DE102021104108B3 - Procedure for determining the fracture deformation behavior of cohesionless contractile loose rock with undrained compression - Google Patents

Abstract

The method enables the fracture deformation of loose rock to be determined over a wide range of effective principal stress ratios, maximum effective principal stresses, proportions of pores, degrees of overconsolidation, proportions of air voids and earth pressure coefficients at rest. To carry out the method, a few passive compression tests are carried out in the triaxial device with differing maximum effective principal stresses, effective principal stress ratios, pore fractions and saturation numbers before passive compression. From all measured values of the effective principal stress ratios, the largest effective principal stresses, the pore fractions and the saturation numbers before passive compression as well as the fracture deformations, conclusions can be drawn about the fracture deformation of the loose rock.

Description

Application of the invention is in soil physics laboratory testing technology, the determination of the effective consolidation principal stresses σ ' _1.2 and σ' _3.2 , the porosity n ₂ , the saturation number S _r2 , the degree of over-consolidation OCR _gr2 , the earth pressure at rest K _0.2 and the Unloading behavior dependent fracture deformation ε _f of cohesionless, contractile soft rock with undrained passive compression. The scope of the method is limited to stress areas in which grain fragmentation does not yet occur.

The properties of loose rock are described with key figures that describe the material and condition. The condition-describing key figures describe the condition in which loose rock is located.

The porosity n and the saturation number S _r describe the storage condition. The state of stress is described by the largest effective principal stress σ' ₁ and the smallest effective principal stress σ' ₃ . The history of a loose rock is described by the degree of overconsolidation OCR. The key figures describing the material describe the condition-independent properties of loose rock (e.g. grain size distribution, grain density).

Compression is the change in length of a loose rock sample under compression.

Passive upsetting is a testing technology-in triaxial testing-in which upsetting of the soft rock sample is accomplished by increasing the externally applied force in the direction of greatest principal stress.

Fracture is the failure of a material under mechanical stress. In soil mechanics, the fracture strength during compression of loose rock is the maximum value of the shear stress before the shear strength drops. The shear strength of a loose rock can increase again after fracture and after falling to the residual shear strength after much larger deformations, but this behavior is no longer part of the fracture behavior.

The object of the present invention is to provide a method which avoids the disadvantages explained below, in particular the time-consuming determination of the fracture deformation of loose rock, in particular the fracture deformation for all possible initial states of a sample of the loose rock.

This object is achieved by a method according to claim 1.

• Die in dieser Beschreibung verwendeten Bezugszeichen und Indizes sind in der Bezugszeichenliste erläutert.
  • 1 zeigt für einen idealisierten passiven Stauchungsversuch die Verläufe von Scherspannung t, Porenwasserdruck u und größter totaler Hauptspannung σ₃ als Funktion der Deformation ε der Probe. Die Bruchdeformation ε_f ist die Deformation, bei der die Scherspannung t ihren Maximalwert erreicht.

The invention is explained below with reference to the figures:

• The reference symbols and indices used in this description are explained in the list of reference symbols.
  • 1 shows the curves of shear stress t, pore water pressure u and maximum total principal stress σ ₃ as a function of the deformation ε of the sample for an idealized passive compression test. The fracture deformation ε _f is the deformation at which the shear stress t reaches its maximum value.

"Effective" is the designation of a reference system in soil mechanics.

The “effective reference system” is characterized by the fact that effective stresses are used as a stress reference for determining strength parameters (in particular the angle of friction).

Effective stresses result from the total stresses (total stresses) in the soil minus the static pore water pressures after consolidation and the excess pore water pressures developing in a sample between consolidation and failure.

The pore fraction is the proportion of pore space (gaseous and liquid phase) in the total volume of loose rock.

The saturation number is the proportion of the liquid phase in the volume of the pore space in loose rock.

Water-saturated means that any remaining gas in the soil is separated from the atmosphere by the pore water.

2 shows the definition of the degrees of overconsolidation OCR and OCR _gr .

Equation 1 shows the definition of the degree of overconsolidation OCR. $$OCR=\frac{\sigma {\text{'}}_{1\text{Max}}}{\sigma {\text{'}}_1}$$

The degree of overconsolidation OCR is the ratio of the greatest effective principal stress in loose rock σ' _1max , to which loose rock was exposed in the course of its formation, and the current greatest effective principal stress σ' ₁ .

The classic definition of the degree of overconsolidation has disadvantages, especially for opencast mine dumps. The history of the dump must be known so that the degree of overconsolidation OCR can be determined. In the vicinity of embankments, groundwater levels that are not parallel to the surface, or surcharges on the terrain surface, the depth dependence of the degree of overconsolidation OCR is not parallel to the surface. The depth dependence of the degree of overconsolidation OCR is therefore locally different.

Therefore, the OCR _gr degree of overconsolidation is used instead of the classic OCR degree of overconsolidation.

