy! were those dark cloaked figures fancy forsooth? Like some evil dreams, indeed, they haunted her mind. And that flash of cruel steel blue light? No fancy that. But what concern could it be of Ruth's? Why, a turn of her wheel would dispel it all. There is no remedy like a little bit of diligent work for troublesome thoughts, or even sad ones. How provoking that the stupid thing had not a shred of flax in it! There it stood in its corner, a beautiful wheel of ebony inlaid with ivory, her father's
Out in the moonlight gift last birthday, but like a fair body without a soul, destitute of the flax. How she could have worked away by the light of the stars which were so brilliant that lamp-light would be an utter superfluity—if only the flax had been to hand!
Unluckily it all lay locked away, a splendid store, in the big oak linen press, atop of the keeping-room staircase; and just the least bit in the world of extra courage was indispensable for traversing those silent passages at this hour. And yet after all, a very little bit, for Ruth was no coward. The chief difficulty was to avoid disturbing Maudlin. It would be such a shame to do that. The old woman lay so comfortable—leagues away in the land of dreams. Ruth could see that, as she peeped at her through the half-open door. So soundly sleeping that she gathered courage, and stepped tiptoe across the floor, out into the corridors beyond, till she could see the sacks away at its furthermost end in the storeroom, all huddled together like hunchbacks under the dim starlight, or—like those cloaked men who had got out of the barge! and then Ruth shivered. But that was little to be wondered at, for the air of the store-room struck icy cold as she stole on—on into the corridor where the linen press stood.
Close beside it a small lattice afforded a glimpse of the river just beyond the bridge. There lay the barge! Still moored up alongside the bank; a huge black blot upon the silvery water.
And the "Queen Ruth?" Nay—as if it was likely to be there now. Why, her pretty little cat Tab had as much to do with the big elephant who lumbered by in the show yesterday, as the merry, graceful, little "Queen Ruth" could have with yonder ugly boat? And yet, and yet—ah! what a consolation it is to make sure of anything! to crush out one's absurd fancies —dead, past all coming to life again! And how temptingly easy in this case! Quite as easy anyhow, as to be standing there, dreaming and talking about it. Only just to steal down by the stairs and through the keeping-room, where the still smouldering fire cast a few dull gleams, and so out by the narrow path to the wicket. Then but a step—but softly, creep low for thy life, Ruth—in the high wall's shadow, and drag the cloak, snatched in haste from a peg, close and well about thy face and shoulders. And what if