Equation 2 shows the definition of the degree of overconsolidation OCR _gr . $$OC{R}_{G\mathrm{right}}=\frac{\sigma {\text{'}}_{1G\mathrm{right}}}{\sigma {\text{'}}_1}=\frac{E_{G\mathrm{right}}\ast {\left(-\text{ln}\left(\frac{n}{n_{G\mathrm{right}0}}\right)\right)}^{\frac{1}{c_{eG\mathrm{right}}}}}{\sigma {\text{'}}_1}$$

The degree of overconsolidation OCR _gr is the ratio of the largest possible principal stress σ' _1gr for the respective porosity n of the sample and the largest effective principal stress σ' ₁ .

The degree of overconsolidation includes the proportion of pores, the tension and the unloading behavior.

Equation 3 shows the definition of the effective principal stress ratio at the beginning of passive compression K' ₂ . $$K{\text{'}}_2=\frac{\sigma {\text{'}}_{1.2}}{\sigma {\text{'}}_{3.2}}$$

The effective principal stress ratio at the beginning of passive compression K' ₂ is the ratio of the greatest effective principal stress before passive compression σ' _1,2 and the smallest effective principal stress before passive compression σ' _3,2 .

The static triaxial device is used as a test apparatus for measuring the fracture deformation. Passive compression tests are carried out to determine the fracture deformation of the loose rock to be examined.

The known test technologies are designed to measure the fracture deformation in tests with defined initial conditions in the static triaxial device.

The measured fracture deformation only applies to the defined initial parameters, eg a defined initial porosity n ₂ , a defined degree of overconsolidation OCR _gr2 , a defined maximum principal stress σ' _1.2 and a defined principal stress ratio K' ₂ .

According to the prior art, in order to determine fracture deformations for different initial states, it is disadvantageous that at least one individual test has to be carried out for each possible combination of initial parameters.

The number of tests required to determine the fracture deformation for all possible initial states of a specimen is very large and is generally not possible for economic reasons.

According to the state of the art, there is no method for determining the fracture deformation as a function of different initial characteristic values from a few tests.

• • in Abhängigkeit von deren größter Anfangshauptspannung σ'_1,2,
• • in Abhängigkeit vom Anfangshauptspannungsverhältnis K'₂,
• • in Abhängigkeit vom Anfangsporenanteil n₂,
• • in Abhängigkeit vom Anfangsluftporenanteil n_a,2,
• • in Abhängigkeit vom Anfangsüberkonsolidierungsgrad OCR_gr2,
• • in Abhängigkeit vom Anfangserdruhedruckbeiwert K_0,2

sowie

• • den maximalen Porenanteil n_gr0 des erdfeuchten Materials im spannungsfreien Zustand und
• • die materialspezifische Konstante C_ent des Entlastungsverhaltens beschreiben.

With the present invention, a test method is thus created, the results of which show the fracture deformation of cohesionless contractile loose rock

• • as a function of their largest initial principal stress σ' _1.2 ,
• • as a function of the initial principal stress ratio K' ₂ ,
• • depending on the initial porosity n ₂ ,
• • as a function of the initial air void fraction n _a,2 ,
• • depending on the initial degree of overconsolidation OCR _gr2 ,
• • as a function of the initial at-rest earth pressure coefficient K _0.2

such as

• • the maximum porosity n _gr0 of the earth-moist material in a tension-free state and
• • describe the material-specific constant C _ent of the unloading behavior.

The method according to the invention is explained in more detail below.

Functions of the general form ε _f = f(σ' _1,2 , K' ₂ , n ₂ , na _,2 , OCR _gr2 , K _0,2 , n _gr0 ) satisfy the requirement that the fracture deformation of loose rock depends on different to describe initial states.

Equation 4 represents a concrete, advantageous form of designing the general function listed. $$e_{ƒ}=\frac{c_{ent}\ast p_{\mathrm{right}}\ast \frac{K{\text{'}}_2}{K_{0.2}}\ast \text{ln}\left(\frac{\sigma {\text{'}}_{1.2}+p_{\mathrm{right}}}{p_{\mathrm{right}}}\right)}{\sigma {\text{'}}_{1.2}+p_{\mathrm{right}}}+e^{\left(\frac{e_n\ast e^{\left(\frac{n_{a\mathrm{,2}}{}^2}{e_{KS\mathrm{right}}}\right)}\ast {\left(n_{G\mathrm{right}0}-n_2\right)}^{e_{\mathrm{\Delta }n}}\ast {\left(\frac{K{\text{'}}_2}{K_{0.2}}\right)}^{e_k}}{OC{R}_{G\mathrm{right}2}{}^{e_{OCR}}}-1\right)}$$

The first summand of Equation 4 describes the elastic part of the fracture deformation.

The second summand of Equation 4 describes the plastic part of the fracture deformation.

To determine the coefficients of Equation 4, several passive compression tests are carried out with samples of the loose rock to be examined.

At the beginning of the passive compression tests, the porosity n ₂ , the saturation number S _r2 , the largest effective principal stress σ' _1.2 and the smallest effective principal stress σ' _3.2 are measured. $$K{\text{'}}_2=\frac{\sigma {\text{'}}_{1.2}}{\sigma {\text{'}}_{3.2}}$$

The degree of overconsolidation OCR _gr2 at the beginning of passive compression is calculated using Equation 2 from the porosity n ₂ and the largest effective principal stress σ' _1.2 . $$OC{R}_{G\mathrm{right}}=\frac{\sigma {\text{'}}_{1G\mathrm{right}}}{\sigma {\text{'}}_1}=\frac{E_{G\mathrm{right}}\ast {\left(-\text{ln}\left(\frac{n}{n_{G\mathrm{right}0}}\right)\right)}^{\frac{1}{c_{eG\mathrm{right}}}}}{\sigma {\text{'}}_1}$$

The proportion of air voids n _a,2 at the beginning of the passive compression is calculated using Equation 5 from the proportion of voids n ₂ and the saturation number S _r2 . $$n_{a\mathrm{,2}}={\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DE102021104108B3\_0023.png,DE102021104108B3\_0025.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\ast \left(1-S_{\mathrm{right}2}\right)$$

In the passive compression tests, the fracture deformation ε _f is measured.

Subsequently, the greatest possible main stress of the loose rock as a function of the pore fraction σ' _1gr = f(n) and the maximum pore fraction n _gr0 of the earth-moist material in the stress-free state according to the in the publication DE 195 35 210 C1 determined according to the method described.

The largest possible principal stress σ' _1gr,2 for the respective porosity n ₂ of a sample is required to calculate the degree of overconsolidation OCR _gr2 before passive compression (equation 2).

The maximum porosity n _gr0 of the earth-moist material in a stress-free state of a sample is required for a fitting calculation.

For the respective initial condition of an undrained passive compression, the measured principal stress ratio K' ₂ = σ' _3.2 / σ' _1.2 is to be compared with the associated earth pressure coefficient K _0.2 .

The material-specific constant c _ent of the unloading behavior is determined from unloading tests.

In the unloading tests, the increase in the proportion of pores n in a sample is measured when the largest effective principal stress σ' ₁ decreases.

3 shows in the n = f(σ' ₁ ) diagram the results of, for example, ten relief tests on a soil sample.

The measurement results are in 3 shown as curves. From the measured values of the proportion of pores n and the largest effective principal stress σ' ₁ as well as the proportion of pores after settlement and sagging (at the beginning of the unloading tests) n ₂ and a reference stress p _r = 1 kPa, the material-specific constant c _ent of the unloading behavior for Equation is determined by means of the compensation calculation 6 calculated. $${\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DE102021104108B3\_0023.png,DE102021104108B3\_0025.png"\; state="\{\{state\}\}">n</figure-callout>}}_2=n_{2.0}-c_{ent}\ast \text{ln}\left(\frac{\sigma {\text{'}}_1+p_{\mathrm{right}}}{p_{\mathrm{right}}}\right)$$

3 also shows the estimated values for the porosity n calculated with Equation 6 as a function of the largest effective principal stress σ' ₁ .

• • die größte wirksame Hauptspannung zu Beginn der passiven Stauchung σ'_1,2,
• • wirksames Hauptspannungsverhältnis zu Beginn der passiven Stauchung K'₂,
• • der Porenanteil zu Beginn der passiven Stauchung n₂,
• • der Luftporenanteil zu Beginn der passiven Stauchung n_a,2,
• • der Überkonsolidierungsgrad zu Beginn der passiven Stauchung OCR_gr2,
• • der Erdruhedruckbeiwert zu Beginn der passiven Stauchung K_0,2 und
• • die Bruchdeformation ε_f.

The following values are measured or calculated in the passive compression tests:

• • the greatest effective principal stress at the beginning of passive compression σ' _1,2 ,
• • effective principal stress ratio at the beginning of passive compression K' ₂ ,
• • the proportion of pores at the beginning of the passive compression n ₂ ,
• • the proportion of air voids at the beginning of passive compression n _a,2 ,
• • the degree of overconsolidation at the beginning of passive compression OCR _gr2 ,
• • the earth pressure coefficient at rest at the beginning of the passive compression K _0.2 and
• • the fracture deformation ε _f .

From all the values of the passive compression tests and the material-specific parameters n _gr0 and c _ent , the equation coefficients of Equation 4 are to be calculated as material-describing parameters by means of the adjustment calculation. A reference voltage p _r =1 kPa is used in Equation 4.

In contrast to the conventional approach, the method offers the user of the laboratory test results the possibility of determining the fracture deformation even for initial states of passive compression of a specimen for which no laboratory tests have been carried out.

The method according to the invention and the application of its results are explained in more detail below on the basis of an exemplary embodiment.

A sample of loose rock is taken from a tilting disk to be examined in the dump of an opencast mine, which sample is representative of the loose rock involved in the construction of the tilting disk.

A series of, for example, ten passive compression tests (appropriately depending on the distribution of the measured values) are carried out with the material from this loose rock sample in the static triaxial device.

The effective principal stress ratios, the greatest effective principal stresses, the proportion of pores and the saturation number before passive compression are different in each passive compression test and should be varied over the widest possible range of values.

In addition, the tests according to DE 195 35 210 C1 and unloading tests were carried out so that the degree of overconsolidation OCR _gr2 , the maximum porosity n _gr0 of the earth-moist material in a stress-free state and the material-specific constant c _ent of the unloading behavior could be determined.

Furthermore, the earth pressure coefficient at rest K _0.2 must be known for the required states. The determination of the earth pressure coefficient K _0.2 at rest in laboratory tests is not explained in detail, since the procedure is known to the person skilled in the art.

Expediently, the consolidations necessary before the passive compression can be carried out when the lateral stretching is impaired. This special consolidation technology provides the required earth pressure coefficients at rest, so that no separate triaxial tests have to be carried out for this.

The fracture deformation is to be determined on a tilted, slightly silty sand as an example. In order to classify this sand, the person skilled in the art determined the following key figures that describe the material. fine grain content 6% fine sand content 15% proportion of medium sand 57% coarse sand content 20% fine gravel content 3% non-uniformity number 3.43 curvature number 1.37 grain density ^2.665 g/cm3 Number of pores with the loosest storage according to DIN 18126 0.461 Number of pores with dense storage according to DIN 18126 0.958

By using the method according to the publication DE 195 35 210 C1 the coefficients of the stress-dependent boundary storage state of this sand were determined in consolidation tests as follows: $${\text{n}}_{\text{big}0}=0.665;{\text{E}}_{\text{big}}=369799\text{kPa};{\text{c}}_{\text{eg}}=0.12134$$

from the in 3 The unloading tests shown result in a value of c _ent = 0.00291.

A total of ten passive compression tests with different pore fractions after consolidation n ₂ and different consolidation stresses σ' _1.2 and σ' _3.2 were carried out with this sand, see table 4 .

• • die größte wirksame Hauptspannung σ'_1,2,
• • das wirksame Hauptspannungsverhältnis K'₂,
• • der Porenanteil n₂,
• • der Luftporenanteil n_a,2,
• • der Überkonsolidierungsgrad OCR_gr2,
• • der zugehörige Erdruhedruckbeiwert K_0,2

die Koeffizienten ε_n, ε_OCR, ε_k, ε_KSr und ε_Δn für die beispielhafte Bodenprobe von Gleichung 4 berechnet. $${\epsilon }_{ƒ}=\frac{c_{ent}\ast p_r\ast \frac{K{\text{'}}_2}{{\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="DE102021104108B3\_0025.png,DE102021104108B3\_0026.png"\; state="\{\{state\}\}"><figure-callout\; id="2"\; label="K"\; filenames="DE102021104108B3\_0023.png,DE102021104108B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout></figure-callout>}}_{\mathrm{0,2}}}\ast \text{ln}\left(\frac{\sigma {\text{'}}_{\mathrm{1,2}}+p_r}{p_r}\right)}{\sigma {\text{'}}_{\mathrm{1,2}}+p_r}+e^{\left(\frac{{\epsilon }_n\ast e^{\left(\frac{n_{a\mathrm{,2}}{}^2}{{\epsilon }_{KSr}}\right)}\ast {\left({\mathrm{<figure-callout\; id="0"\; label="n\; g\; r"\; filenames="DE102021104108B3\_0025.png,DE102021104108B3\_0026.png"\; state="\{\{state\}\}">n</figure-callout>}}_{gr}-n_2\right)}^{{\epsilon }_{\mathrm{\Delta }n}}\ast {\left(\frac{K{\text{'}}_2}{{\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="DE102021104108B3\_0025.png,DE102021104108B3\_0026.png"\; state="\{\{state\}\}">K</figure-callout>}}_{\mathrm{0,2}}}\right)}^{{\epsilon }_k}}{OC{\mathrm{<figure-callout\; id="2"\; label="R\; g\; r"\; filenames="DE102021104108B3\_0023.png,DE102021104108B3\_0025.png"\; state="\{\{state\}\}">R</figure-callout>}}_{gr}{}^{{\epsilon }_{OCR}}}-1\right)}$$

After the passive compression tests have been completed, the fracture deformations ε _f and the characteristic values of the initial state before the passive compression are obtained

• • the largest effective principal stress σ' _1.2,
• • the effective principal stress ratio K' ₂ ,
• • the porosity n ₂ ,
• • the proportion of air voids n _a,2 ,
• • the degree of overconsolidation OCR _gr2 ,
• • the associated earth pressure coefficient at rest K _0.2

calculated the coefficients ε _n , ε _OCR , ε _k , ε _KSr , and ε _Δn for the exemplary soil sample of Equation 4. $$e_{ƒ}=\frac{c_{ent}\ast p_{\mathrm{right}}\ast \frac{K{\text{'}}_2}{K_{0.2}}\ast \text{ln}\left(\frac{\sigma {\text{'}}_{1.2}+p_{\mathrm{right}}}{p_{\mathrm{right}}}\right)}{\sigma {\text{'}}_{1.2}+p_{\mathrm{right}}}+e^{\left(\frac{e_n\ast e^{\left(\frac{n_{a\mathrm{,2}}{}^2}{e_{KS\mathrm{right}}}\right)}\ast {\left(n_{G\mathrm{right}0}-n_2\right)}^{e_{\mathrm{\Delta }n}}\ast {\left(\frac{K{\text{'}}_2}{K_{0.2}}\right)}^{e_k}}{OC{R}_{G\mathrm{right}2}{}^{e_{OCR}}}-1\right)}$$

The numerical values in the 4 until 11 apply exclusively to the measurements carried out on the exemplary soil sample.

4 shows the measured values of the passive compression tests (n ₂ , σ' _1.2 , σ' _3.2 , S _r2 , ε _f ) and the characteristic values K' ₂ , OCR _gr2 and K _0.2 calculated from the measured values.

5 shows the coefficients of Equation 4 ε _n , ε _OCR , ε _k , ε _KSRr and ε _{Δn calculated with fitting calculation} for the exemplary soil sample.

In 6 sind unter der Bezeichnung „Fehler ε_f“ die Fehler bei der Abschätzung der Bruchdeformationen ε_f der beispielhaften Bodenprobe abgeschätzt.The coefficients of Equation 4 were calculated for the example soil sample as follows: $${\mathrm{e}}_{\text{n}}=-5.50*{10}^{-6};{\mathrm{e}}_{\text{OCR}}=-6.71*{10}^{-3};{\mathrm{e}}_{\text{k}}=1.05;{\mathrm{e}}_{\text{KSr}}=1.22*{10}^{-3};{\mathrm{e}}_{\mathrm{\Delta }\text{n}}=-10.3$$

In 6 the errors in estimating the fracture deformations ε _f of the exemplary soil sample are estimated under the designation "Error ε _f ".

The error in estimating the fracture strain is the difference between the measured and the estimated fracture strain.

The size of the error when estimating the fracture deformation ε _f depends on the size of the fracture deformation, since the fracture deformations can cover a size range of four powers of ten.

In 6 the error for four defined fracture deformations ε _f was determined.

With a fracture deformation ε _f = 0.0005, the example soil sample resulted in a fracture deformation error of 0.00025. With a fracture deformation ε _f = 0.1, the exemplary soil sample had an error in fracture deformation of 0.0503.

7 shows that using Equation 4 and the coefficients 5 calculated estimated values of the fracture deformation _εf,reg for the exemplary soil sample.

In 7 the differences between the fracture deformations _εf,reg calculated using Equation 4 and the fracture deformations ε _f measured in the tests are given under the heading "Error ε _f ".

In 8th the measured values and estimated values of the fracture deformation ε _f are plotted against the saturation numbers before passive compression S _r2 and the proportion of pores before passive compression n ₂ .

In 9 shows the measured values and estimated values of the fracture deformation ε _f over the degrees of overconsolidation before passive compression OCR _gr2 and the effective principal stress ratios before passive compression K' ₂ .

As a result of the procedure shows 10 the family of characteristics ε _f = f(σ' _1,2 ) of the soil sample for constant porosity before passive compression n ₂ , constant effective principal stress ratios before passive compression K' ₂ and constant saturation numbers before passive compression S _r2 .

11 finally shows the family of characteristics ε _f = f(σ' _1,2 ) of the soil sample for constant initial pore fractions n ₀ , constant initial saturation factors S _r0 , constant effective principal stress ratios before passive compression K' ₂ and constant groundwater levels GWS.

In 11 the largest effective principal stress at groundwater level σ' _1,2 , _GWS is also given. The greatest effective principal stress at the level of the groundwater level σ' _1,2,GWS is the product of the mean specific gravity of the earth-moist covering γ _ef and the groundwater table distance Z _GWS according to Equation 7. $$\sigma {\text{'}}_{\mathrm{1,}eƒ}=g_{eƒ}\ast {\mathrm{e.g}}_{GWS}$$

The value of the greatest effective principal stress at the groundwater level σ' _1,2,GWS characterizes the position of the groundwater level at a certain stress σ' _1,2 in the ε _f = f(σ' _1,2 ) diagram. The fracture deformation ε _f is only determined below the water table (σ' _1.2 >σ' _1.2,GWS ).

10 and 11 differ in the underlying porosity n.

10 was determined assuming a defined, constant proportion of pores at the beginning of the passive compression n ₂ .

11 was determined assuming a defined, constant initial pore fraction (built-in pore fraction) n ₀ , from which the pore fraction n ₂ at the beginning of passive compression was calculated.

When proceeding according to the procedure of the present invention, the configuration of the static triaxial tests with regard to the greatest effective main stress, effective main stress ratio, proportion of pores and saturation number is advantageously independent of the requirements for the test results, which usually only arise during the soil-mechanical processing of the existing problem or change.

In a conventional implementation of the passive compression tests to determine the apparent fracture behavior, this causes delays, since the specifications of the soil mechanic must first be awaited in the laboratory. If the specifications change after the passive compression tests have been carried out during processing, conventional processing has the disadvantage that estimates have to be used or the passive compression tests have to be repeated with the new initial conditions. When using the method according to the invention, these problems no longer occur in an advantageous manner, since the fracture deformation of loose rock is known and the effects of changes in the boundary conditions are solved numerically by the soil mechanic or taken from the characteristic curves ( 9 , 10 ) be able.

Furthermore, the evaluation of the test and the delivery of the test results are simplified in an advantageous manner, since all the information sought on the fracture deformation of loose rock is contained in the coefficients of equation 4 in an advantageous manner--as explained.

$$OC{R}_{gr}=\frac{\sigma {\text{'}}_{1gr}}{\sigma {\text{'}}_1}=\frac{E_{gr}\ast {\left(-\text{ln}\left(\frac{n}{n_{gr0}}\right)\right)}^{\frac{1}{c_{egr}}}}{\sigma {\text{'}}_1}$$

$$K{\text{'}}_2=\frac{\sigma {\text{'}}_{\mathrm{1,2}}}{\sigma {\text{'}}_{\mathrm{3,2}}}$$

$${\epsilon }_{ƒ}=\frac{c_{ent}\ast p_r\ast \frac{K{\text{'}}_2}{K_{\mathrm{0,2}}}\ast \text{ln}\left(\frac{\sigma {\text{'}}_{\mathrm{1,2}}+p_r}{p_r}\right)}{\sigma {\text{'}}_{\mathrm{1,2}}+p_r}+e^{\left(\frac{{\epsilon }_n\ast e^{\left(\frac{n_{a\mathrm{,2}}{}^2}{{\epsilon }_{KSr}}\right)}\ast {\left(n_{gr0}-n_2\right)}^{{\epsilon }_{\mathrm{\Delta }n}}\ast {\left(\frac{K{\text{'}}_2}{K_{\mathrm{0,2}}}\right)}^{{\epsilon }_k}}{OC{R}_{gr2}{}^{{\epsilon }_{OCR}}}-1\right)}$$

$$n_{a\mathrm{,2}}=n_2\ast \left(1-S_{r2}\right)$$

$$n_2=n_{\mathrm{2,0}}-c_{ent}\ast \text{ln}\left(\frac{\sigma {\text{'}}_1+p_r}{p_r}\right)$$

$$\sigma {\text{'}}_{\mathrm{1,}eƒ}={\gamma }_{eƒ}\ast z_{GWS}$$

Compilation of the equations used: $$OCR=\frac{\sigma {\text{'}}_{1\text{Max}}}{\sigma {\text{'}}_1}$$

$$OC{R}_{G\mathrm{right}}=\frac{\sigma {\text{'}}_{1G\mathrm{right}}}{\sigma {\text{'}}_1}=\frac{E_{G\mathrm{right}}\ast {\left(-\text{ln}\left(\frac{n}{n_{G\mathrm{right}0}}\right)\right)}^{\frac{1}{c_{eG\mathrm{right}}}}}{\sigma {\text{'}}_1}$$

$$K{\text{'}}_2=\frac{\sigma {\text{'}}_{1.2}}{\sigma {\text{'}}_{3.2}}$$

$$e_{ƒ}=\frac{c_{ent}\ast p_{\mathrm{right}}\ast \frac{K{\text{'}}_2}{K_{0.2}}\ast \text{ln}\left(\frac{\sigma {\text{'}}_{1.2}+p_{\mathrm{right}}}{p_{\mathrm{right}}}\right)}{\sigma {\text{'}}_{1.2}+p_{\mathrm{right}}}+e^{\left(\frac{e_n\ast e^{\left(\frac{n_{a\mathrm{,2}}{}^2}{e_{KS\mathrm{right}}}\right)}\ast {\left(n_{G\mathrm{right}0}-n_2\right)}^{e_{\mathrm{\Delta }n}}\ast {\left(\frac{K{\text{'}}_2}{K_{0.2}}\right)}^{e_k}}{OC{R}_{G\mathrm{right}2}{}^{e_{OCR}}}-1\right)}$$

$$n_{a\mathrm{,2}}={\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DE102021104108B3\_0023.png,DE102021104108B3\_0025.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\ast \left(1-S_{\mathrm{right}2}\right)$$

$${\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DE102021104108B3\_0023.png,DE102021104108B3\_0025.png"\; state="\{\{state\}\}">n</figure-callout>}}_2=n_{2.0}-c_{ent}\ast \text{ln}\left(\frac{\sigma {\text{'}}_1+p_{\mathrm{right}}}{p_{\mathrm{right}}}\right)$$

$$\sigma {\text{'}}_{\mathrm{1,}eƒ}=g_{eƒ}\ast {\mathrm{e.g}}_{GWS}$$

reference list

'

wirksam (totale Spannung abzüglich Porenwasserdruck)

1

größte Hauptspannung

3

kleinste Hauptspannung

Allgemeine Zustandsindizes:

0

in situ Ablagerungszeitpunkt des Lockergesteins, im Versuch Einbauzustand, spannungsfrei (σ ≈ 0); bei Spannungsverhältnissen K in situ Erdruhedruckbedingungen, im Versuch behinderte Seitendehnung

1

erdfeuchter Zustand, in situ vor Aufgang des Grundwassers, im Versuch vor Aufsättigung der Probe mit Wasser

2

in situ Zustand des wassergesättigten Lockergesteins, im Versuch vor Beginn der Stauchung

f

Bruchzustand

Allgemeine Bezugsindizes:

gr

Zustand der lockersten möglichen Lagerung

max

Maximum in der Lockergesteinsgenese

GWS

Grundwasserstand

General stress indices:

'

effective (total stress minus pore water pressure)

1

greatest principal stress

3

smallest principal stress

General condition indices:

0

in situ deposition time of the loose rock, in the test installed condition, stress-free (σ ≈ 0); at stress ratios K in situ earth pressure conditions at rest, in the experiment restrained lateral strain

1

Earth-moist condition, in situ before the groundwater rises, in the test before the sample was saturated with water

2

In situ condition of the water-saturated loose rock, in the test before the start of compression

f

state of fracture

General Reference Indexes:

big

State of the loosest possible storage

Max

Maximum in the soft rock genesis

GWS

groundwater level

σ'1,2

größte wirksame Hauptspannung des wassergesättigten Lockergesteins

σ'3,2

kleinste wirksame Hauptspannung vor der passiven Stauchung

σ'1gr

für aktuellen Porenanteil die größtmögliche größte wirksame Hauptspannung

σ'1

größte wirksame Hauptspannung

σ'3

kleinste wirksame Hauptspannung

σ3

kleinste totale Hauptspannung

σ'1max

Maximalwert der größten wirksamen Hauptspannung im Versuch oder in situ während der Lockergesteinsgenese

σ'1,2,GWS

in situ größte wirksame Hauptspannung auf Höhe des Grundwasserspiegels

n

Porenanteil

n0

Anfangsporenanteil (im Versuch Einbauporenanteile, in situ Schüttporenanteil)

n2

Porenanteil des wassergesättigten Lockergesteins

n2,0

lagerungsspezifischer Porenanteil des wassergesättigten Lockergesteins bei vollständiger Entlastung

na,2

Luftporenanteil des wassergesättigten Lockergesteins

na

Luftporenanteil

ngr0

maximaler Porenanteil des erdfeuchten Materials im spannungsfreien Zustand

Sr

Sättigungszahl

Sr0

in situ Sättigungszahl direkt unterhalb des Grundwasserspiegels bei einem Porenwasserduck von 0 kPa, im Versuch direkt nach Aufsättigung der Bodenproben mit Wasser

Sr2

in situ Sättigungszahl unterhalb des Grundwasserspiegels bei Porenwasserdrücken > 0 kPa, im Versuch Sättigungszahlen nach der Aufsättigung (z.B. nach weiteren Konsolidierungen, Porenwasserdruckerhöhungen usw.)

OCR

auf σ'_1max bezogener Überkonsolidierungsgrad

OCRgr

auf die bei dem Porenanteil n größtmögliche Hauptspannung σ'_1gr bezogener Überkonsolidierungsgrad

OCRgr2

auf die bei dem Porenanteil n₂ größtmögliche Hauptspannung σ'_1gr bezogener Überkonsolidierungsgrad

K0

Erdruhedruckbeiwert

K0,2

Erdruhedruckbeiwert des wassergesättigtes Lockergesteins

K'2

Hauptspannungsverhältnis des wassergesättigten Lockergesteins

εf

auf den Stauchungsbeginn bezogene Bruchdeformation

εf,reg

Schätzwert der auf den Stauchungsbeginn bezogenen Bruchdeformation

ε

bezogene Deformation

εn

materialspezifischer Koeffizient der Gleichung 4

εOCR

materialspezifischer Koeffizient der Gleichung 4

εk

materialspezifischer Koeffizient der Gleichung 4

εKSr

materialspezifischer Koeffizient der Gleichung 4

εΔn

materialspezifischer Koeffizient der Gleichung 4

t

Scherspannung

u

Porenwasserdruck

cent

materialspezifische Konstante des Entlastungsverhaltens

pr

Referenzspannung Entlastungsverhalten

GWS

Grundwasserstand allgemein

zGWS

Grundwasserflurabstand

γef

erdfeuchte Überdeckung

Consecutive number indices are separated by a comma when concatenated. For stresses σ..,... the general stress indices are given first and then the general state indices.

σ'1.2

greatest effective principal stress of the water-saturated loose rock

σ'3.2

smallest effective principal stress before passive compression

σ'1gr

the largest possible effective principal stress for the current porosity

σ'1

largest effective principal stress

σ'3

smallest effective principal stress

σ3

smallest total principal stress

σ'1max

Maximum value of the largest effective principal stress in the test or in situ during the formation of loose rock

σ'1,2,GWS

in situ greatest effective principal stress at groundwater level

n

porosity

n0

Initial porosity (in the test built-in porosity, in situ bulk porosity)

n2

Percentage of pores in the water-saturated loose rock

n2.0

storage-specific pore fraction of the water-saturated loose rock with complete relief

well, 2

Percentage of air voids in the water-saturated loose rock

n / A

air entrainment

ngr0

Maximum porosity of the earth-moist material in the stress-free state

sir

saturation number

Sr0

in situ saturation number directly below the groundwater level at a pore water pressure of 0 kPa, in the test directly after saturation of the soil samples with water

Sr2

in situ saturation number below the groundwater table at pore water pressures > 0 kPa, in the experiment saturation numbers after saturation (e.g. after further consolidation, pore water pressure increases, etc.)

OCR

Degree of overconsolidation related to σ' _1max

OCRgr

degree of overconsolidation related to the largest possible main stress σ' _1gr for the porosity n

OCRgr2

degree of overconsolidation related to the largest possible main stress σ' _1gr for the porosity n ₂

K0

earth pressure coefficient

K0.2

Resting earth pressure coefficient of the water-saturated loose rock

K'2

Main stress ratio of the water-saturated loose rock

εf

fracture deformation related to the start of compression

εf,reg

Estimate of the fracture deformation related to the onset of compression

e

related deformation

on

material-specific coefficient of equation 4

εOCR

material-specific coefficient of equation 4

εk

material-specific coefficient of equation 4

εKSr

material-specific coefficient of equation 4

εΔn

material-specific coefficient of equation 4

t

shear stress

and

pore water pressure

cent

material-specific constant of the unloading behavior

per

Reference voltage relief behavior

GWS

groundwater level in general

zGWS

Depth to groundwater

γef

earth-moist covering

Claims (2)

Method for determining the fracture deformation behavior of a preferably non-cohesive, contractile, water-saturated loose rock, whereby a static triaxial device is used to conduct undrained passive compression tests on several sub-samples of a loose rock sample which, with regard to their initial conditions, are effective principal stress ratio (K' ₂ ), greatest effective principal stress (σ' _1.2 ), proportion of pores (n ₂ ) and proportion of air voids (n _a,2 ) before the respective undrained passive compression test, with the following steps: a) Determination of the material-specific constant (c _ent ) describing the relief behavior of the loose rock sample from the measured values of relief phases of the sub-samples in unloading tests carried out using the triaxial device, b) determination of the earth pressure behavior at rest of the loose rock sample from measured values, which were taken on the sub-samples in consolidation phases of the triaxial tests with impeded lateral expansion before the un drained passive compression tests are carried out and determination of the earth pressure coefficients (K ₀ , ₂ ), c) determination of the coefficients (n _gr0 , E _gr , c _egr ) of the stress-dependent boundary storage condition of the sub-samples of the loose rock sample from the parameter data (n ₁ , σ ₁ ) in consolidation tests carried out using the triaxial device, d) determining the associated overconsolidation numbers (OCR _gr2 ) and the maximum proportion of pores (n _gr0 ) of the earth-moist material in the stress-free state with the loosest storage of the earth-moist material for the respective initial conditions in the undrained passive compression tests, e) conducting of undrained passive compression tests on the sub-samples of the loose rock sample, whereby the initial conditions and the fracture deformation (ε _f ) are measured, and determination of the principal stress ratio (K' ₂ ) and the proportion of air voids (n _a,2 ) depending on the initial conditions, f) calculation of the coefficients from the measured values obtained according to an equation (4) of the general form Ef = f (K' ₂ , σ' _1,2 , n ₂ , n _a,2 ) for the fracture deformations (ε _f ) related to the start of compression. procedure after claim 1 , characterized in that the fracture deformations (Ef) related to the start of compression of the sub-samples of the loose rock sample are calculated with equation (4) $$e_{ƒ}=\frac{c_{ent}\ast p_{\mathrm{right}}\ast \frac{K{\text{'}}_2}{K_{0.2}}\ast \text{ln}\left(\frac{\sigma {\text{'}}_{1.2}+p_{\mathrm{right}}}{p_{\mathrm{right}}}\right)}{\sigma {\text{'}}_{1.2}+p_{\mathrm{right}}}+e^{\left(\frac{e_n\ast e^{\left(\frac{n_{a\mathrm{,2}}{}^2}{e_{KS\mathrm{right}}}\right)}\ast {\left(n_{G\mathrm{right}0}-n_2\right)}^{e_{\mathrm{\Delta }n}}\ast {\left(\frac{K{\text{'}}_2}{K_{0.2}}\right)}^{e_k}}{OC{R}_{G\mathrm{right}2}{}^{e_{OCR}}}-1\right)}$$

are calculated, whereby the equation coefficients (ε _n , ε _OCR , ε _k , ε _KSRr and ε _Δn ) are calculated from the fracture deformations (Ef) measured in the fracture state (f) for the initial conditions of the respective undrained passive compression tests using the material-specific constant (C _ent ) of the unloading behavior taking into account (p _r ) a reference stress of the unloading behavior and the maximum porosity (n _gr0 ) of the earth-moist material in the stress-free state as well as the values of the overconsolidation number (OCR _gr ) and the earth pressure coefficient (K ₀ , ₂ ) belonging to the initial conditions where the equation coefficients (ε _n , ε _OCR , ε _k , ε _KSRr and ε _Δn ) are material constants which describe the dependence of the fracture deformation (ε _f ) on the initial conditions.

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